Ripples and Dunes (A review with a bit of additional information)
A sketch of a ripple or dune like the one in lecture:
http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/duneXStrat.jpg
Remember where the separation point and attachment point are located. The geometry of the flow tracks these points. Erosion can only occur where there the bed shear stress is high enough to move sediment. In other words, the the main flow must be near the sediment surface. Sediment accumulates into a deposit in the flow shadow downstream of the ripple or dune crest; sediment accumulates in the flow detachment zone. Laminae are visible where deposition occurs due to variations in flow speed which cause variations in grain sizes transported and deposited.
Sets of laminae are separated by erosion surfaces which form on the upstream side of the ripples or dunes. They represent deposition on the downstream side. The shape of the laminae reflects the shape of the depositional surface and the geometry of sediment accumulation. If the depositional surface is curved, the base of the laminae is curved. Areas with higher deposition produce thicker laminae. Also, the maximum distance between erosion surfaces is less than the maximum height of the ripple or dune; since the erosion surfaces form on the upstream sides, they are closer to the underlying erosion surfaces than the ripple/dune crests. Thus, the maximum separation of erosion surfaces represents a minimum height for the ripple or dune.
Dunes and ripples behave similarly at the level of detail that I have been describing them. Their cross stratification geometries are similar. However, dunes are larger than ripples. If the distance between erosion surfaces defining cross sets is greater than a few centimeters, the cross stratification has to be from a dune. Ripples are only a few centimeters tall, and they cannot create laminae that are higher than the ripple crest-to-trough distance. Thus, if cross sets are greater than a few centimeters high, the cross stratification must be from dunes. However, if the cross sets are only one centimeter high, the cross stratification could be due to either ripples or dunes. It is possible for ALL sediment to be eroded as a dune migrates, leaving no cross stratification. If only a small amount of sediment accumulates, the cross sets might be only a centimeter high, much like ripples. In the field, grain size variations and changes in cross stratification along an outcrop can help you distinguish between ripples and dunes in a case like this. For example, you could look for an instance where the cross stratification is more than a few centimeters high. If you did not find one, that might suggest ripple cross lamination rather than dune cross stratification. Or maybe the grain size is wrong for one or the other.
Variations in Geometry and Bedform
Dunes and ripples are often irregular in plan view. This affects the geometry of the cross stratifcation/lamination. The laminae are always approximately parallel to the dip on the lee sides of the ripples or dunes. If the direction that these dip varies, the orientation of the laminae also varies. When looking at deposited cross stratification/lamination, these variations appear as variable dips in the laminae because you are viewing them at different angles.
Watch the USGS bedform movies described at: http://mygeologypage.ucdavis.edu/sumner/gel109/labs/USGSBedforms.html
Remember that the structures also change with flow speed, both in terms of their geometry and which ones form. Grain size is also important. The sequence of structures in granules with increasing flow is:
1) no transport
2) faint planar lamination - the lamination is poorly developed because the sediment is often poorly sorted and not much transport is occurring
3) dunes - the flow is strong enough to erode at the attachment point
4) upper planar lamination
5) antidunes
In contrast, the sequence of structures in silt is:
1) no transport
2) ripples
3) upper planar lamination
4) antidunes
Antidunes - Antidunes form at flow speeds greater than planar lamination when shallow water moves very quickly (Putah Creek in flood; tidal channels; creeks flowing across beaches - see http://mygeologypage.ucdavis.edu/sumner/gel109/sedstructures/Lg/ScottAntidunes.jpg). Irregularities form on the planar beds, but there is no flow separation. Instead, the water surface mimics the bedding surface. On the down flow side of the antidunes, there is a very strong erosional force (from the Bernoulli Effect) and sediment gets plastered onto the upstream side. Thus, antidunes produce laminae that dip upstream, and they migrate upstream (anti normal dune behavior). Sediment is still transported downstream; it is just the peak of the dune itself that moves upstream. At even higher flow, the waves on the surface of the water break, and the dunes become very irregular. Antidunes are rarely preserved in the rock record because they are reworked into other sedimentary structures as the flow speed decreases.
Other Types of Flows - Not all flows are uniform in one direction. For example, waves move water back and forth, transporting sand back and forth. Because the transport direction varies through time, the orientation of cross laminations vary through time. Compare the ripple types at http://mygeologypage.ucdavis.edu/sumner/gel109/sedstructures/ARipples.html Note that wave ripple lamination dips in two directions and the ripple crests are symmetric rather than steeper on the lee slope than the stoss slope. Flows can also be irregular due to combinations of currents and waves, etc. Some of these flows are very characteristic of specific environments, for example, storm-influenced beaches. The structures they produce are very useful for interpreting ancient rocks, and we will highlight them as we discuss different sedimentary environments.
Showing posts with label Bernouli effect. Show all posts
Showing posts with label Bernouli effect. Show all posts
Wednesday, January 23, 2013
Wednesday, January 16, 2013
Sedimentary Structures
Key Points of Sediment Transport in Water
1) Faster flows have more bed shear stress. Thus, faster flows move larger grains (when considering sand sizes and larger).
2) Sediment is transported as bedload and in suspension. Bedload consists of rolling and saltating grains.
3) Grain size, density and flow strength (Re) determine how grains are transported.
4) As flow strength changes, grains are eroded or deposited. These relationships are represented in the Hjulstrom diagram.
A Few Definitions:
1) "Stratification" - layers in rocks; stratified rocks are those organized into beds
See Grand Canyon Beds: http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/L1/12GrandCanyon.jpg
2) “Beds” are separated by “bedding planes” - cm to m thick units of sedimentary rock that were deposited approximately horizontally (beds) and are separated by horizontal planes (bedding planes); the rocks typically weather more along these planes. Beds are usually fairly uniform or change gradationally in composition. Bedding planes usually represent breaks in sedimentation or changes in grain size. In other words, they usually represent changes in flow characteristics.
See Cache Creek Turbidite Beds and Bedding Planes: http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/L1/13tiltedturbidites.jpg
3) "Laminae" are color, composition, or grain size variations defining surfaces within a bed. They typically represent variations in flow velocity, sediment supply, sediment composition, etc. Planar Laminae are parallel to bedding, e.g. planar.
4) "Cross Lamination”, "Cross Stratification" or "Cross Bedding" are laminations or layers that are oriented obliquely to bedding. They truncate older laminae and are truncated by younger laminae. The erosional surfaces that separate “sets” of similarly oriented laminae are called “bounding surfaces”. There are lots of subdivisions of cross stratification; different types represent different types of bedforms and different flow conditions.
See Burns Cliff on Mars observed by Opportunity: http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/L4/3BurnsCliff.jpg The upper part of the image has planar lamination, and the lower part to the far left has cross lamination or stratification.
See: http://mygeologypage.ucdavis.edu/sumner/gel109/SedStructures/Lg/TroughXStrat3.jpg for trough cross stratification and other examples of dune cross stratification at: http://mygeologypage.ucdavis.edu/sumner/gel109/SedStructures/Dunes.html
See ripple cross lamination on Mars: http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/L4/5MartianRipples.jpg
Bedforms
When sediments get deposited from turbulent flows, the sediment interacts with the geometry of the flow. Depending on the flow speed, turbulence, and sediment characteristics, different structures or bedforms develop.
See: http://faculty.gg.uwyo.edu/heller/SedMovs/mcbriderips.htm
Bed Geometry and Flow Separation - Until now, we have been implicitly assuming that the bases of beds are flat and smooth, but if sediment is present, they are not. If you start with a smooth bed of sand and increase water speed above it, irregularities form from irregularities in the flow and develop into ripples. First, a few grains pile up. Once the height of the pile is several grains high, there is a flow shadow down stream of them, and the laminar sublayer detaches from the base of the flow. The water has enough momentum that it does not hug the bed surface and instead, goes shooting out over the top. This point is called the separation point. The water flows forward and downward and reconnects with the bed at the attachment point. At the attachment point, water is flowing directly towards the sediment with a lot of force. This force moves the grains and causes erosion. In contrast, the area between the separation point and the attachment point has very low flow. In fact there are back eddies, where the flow is upstream. Thus, sediment transport is very irregular along the bedding surface at a local scale.
Sediment Transport Over a Ripple - Sediment grains are mobilized at the attachment point - more so than in normal flow because the water is shooting directly into the sediment - and the grains are moved downstream by saltation and traction. As the flow becomes parallel to the sediment surface again, its ability to transport sediment decreases. Thus, the grains tend to pile up and a new mound forms. This gives a periodic chain of mounds - the beginnings of ripples. As flow continues, grains roll and saltate up the stoss (upcurrent) side of the ripples. Once they pass the crest, they reach the low flow on the lee side of the ripple. The larger grains settle out and roll partway down the slope; this is the site of net deposition. As the process of deposition on the lee side and erosion on the stoss side continues, the ripples migrate downstream. If there is net deposition of sediment, the ripples leave behind distinctive dipping layers between two erosional surfaces that can be preserved in the rock record. These layers slope downstream and are one type of cross lamination.
A sketch of a ripple or dune like the one in lecture:
http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/duneXStrat.jpg
Watch the USGS bedform movies described at: http://mygeologypage.ucdavis.edu/sumner/gel109/labs/USGSBedforms.html
Bedforms and Flow Velocity- The size and shape of subaqueous bedforms depends on flow strength and grain size and can be used to interpret ancient flow characteristics in a depositional environment from looking at sedimentary rocks. See Nichols (2009, Sedimentology and Stratigraphy, section 4.3) for bedform, flow speed, and grain size relationships.
Ripples (crest-to-crest differences of less than 50 cm and heights of less than 4 cm) – The minimum flow for ripples is determined by the minimum velocity for sediment transport. Once this flow speed is reached, ripples form if the sediment is transported as bedload. The maximum flow speed for ripples depends on the location of the attachment point on the stoss side of the ripples. As flow gets faster, too much erosion occurs at the crests of the ripples - the point of attachment is too far up the stoss side of the ripple- and the ripples flatten out. Dunes develop.
Dunes (60 cm-100’s m wavelength and 10’s of cm to meters in height) - Dunes develop as ripples flatten out because large scale irregularities start to develop. The basic ideas of dune and ripple formation are the same. The difference is that the area of flow separation is much larger (see Fig 4.17, Nichols 2009). Roller vortexes (e.g. upstream flows along the lee sides of dunes) are common, and the upstream flow can be strong enough to form ripples that migrate upstream. As flow speeds increase, the dunes start to flatten out.
Planar/Flat Lamination – Planar lamination forms when the flow is strong enough that the beds flatten out. The momentum of the transported grains and fluid are high enough that they tend to move horizontally, eroding any irregularities in the bed. This zone of planar lamination is called “upper flow regime”. (Why “upper”? - there is a zone of planar lamination in coarse grained sediment at low flow velocities.)
Antidunes - Antidunes form at flow speeds greater than planar lamination when shallow water moves very quickly (Putah Creek in flood; tidal channels; creeks flowing across beaches - see http://mygeologypage.ucdavis.edu/sumner/gel109/sedstructures/Lg/ScottAntidunes.jpg). Irregularities form on the planar beds, but there is no flow separation. Instead, the water surface mimics the bedding surface. On the down flow side of the antidunes, there is a very strong erosional force (from the Bernoulli Effect) and sediment gets plastered onto the upstream side. Thus, antidunes produce laminae that dip upstream, and they migrate upstream (anti normal dune behavior). Sediment is still transported downstream; it is just the peak of the dune itself that moves upstream. At even higher flow, the waves on the surface of the water break, and the dunes become very irregular. Antidunes are rarely preserved in the rock record because they are reworked into other sedimentary structures as the flow speed decreases.
Other Types of Flows - Not all flows are uniform in one direction. For example, waves move water back and forth, transporting sand back and forth. Because the transport direction varies through time, the orientation of cross laminations vary through time. Compare the ripple types at http://mygeologypage.ucdavis.edu/sumner/gel109/sedstructures/ARipples.html. Note that wave ripple lamination dips in two directions and the ripple crests are symmetric rather than steeper on the lee slope than the stoss slope. Flows can also be irregular due to combinations of currents and waves, etc. Some of these flows are very characteristic of specific environments, for example, storm-influenced beaches. The structures they produce are very useful for interpreting ancient rocks, and we will highlight them as we discuss different sedimentary environments.
Bedforms and Grain Size - Bedforms also vary with grain size (see Figure 4.20, Nichols, 2009). Very fine sand and silt are very easy to transport and erode. They form nice ripples, but do not form dunes when transported by water. Instead, ripples transition into planar laminae. Coarse sand and larger sediment is too hard to transport and erode to get ripples. The erosional force at the reattachment point is not strong enough to erode the coarse grains and produce the erosional surfaces on the backs of ripples. Without this erosion, troughs do not form and without troughs, crests do not form. The sequence of structures in granules with increasing flow is:
1) no transport
2) faint planar lamination - the lamination is poorly developed because the sediment is often poorly sorted and not much transport is occurring
3) dunes - the flow is strong enough to erode at the attachment point
4) upper planar lamination
5) antidunes
In contrast, the sequence of structures in silt is:
1) no transport
2) ripples
3) upper planar lamination
4) antidunes
Extra
High Sediment Loads - Sometimes with slope failures on land or under water, much more sediment can be put into motion than the flow would normally erode. Depending on the amount of water mixed with the sediment, the flow characteristics are different. When abundant water is present, the sediment can form a thick slurry with a higher density than sediment-free water, commonly leading to a higher Re and more turbulent flow (Re=u*l*r/µ). Also, collisions between grains become extremely important. Both of these tend to keep the sediment moving. Grain-to-grain collisions also have an important effect on grain sorting. The collisions tend to make sorting much less efficient and the sediment that gets deposited tends to consist of which ever grains make it to the base of the flow and are not kicked back up again. Usually, the largest grains are part of this first deposit because they weigh more, but small grains are also present. As the amount of sediment decreases, the flow becomes more like typical water flows. Turbidites are subaqueous flows that start out with a very high sediment load and decrease in time to more normal flows. They have characteristic sedimentary structures associated with them that reflect these changes.
If there is very little water associated with a clay-rich sediment flow, the flow can be very viscous due to the charge attraction among clay particles. The high viscocity makes the flow laminar (Re=u*l*r/µ). Debris flows with lots of cohesive mud are like this. In laminar flows, there is no mixing of the water or grains (or ice) and there is no sorting of grain sizes. Thus, the sediment remains mixed up with large grains, sometimes boulders, “floating” in mud. They flow down hill pulled by gravity until the flow seizes up and stops. This can be due to too low a slope or loss of water. Underwater debris flows can also be diluted by water that gets incorporated at the edges of the flow and become less viscous and more turbulent.
There also are dry sediment flows in which air is present between grains. For example, rock avalanches and some pyroclastic flows from volcanoes lack water. For these to move significant distances, large amounts of energy from either gravity or explosions are necessary to keep the sediment in motion.
1) Faster flows have more bed shear stress. Thus, faster flows move larger grains (when considering sand sizes and larger).
2) Sediment is transported as bedload and in suspension. Bedload consists of rolling and saltating grains.
3) Grain size, density and flow strength (Re) determine how grains are transported.
4) As flow strength changes, grains are eroded or deposited. These relationships are represented in the Hjulstrom diagram.
A Few Definitions:
1) "Stratification" - layers in rocks; stratified rocks are those organized into beds
See Grand Canyon Beds: http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/L1/12GrandCanyon.jpg
2) “Beds” are separated by “bedding planes” - cm to m thick units of sedimentary rock that were deposited approximately horizontally (beds) and are separated by horizontal planes (bedding planes); the rocks typically weather more along these planes. Beds are usually fairly uniform or change gradationally in composition. Bedding planes usually represent breaks in sedimentation or changes in grain size. In other words, they usually represent changes in flow characteristics.
See Cache Creek Turbidite Beds and Bedding Planes: http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/L1/13tiltedturbidites.jpg
3) "Laminae" are color, composition, or grain size variations defining surfaces within a bed. They typically represent variations in flow velocity, sediment supply, sediment composition, etc. Planar Laminae are parallel to bedding, e.g. planar.
4) "Cross Lamination”, "Cross Stratification" or "Cross Bedding" are laminations or layers that are oriented obliquely to bedding. They truncate older laminae and are truncated by younger laminae. The erosional surfaces that separate “sets” of similarly oriented laminae are called “bounding surfaces”. There are lots of subdivisions of cross stratification; different types represent different types of bedforms and different flow conditions.
See Burns Cliff on Mars observed by Opportunity: http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/L4/3BurnsCliff.jpg The upper part of the image has planar lamination, and the lower part to the far left has cross lamination or stratification.
See: http://mygeologypage.ucdavis.edu/sumner/gel109/SedStructures/Lg/TroughXStrat3.jpg for trough cross stratification and other examples of dune cross stratification at: http://mygeologypage.ucdavis.edu/sumner/gel109/SedStructures/Dunes.html
See ripple cross lamination on Mars: http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/L4/5MartianRipples.jpg
Bedforms
When sediments get deposited from turbulent flows, the sediment interacts with the geometry of the flow. Depending on the flow speed, turbulence, and sediment characteristics, different structures or bedforms develop.
See: http://faculty.gg.uwyo.edu/heller/SedMovs/mcbriderips.htm
Bed Geometry and Flow Separation - Until now, we have been implicitly assuming that the bases of beds are flat and smooth, but if sediment is present, they are not. If you start with a smooth bed of sand and increase water speed above it, irregularities form from irregularities in the flow and develop into ripples. First, a few grains pile up. Once the height of the pile is several grains high, there is a flow shadow down stream of them, and the laminar sublayer detaches from the base of the flow. The water has enough momentum that it does not hug the bed surface and instead, goes shooting out over the top. This point is called the separation point. The water flows forward and downward and reconnects with the bed at the attachment point. At the attachment point, water is flowing directly towards the sediment with a lot of force. This force moves the grains and causes erosion. In contrast, the area between the separation point and the attachment point has very low flow. In fact there are back eddies, where the flow is upstream. Thus, sediment transport is very irregular along the bedding surface at a local scale.
Sediment Transport Over a Ripple - Sediment grains are mobilized at the attachment point - more so than in normal flow because the water is shooting directly into the sediment - and the grains are moved downstream by saltation and traction. As the flow becomes parallel to the sediment surface again, its ability to transport sediment decreases. Thus, the grains tend to pile up and a new mound forms. This gives a periodic chain of mounds - the beginnings of ripples. As flow continues, grains roll and saltate up the stoss (upcurrent) side of the ripples. Once they pass the crest, they reach the low flow on the lee side of the ripple. The larger grains settle out and roll partway down the slope; this is the site of net deposition. As the process of deposition on the lee side and erosion on the stoss side continues, the ripples migrate downstream. If there is net deposition of sediment, the ripples leave behind distinctive dipping layers between two erosional surfaces that can be preserved in the rock record. These layers slope downstream and are one type of cross lamination.
A sketch of a ripple or dune like the one in lecture:
http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/duneXStrat.jpg
Watch the USGS bedform movies described at: http://mygeologypage.ucdavis.edu/sumner/gel109/labs/USGSBedforms.html
Bedforms and Flow Velocity- The size and shape of subaqueous bedforms depends on flow strength and grain size and can be used to interpret ancient flow characteristics in a depositional environment from looking at sedimentary rocks. See Nichols (2009, Sedimentology and Stratigraphy, section 4.3) for bedform, flow speed, and grain size relationships.
Ripples (crest-to-crest differences of less than 50 cm and heights of less than 4 cm) – The minimum flow for ripples is determined by the minimum velocity for sediment transport. Once this flow speed is reached, ripples form if the sediment is transported as bedload. The maximum flow speed for ripples depends on the location of the attachment point on the stoss side of the ripples. As flow gets faster, too much erosion occurs at the crests of the ripples - the point of attachment is too far up the stoss side of the ripple- and the ripples flatten out. Dunes develop.
Dunes (60 cm-100’s m wavelength and 10’s of cm to meters in height) - Dunes develop as ripples flatten out because large scale irregularities start to develop. The basic ideas of dune and ripple formation are the same. The difference is that the area of flow separation is much larger (see Fig 4.17, Nichols 2009). Roller vortexes (e.g. upstream flows along the lee sides of dunes) are common, and the upstream flow can be strong enough to form ripples that migrate upstream. As flow speeds increase, the dunes start to flatten out.
Planar/Flat Lamination – Planar lamination forms when the flow is strong enough that the beds flatten out. The momentum of the transported grains and fluid are high enough that they tend to move horizontally, eroding any irregularities in the bed. This zone of planar lamination is called “upper flow regime”. (Why “upper”? - there is a zone of planar lamination in coarse grained sediment at low flow velocities.)
Antidunes - Antidunes form at flow speeds greater than planar lamination when shallow water moves very quickly (Putah Creek in flood; tidal channels; creeks flowing across beaches - see http://mygeologypage.ucdavis.edu/sumner/gel109/sedstructures/Lg/ScottAntidunes.jpg). Irregularities form on the planar beds, but there is no flow separation. Instead, the water surface mimics the bedding surface. On the down flow side of the antidunes, there is a very strong erosional force (from the Bernoulli Effect) and sediment gets plastered onto the upstream side. Thus, antidunes produce laminae that dip upstream, and they migrate upstream (anti normal dune behavior). Sediment is still transported downstream; it is just the peak of the dune itself that moves upstream. At even higher flow, the waves on the surface of the water break, and the dunes become very irregular. Antidunes are rarely preserved in the rock record because they are reworked into other sedimentary structures as the flow speed decreases.
Other Types of Flows - Not all flows are uniform in one direction. For example, waves move water back and forth, transporting sand back and forth. Because the transport direction varies through time, the orientation of cross laminations vary through time. Compare the ripple types at http://mygeologypage.ucdavis.edu/sumner/gel109/sedstructures/ARipples.html. Note that wave ripple lamination dips in two directions and the ripple crests are symmetric rather than steeper on the lee slope than the stoss slope. Flows can also be irregular due to combinations of currents and waves, etc. Some of these flows are very characteristic of specific environments, for example, storm-influenced beaches. The structures they produce are very useful for interpreting ancient rocks, and we will highlight them as we discuss different sedimentary environments.
Bedforms and Grain Size - Bedforms also vary with grain size (see Figure 4.20, Nichols, 2009). Very fine sand and silt are very easy to transport and erode. They form nice ripples, but do not form dunes when transported by water. Instead, ripples transition into planar laminae. Coarse sand and larger sediment is too hard to transport and erode to get ripples. The erosional force at the reattachment point is not strong enough to erode the coarse grains and produce the erosional surfaces on the backs of ripples. Without this erosion, troughs do not form and without troughs, crests do not form. The sequence of structures in granules with increasing flow is:
1) no transport
2) faint planar lamination - the lamination is poorly developed because the sediment is often poorly sorted and not much transport is occurring
3) dunes - the flow is strong enough to erode at the attachment point
4) upper planar lamination
5) antidunes
In contrast, the sequence of structures in silt is:
1) no transport
2) ripples
3) upper planar lamination
4) antidunes
Extra
High Sediment Loads - Sometimes with slope failures on land or under water, much more sediment can be put into motion than the flow would normally erode. Depending on the amount of water mixed with the sediment, the flow characteristics are different. When abundant water is present, the sediment can form a thick slurry with a higher density than sediment-free water, commonly leading to a higher Re and more turbulent flow (Re=u*l*r/µ). Also, collisions between grains become extremely important. Both of these tend to keep the sediment moving. Grain-to-grain collisions also have an important effect on grain sorting. The collisions tend to make sorting much less efficient and the sediment that gets deposited tends to consist of which ever grains make it to the base of the flow and are not kicked back up again. Usually, the largest grains are part of this first deposit because they weigh more, but small grains are also present. As the amount of sediment decreases, the flow becomes more like typical water flows. Turbidites are subaqueous flows that start out with a very high sediment load and decrease in time to more normal flows. They have characteristic sedimentary structures associated with them that reflect these changes.
If there is very little water associated with a clay-rich sediment flow, the flow can be very viscous due to the charge attraction among clay particles. The high viscocity makes the flow laminar (Re=u*l*r/µ). Debris flows with lots of cohesive mud are like this. In laminar flows, there is no mixing of the water or grains (or ice) and there is no sorting of grain sizes. Thus, the sediment remains mixed up with large grains, sometimes boulders, “floating” in mud. They flow down hill pulled by gravity until the flow seizes up and stops. This can be due to too low a slope or loss of water. Underwater debris flows can also be diluted by water that gets incorporated at the edges of the flow and become less viscous and more turbulent.
There also are dry sediment flows in which air is present between grains. For example, rock avalanches and some pyroclastic flows from volcanoes lack water. For these to move significant distances, large amounts of energy from either gravity or explosions are necessary to keep the sediment in motion.
Monday, January 14, 2013
Homework: Fluid Flow 1
1. Calculate the Reynolds number, flow speed, or water depth for the following flows using the Reynolds equation. The density of water is 1000 kg/m3, and it has a viscosity of 0.001 kg/(m*s). (6 points)
a) Calculate the Reynolds number for a flow with speed = 1 m/s and depth = 1 m. Is the flow laminar, transitional, or turbulent?
b) Calculate the Reynolds number for a flow with speed = 0.1 m/s and depth = 0.1 m. Is the flow laminar, transitional, or turbulent?
c) What is the maximum water depth for a laminar flow if the flow speed is 0.01 m/s?
2. Where in any water flow is there laminar flow even if the flow speed is 0.45 m/s and the depth is 10’s of centimeters? Why is it laminar? (Assume that the bed it is flowing over is smooth. You can watch this video: http://tinyurl.com/7lcc4o for a big hint!) (4 points)
3. Watch the video at http://youtu.be/TKH1DyV9vNU called Sports Car Aerodynamics: Spoiler Alert! Using the description of pressure in airflow over cars with spoilers vs. airfoils vs neither, sketch the laminar and turbulent areas of flow over a round sedimentary grain sitting on a flat surface. Show the areas of low and high pressure and the forces on the grain. (6 points)
4. In words, briefly describe the process (Bernouli Effect) that causes grains to be picked up off the bed and entrained in the flow (at least temporarily). This description should be consistent with your sketch in question 3. (4 points)
Fluid Flow and Sediment Transport
Key Concepts from Lecture 2
Reynolds Number - Reynolds number predicts the extent of turbulence in a fluid based on how fast the fluid is flowing, the geometry of the flow (how deep and wide it is, etc.), and the density and viscosity the of the fluid. Re = (fluid inertial forces)/(fluid viscous forces) = l*u*r/µ where the variables are flow velocity (u), characteristic length (l) which represents flow geometry, say river depth, fluid density (r), and fluid viscosity (µ). Turbulent flow has Re is greater than 2000 and laminar flow has Re is less than 500. Flow with Re between 500 and 2000 is transitional and has some characteristics of laminar flow, but some turbulence as well.
Boundary Layer and Laminar Sublayer - There is boundary layer at the edge of every flow where flow speed decreases due to friction. Within the boundary layer, right next to the surface, the flow speed is very low, creating a laminar sublayer.
Sediment Transport
Bed Shear Stress: The boundary layer determines the amount of “Bed Shear Stress” which corresponds to the forces that tend to roll particles along the bed and the pressure differences above and below the grain which tend to lift them off the bed. Bed shear stress is related to the thickness of the laminar sublayer. The narrower it is, the more bed shear stress. It also depends on the slope. If the slope is steep, gravity helps pull grains down the slope, increasing bed shear stress. Also, the roughness of the bed is a factor. A rough bed deflects flows and increases turbulence, which increases the bed shear stress, particularly in places where flow is directed into the sediment and the boundary layer is compressed. (See http://en.wikipedia.org/wiki/Sediment_transport#Bed_shear_stress for more detailed information.)
The Bernoulli Effect
A pressure difference “pulls” grains off the bed. The pressure difference comes from a difference in water (or air) speed above and below the grain. As water flows faster, there are fewer collisions between the water and a surface it flows over than there are between standing water and a similar surface. Pressure is due to collisions. Thus, fewer collisions means lower pressure. The upstream side of a grain experiences the most collisions because the water is flowing into it. The downstream side experiences the fewest collisions, and the sides of the grain experience fewer collisions where flow is faster and more where the flow is slower. The net result is a low pressure zone above and slightly downstream of a grain. If the force exerted by this pressure difference is larger than the force of gravity, the grain will lift off the bed. This lift due to the pressure difference is the Bernouli Effect.
Which Grains Move? Which grains get entrained in the flow depends on their size and density (how much they weigh) because that determines the force of gravity holding them down. It also depends on the shape of the grain. One with a large area to experience the low pressure (like a plate) will be more susceptible to being picked up than a round grain of the same mass (although flat grains may see a smaller flow difference from top to bottom if the boundary layer is thick, and flat grains may experience a lower Bernoulli Effect per unit area.) The other thing that really matters is the position of a grain relative to surrounding grains. If a grain is sandwiched between larger grains, i.e. in their flow shadows, it will not experience as big a pressure difference as if it is on a flat surface. Also, if a grain is upstream of a big grain, it has to be lifted over it, so a larger pressure difference is needed. Thus, things can get complicated if you are trying to predict the behavior of a specific grain. However, we have some general guidelines based on experiments and theory that nicely predict how grains behave on average.
Bedload and Suspended Load Transport
Two things can happen once a grain is lifted into the flow: 1) it can fall back down or 2) it can stay there. It depends on how quickly the grain settles out versus how turbulent the water is (back to Re...). Bedload refers to the grains that are transported along the sedimentary bed, e.g. grains that are rolling and being lifted off the bed, but they fall back quickly. The name bedload comes from the fact that the grains moving by traction and saltation never get too far from the bed and “load” is an engineering term for the amount of sediment transported by a river. Rolling grains are in traction. Grains that are pulled off the bed with the Bernoulli effect but are large enough that gravity causes them to fall “quickly” back to the bed are said to be saltating. (The word saltating refers to the way salt from a salt shaker bounces when it is shaken onto a hard surface. The word is derived from a Latin word meaning dance.) Bedload grains are the ones that form sedimentary structures in flowing water.
Here is a playlist with movies related to sediment transport: Sumnerd’s Sed Transport Playlist and an extra movie at
http://faculty.gg.uwyo.edu/heller/SedMovs/bedload.htm (7.8 Mb)
Suspended sediment consists of grains that are light enough that they do not settle out of the water; the turbulent bursts of water keep them in the flow. The more turbulence in the water, e.g. the higher the Reynolds number, the larger the grains in suspension will be. The upward motions of turbulent flow are faster than the rate these grains settle, so gravity is counteracted and they stay “floating” in the water even though they are denser than the water. Very small grains do not settle out of flows unless the Reynolds number is low, which means that the flows need to be standing or very shallow.
Photo of suspended sediment in a Costa Rica River: http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/L3/CostaRicaRiver.jpg
YouTube video of white clay in a turbulent flow in a flume: http://tinyurl.com/78kg3z The pulsing in the flow is (probably) due to the pump that is making the water flow.
Hjulstrom Diagrams
The flows that are required to pick up grains of certain sizes have been extensively studied in experiments and the results are plotted in Hjulstrom diagrams. Hjulstrom diagrams show grain entrainment on a plot of log grain size versus log flow speed. This diagram shows the areas where grains of different sizes are left on the bed, where they get moved sometimes (this is the gray zone), and where they get lifted up often and eroded away. Note that larger grains require higher flows - in general. The water speed that is required to transport a grain is call the critical velocity. This is important. If there is gravel in a sedimentary deposit, you can say that the water flow had to be above the critical threshold for it to get there! That might require a fast flowing river or strong wave action, thus, a large part of narrowing down the depositional environment has already been done!
A copy of the Hjulstrom Diagram can be found on Wikipedia: http://en.wikipedia.org/wiki/Hjulstr%C3%B6m_curve
Deeper flows can move larger grains at the same flow velocity because they are more turbulent: Re=u*l*r/µ and l is larger. This is because deeper flows can have larger variations in flow speed and the laminar flow layers are very thin. They can have bursts of very rapid flow relative to the average flow speed and these bursts can pick up larger grains. Actual flow characteristics are much more complex in detail than just Hjulstrom diagrams, which summarize a lot of characteristics into two axes. However, like a lot of people, we will use the diagram anyway, because it is very useful as a rule of thumb. Just remember that it is not a completely accurate representation of what will happen - it represents a reasonable guess.
Silt and Clay - Notice that for the small end of grain size, the speed of flow required for erosion actually increases. One reason small grains are hard to erode is that they tend not to stick up through the laminar sublayer; they are just too small. Thus, thinner boundary layers are necessary to roll them or for the pressure differences to pick them up off the bed. Also, the surfaces of clay minerals tend to be charged and the grains stick together. This is most obvious when big clumps of mud stick to your shoes. That just does not happen with sand (unless there is something gross in it). The stickiness of the clay grains makes them difficult to erode, so faster water flows (a greater pressure difference or larger turbulent burst down to the sediment surface) are required to move them. The smaller the grains, the more surface charges stick the grains together, thus the stronger the flow needed to erode them. The stickiness of the clay grains also depends on the amount of water between them and the mineralogy, so there is a big gray zone where a clay may or may not erode.
In the Hjulstrom diagram, there is an interesting area where the flow is not strong enough to move any of the particles on the bed, but those that are in the suspended load do not settle out either. This zone includes many of the waters on the surface of the earth. In flows with low velocity or that are very deep, Re is high enough to keep some clay in suspension. Clay deposition usually occurs very slowly, e.g. when the rate of settling is just slightly faster than the average rate at which turbulence moves clay particles upward or when the clays clump together to form larger grains (which is common when fresh and salty waters mix).
A few more words about saltation: Saltation is a very interesting and important process in sediment transport, because the force of the impact when the grains land tends to knock new grains up into the flow even if the flow is not fast enough to lift them with the Bernoulli Effect. These new grains can kick up more grains when they land, etc. This increases the rate of sediment transport above the amount the flow can lift grains off of the bed. This is one of the causes of the gray zone in the Hjulstrom diagram at larger grain sizes. Once saltation starts, it can trigger sediment transport that would not otherwise occur.
Watch grains transported by saltation and traction in these movies: http://faculty.gg.uwyo.edu/heller/SedMovs/Dietrich.htm (11 Mb)
http://faculty.gg.uwyo.edu/heller/SedMovs/sand_sheet.htm (14 Mb)
You can also see bedload transport in a movie that describes why we think we have found evidence of a river on mars: http://www.youtube.com/watch?v=HYHc2alzdUk My friend Sanjeev narrates it. He is a professor at Imperial College in London. More information and graphics are at http://mars.jpl.nasa.gov/msl/news/index.cfm?FuseAction=ShowNews&newsid=1360
Deposition: Deposition is the accumulation of grains. If a flow starts slowly and gains speed, it will start to move larger and larger grains. As it slows down, it can only move the smaller ones. Deposition happens when a flow slows down and starts to leave grains on the bed. The combination of changing average flow speeds and local variations in flow speed caused by topography on the bed give rise to very informative sedimentary structures – including cross stratification - which are extremely useful for interpreting depositional environments.
Ripples and Other Bedforms
Structures form on the surface of a bed when topography influences the strength of the flow (and thus the strength of the Bernouli Effect). Erosion occurs where flow is strongest and directed into the bed. Deposition occurs where flow is slower. Deposition almost always creates laminae that are parallel to the depositional surface. Thus, laminae preserved in rocks reflect the shape of the ancient depositional surface. Small ripples have small laminae that dip downstream because that is where deposition occurs; flat beds have flat laminae; large dunes have coarser laminae that dip downstream.
Next Time: We will talk about the details about sedimentary structures.
Reynolds Number - Reynolds number predicts the extent of turbulence in a fluid based on how fast the fluid is flowing, the geometry of the flow (how deep and wide it is, etc.), and the density and viscosity the of the fluid. Re = (fluid inertial forces)/(fluid viscous forces) = l*u*r/µ where the variables are flow velocity (u), characteristic length (l) which represents flow geometry, say river depth, fluid density (r), and fluid viscosity (µ). Turbulent flow has Re is greater than 2000 and laminar flow has Re is less than 500. Flow with Re between 500 and 2000 is transitional and has some characteristics of laminar flow, but some turbulence as well.
Boundary Layer and Laminar Sublayer - There is boundary layer at the edge of every flow where flow speed decreases due to friction. Within the boundary layer, right next to the surface, the flow speed is very low, creating a laminar sublayer.
Sediment Transport
Bed Shear Stress: The boundary layer determines the amount of “Bed Shear Stress” which corresponds to the forces that tend to roll particles along the bed and the pressure differences above and below the grain which tend to lift them off the bed. Bed shear stress is related to the thickness of the laminar sublayer. The narrower it is, the more bed shear stress. It also depends on the slope. If the slope is steep, gravity helps pull grains down the slope, increasing bed shear stress. Also, the roughness of the bed is a factor. A rough bed deflects flows and increases turbulence, which increases the bed shear stress, particularly in places where flow is directed into the sediment and the boundary layer is compressed. (See http://en.wikipedia.org/wiki/Sediment_transport#Bed_shear_stress for more detailed information.)
The Bernoulli Effect
A pressure difference “pulls” grains off the bed. The pressure difference comes from a difference in water (or air) speed above and below the grain. As water flows faster, there are fewer collisions between the water and a surface it flows over than there are between standing water and a similar surface. Pressure is due to collisions. Thus, fewer collisions means lower pressure. The upstream side of a grain experiences the most collisions because the water is flowing into it. The downstream side experiences the fewest collisions, and the sides of the grain experience fewer collisions where flow is faster and more where the flow is slower. The net result is a low pressure zone above and slightly downstream of a grain. If the force exerted by this pressure difference is larger than the force of gravity, the grain will lift off the bed. This lift due to the pressure difference is the Bernouli Effect.
Which Grains Move? Which grains get entrained in the flow depends on their size and density (how much they weigh) because that determines the force of gravity holding them down. It also depends on the shape of the grain. One with a large area to experience the low pressure (like a plate) will be more susceptible to being picked up than a round grain of the same mass (although flat grains may see a smaller flow difference from top to bottom if the boundary layer is thick, and flat grains may experience a lower Bernoulli Effect per unit area.) The other thing that really matters is the position of a grain relative to surrounding grains. If a grain is sandwiched between larger grains, i.e. in their flow shadows, it will not experience as big a pressure difference as if it is on a flat surface. Also, if a grain is upstream of a big grain, it has to be lifted over it, so a larger pressure difference is needed. Thus, things can get complicated if you are trying to predict the behavior of a specific grain. However, we have some general guidelines based on experiments and theory that nicely predict how grains behave on average.
Bedload and Suspended Load Transport
Two things can happen once a grain is lifted into the flow: 1) it can fall back down or 2) it can stay there. It depends on how quickly the grain settles out versus how turbulent the water is (back to Re...). Bedload refers to the grains that are transported along the sedimentary bed, e.g. grains that are rolling and being lifted off the bed, but they fall back quickly. The name bedload comes from the fact that the grains moving by traction and saltation never get too far from the bed and “load” is an engineering term for the amount of sediment transported by a river. Rolling grains are in traction. Grains that are pulled off the bed with the Bernoulli effect but are large enough that gravity causes them to fall “quickly” back to the bed are said to be saltating. (The word saltating refers to the way salt from a salt shaker bounces when it is shaken onto a hard surface. The word is derived from a Latin word meaning dance.) Bedload grains are the ones that form sedimentary structures in flowing water.
Here is a playlist with movies related to sediment transport: Sumnerd’s Sed Transport Playlist and an extra movie at
http://faculty.gg.uwyo.edu/heller/SedMovs/bedload.htm (7.8 Mb)
Suspended sediment consists of grains that are light enough that they do not settle out of the water; the turbulent bursts of water keep them in the flow. The more turbulence in the water, e.g. the higher the Reynolds number, the larger the grains in suspension will be. The upward motions of turbulent flow are faster than the rate these grains settle, so gravity is counteracted and they stay “floating” in the water even though they are denser than the water. Very small grains do not settle out of flows unless the Reynolds number is low, which means that the flows need to be standing or very shallow.
Photo of suspended sediment in a Costa Rica River: http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/L3/CostaRicaRiver.jpg
YouTube video of white clay in a turbulent flow in a flume: http://tinyurl.com/78kg3z The pulsing in the flow is (probably) due to the pump that is making the water flow.
Hjulstrom Diagrams
The flows that are required to pick up grains of certain sizes have been extensively studied in experiments and the results are plotted in Hjulstrom diagrams. Hjulstrom diagrams show grain entrainment on a plot of log grain size versus log flow speed. This diagram shows the areas where grains of different sizes are left on the bed, where they get moved sometimes (this is the gray zone), and where they get lifted up often and eroded away. Note that larger grains require higher flows - in general. The water speed that is required to transport a grain is call the critical velocity. This is important. If there is gravel in a sedimentary deposit, you can say that the water flow had to be above the critical threshold for it to get there! That might require a fast flowing river or strong wave action, thus, a large part of narrowing down the depositional environment has already been done!
A copy of the Hjulstrom Diagram can be found on Wikipedia: http://en.wikipedia.org/wiki/Hjulstr%C3%B6m_curve
Deeper flows can move larger grains at the same flow velocity because they are more turbulent: Re=u*l*r/µ and l is larger. This is because deeper flows can have larger variations in flow speed and the laminar flow layers are very thin. They can have bursts of very rapid flow relative to the average flow speed and these bursts can pick up larger grains. Actual flow characteristics are much more complex in detail than just Hjulstrom diagrams, which summarize a lot of characteristics into two axes. However, like a lot of people, we will use the diagram anyway, because it is very useful as a rule of thumb. Just remember that it is not a completely accurate representation of what will happen - it represents a reasonable guess.
Silt and Clay - Notice that for the small end of grain size, the speed of flow required for erosion actually increases. One reason small grains are hard to erode is that they tend not to stick up through the laminar sublayer; they are just too small. Thus, thinner boundary layers are necessary to roll them or for the pressure differences to pick them up off the bed. Also, the surfaces of clay minerals tend to be charged and the grains stick together. This is most obvious when big clumps of mud stick to your shoes. That just does not happen with sand (unless there is something gross in it). The stickiness of the clay grains makes them difficult to erode, so faster water flows (a greater pressure difference or larger turbulent burst down to the sediment surface) are required to move them. The smaller the grains, the more surface charges stick the grains together, thus the stronger the flow needed to erode them. The stickiness of the clay grains also depends on the amount of water between them and the mineralogy, so there is a big gray zone where a clay may or may not erode.
In the Hjulstrom diagram, there is an interesting area where the flow is not strong enough to move any of the particles on the bed, but those that are in the suspended load do not settle out either. This zone includes many of the waters on the surface of the earth. In flows with low velocity or that are very deep, Re is high enough to keep some clay in suspension. Clay deposition usually occurs very slowly, e.g. when the rate of settling is just slightly faster than the average rate at which turbulence moves clay particles upward or when the clays clump together to form larger grains (which is common when fresh and salty waters mix).
A few more words about saltation: Saltation is a very interesting and important process in sediment transport, because the force of the impact when the grains land tends to knock new grains up into the flow even if the flow is not fast enough to lift them with the Bernoulli Effect. These new grains can kick up more grains when they land, etc. This increases the rate of sediment transport above the amount the flow can lift grains off of the bed. This is one of the causes of the gray zone in the Hjulstrom diagram at larger grain sizes. Once saltation starts, it can trigger sediment transport that would not otherwise occur.
Watch grains transported by saltation and traction in these movies: http://faculty.gg.uwyo.edu/heller/SedMovs/Dietrich.htm (11 Mb)
http://faculty.gg.uwyo.edu/heller/SedMovs/sand_sheet.htm (14 Mb)
You can also see bedload transport in a movie that describes why we think we have found evidence of a river on mars: http://www.youtube.com/watch?v=HYHc2alzdUk My friend Sanjeev narrates it. He is a professor at Imperial College in London. More information and graphics are at http://mars.jpl.nasa.gov/msl/news/index.cfm?FuseAction=ShowNews&newsid=1360
Deposition: Deposition is the accumulation of grains. If a flow starts slowly and gains speed, it will start to move larger and larger grains. As it slows down, it can only move the smaller ones. Deposition happens when a flow slows down and starts to leave grains on the bed. The combination of changing average flow speeds and local variations in flow speed caused by topography on the bed give rise to very informative sedimentary structures – including cross stratification - which are extremely useful for interpreting depositional environments.
Ripples and Other Bedforms
Structures form on the surface of a bed when topography influences the strength of the flow (and thus the strength of the Bernouli Effect). Erosion occurs where flow is strongest and directed into the bed. Deposition occurs where flow is slower. Deposition almost always creates laminae that are parallel to the depositional surface. Thus, laminae preserved in rocks reflect the shape of the ancient depositional surface. Small ripples have small laminae that dip downstream because that is where deposition occurs; flat beds have flat laminae; large dunes have coarser laminae that dip downstream.
Next Time: We will talk about the details about sedimentary structures.
Wednesday, January 9, 2013
Fluid Flow Part 1
Key Concepts from Lecture 1
The Principle of Uniformitarianism – the processes that formed ancient deposits are the same as those that form modern deposits.
The Principle of Original Horizontality - strata (or sedimentary rock layers) are deposited in a nearly horizontal position. If they are no longer horizontal, later deformation much have changed their orientation.
The Law of Superposition - younger sediments overlie older sediments.
Walther’s Law
Key Concept: (Walther’s Law) Depositional environments vary in space and time such that “The facies [rock types] that occur conformably next to one another in a vertical section of rock will be the same as those found in laterally adjacent depositional environments” (Johannes Walther, 1894).
One of the most important implications of Walther’s Law is that rocks of the same type are not necessarily deposited at the same time. There is a BIG difference between correlating rocks based on having the same lithology and rock being deposited at the same time. This is a critical conceptual idea that we will focus on throughout the class.
Let’s look at an alluvial fan in Gale Crater, Mars: http://tinyurl.com/be39pmv
Where are there differences in environment laterally? If the fan grew through time, how would you predict the deposits to change vertically?
For more information on ancient stream flows on Mars, see:
http://mars.jpl.nasa.gov/msl/news/whatsnew/index.cfm?FuseAction=ShowNews&NewsID=1360
Summary of Walther’s Law: http://www.youtube.com/watch?v=ZSsULiPouTo
Sediment Transport
Most sediment transport is due to gravity. Things fall down hill in slumps, debris flows, and mudflows, and are transported downhill by fluids, like water, ice, and air. In some cases, processes like waves, currents, and wind transport sediment up a slope such as a beach or up mountain sides. This transport goes against gravity and is driven by the processes of fluid dynamics. Fluid dynamics is the main topic of today's and Monday’s lectures. We will come back to mass wasting processes when we talk about erosion. Mass wasting is important for transporting large volumes of sediment short distances, but fluid transport is required to move sediments long distances and is responsible for most sediment transport. To understand sediment transport, it is essential to understand the mechanics of fluid flow.
Fluid Flow
There are two end member ways fluids flow: 1) laminar flow and 2) turbulent flow. There is a wide gradation between these two end members, specifically "transitional" flows.
Laminar Flow - In laminar flow, water molecules move in straight, parallel lines down current. If you add a dye to water that is in the laminar flow regime, the dye would not mix into the water; it would streak out in an approximately straight line. Laminar flow is characteristic of very slow moving, shallow water, which is uncommon in nature. It is also characteristic of flows in "fluids" that are very viscous, like glacial ice or mud flows that have little water.
Turbulent Flow - In contrast, turbulent flow is characterized by complex motion of water (or other) molecules. Molecules move in all directions in bursts of upward, downward, and forward motion, and even some backward movement. There is abundant mixing in the flow because neighboring molecules move in different directions, and an added dye mixes into the water very quickly. Most water and air flows are turbulent, at least to some degree. Turbulence is important for sediment transport in water and air because it makes grains easier to transport and tends to keep them moving longer.
Transitional Flow – Transitional flows have some characteristics of laminar flow and some of turbulent flow. For example, dye may take some time to mix into the flow, but it does mix.
Movies of Laminar and Turbulent Flow: YouTube Fluid Dynamics Playlist
Image of rivers mixing: http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/L3/CostaRicaRiver.jpg
Images of glaciers: http://mygeologypage.ucdavis.edu/sumner/gel109/SedStructures/Lg/GlacierTrails.jpg
Is the flow in glaciers laminar or turbulent? How can you tell? What properties of ice make it behave differently than water in terms of the amount of turbulence?
Reynolds Number - The Reynolds number predicts the extent of turbulence in a fluid based on how fast the fluid is flowing, the geometry of the flow (how deep and wide it is, etc.), and the density and viscosity the of the fluid.
Back to the Reynolds number. The variables for the Reynolds number (Re) are: flow velocity (u), characteristic length (l) which represents flow geometry, say river depth, fluid density (ρ), and fluid viscosity (µ). The book uses µ/ρ = v (kinematic viscosity). Re = (fluid inertial forces)/(fluid viscous forces) = l*u*ρ/µ. The units for this equation are typically (length)*(length/time)*(mass/length3)/(mass/(length*time)). These all cancel out to form a unitless number, if you choose the same set of units for each variable, which you should always do.
Re can be viewed as inertial forces divided by viscous forces. Inertia is the resistance to change in motion, and inertial forces tend to make a bit of the fluid keep flowing in its own direction if it is misdirected from the main flow direction. Thus, high inertial forces tend to cause more turbulence. In contrast, viscous forces tend to suppress turbulence by damping out variations in motion through friction. Thus, a flow with a high viscosity (ice) tends to have less turbulence than a low viscosity flow (air).
The magnitude of Re gives an idea of whether the flow is turbulent or laminar. Turbulent flow has Re greater than 2000 and laminar flow has Re less than 500. Flow with Re between 500 and 2000 is transitional and has some characteristics of laminar flow, but some turbulence as well. In most cases, water and air flows have high Re because l is large, u is high and µ is low. Rivers and wind storms are good examples of turbulent flow. In contrast, ice has a high µ and flows slowly (u is low), so it is usually laminar. Also, very thin, slow flows of water, such as water flowing off a smooth cement parking lot, have low Re because l and u are small. Thus, it can be laminar. Laminar flow also occurs locally in turbulent flows right at the contact between the fluid and a smooth surface because u becomes very slow. This is really important for sediment transport, and we'll talk more about it in a few minutes.
It is useful to think about which variables are important for different comparisons. When comparing ice and water, the main difference is viscosity; the viscosity of ice ranges from about 103 kg/(m*s) up to more than 1020 kg/(m*s) depending on temperature. In contrast, the viscosity of water is ~10-3 kg/(m*s). The density of both is very close to 1000 kg/m3. Thus, ice is almost always laminar but water is usually turbulent, although it can be laminar. When considering water flows, the flow speed and water depth are both very important. The viscosity and density change a little bit with temperature, but variations in flow speed and water depth are typically much larger effects.
Images of glaciers:
high ice viscosity: http://tinyurl.com/yhyrob9
For air, both the density and viscosity are low, so does Re tend to be high or low? The density of dry air at 1 atm at 15°C is 1.225 kg/m3, and its viscosity is 1.8x10-5 kg/(m*s), giving an inverse “kinematic viscosity” of p/µ=6.8x105 s/m2 for air versus 1.0x106 s/m2 for water. Thus, air would have a slightly lower value for Re than water for the same flow depth and speed. However, the thickness of typical air flows (meters to 100’s of meters) promotes turbulence. p/µ for ice is 1 to 10-17 s/m2, which is why it is essentially always in a laminar flow regime.
Here is a video of a gust of wind that probably has a maximum u somewhere around 40 m/s: http://www.youtube.com/watch?v=iXlYEJaJ66A That’s me putting rocks on the fly of the tent. Note the turbulence and the snow transport.
Boundary Layer
There is boundary layer at the edge of every flow, and it is illustrated in the video above. Flows have an average speed in the middle, but friction with immobile surfaces slows down the speed of the flow right at the surface. This creates a boundary layer that has different flow characteristics than the rest of the flow. Right at the surface, the water does not move, but as you go higher into the flow it starts to move more like the average flow. The area of the flow that has a reduced speed is called the boundary layer. The thickness of the boundary layer depends on Re (i.e. the amount of turbulence) and the roughness of the surface the flow is moving past. If the main water flow is very turbulent, it changes the velocity distribution because more of the high speed water is mixed down into the lower speed areas. Thus, the boundary layer tends to be thin. In less turbulent flow, there is little mixing of water from the center of the flow toward the edge of the flow, so the boundary layer tends to be thicker.
Viscous/Laminar Sublayer - Within the boundary layer, right next to the surface, there is a laminar sublayer. Re=u*l*ρ/µ - remember this defines the difference between laminar and turbulent flow. Because u (water speed) is very low at the base of the boundary layer, the Re is low there and the flow is laminar. The laminar flow part of the boundary layer is called the viscous or laminar sublayer, “viscous” because the viscous properties of the fluid are more important than the inertial effects. The fluid is NOT more viscous here; rather, the inertia of the fluid is lower because u is lower, and the viscous properties dominate the behavior of the fluid. Farther up in the flow, u is higher, so the inertial properties of the flow dominate, and the flow is typically turbulent. If grains do not extend above the top of the laminar sublayer, they do not “see” much turbulence, and they are less likely to be transported. If they do stick up beyond the laminar sublayer because the laminar sublayer is thin or the grains are large, the grains feel the force of the turbulent flow.
Bed roughness or the characteristics of the surface also affect the boundary layer by affecting the amount of water that interacts with the surface. A very smooth bed, say one made of mud, does not deflect the water at all, so there is less mixing and less turbulence. There is a well developed laminar sublayer. In contrast, a bed with pebbles or boulders disrupts the direction of water flow in the boundary layer. The water gets deflected around the pebbles. Water from above tends to take its place. Since it is moving faster, the average water speed in the boundary layer increases. Thus, a rough bed reduces the thickness of the boundary layer much like a more turbulent flow does. A rough bed also disrupts the laminar sublayer by forcing the flow to move around objects. The laminar sublayer is developed locally, but in general, rough beds increase the amount of turbulence in a flow.
Sediments and Flow
Key Concept: The boundary layer strongly affects the amount of “Bed Shear Stress” which corresponds to the forces that tend to roll particles along the bed and the pressure differences above and below grains, which tend to lift them off the bed.
Bed Shear Stress - Sediments are affected by the difference in flow speeds from the bottom to the top of the boundary layer, gravity, and friction with the ground. Bed shear stress is a measure of these differences; it is the differential force that a grain feels from top to bottom. In a thick boundary layer, the speed of water flow at the top of the grains is not much different from the bottom, so bed shear stress is lower, and sediment is less likely to move. In a thin boundary layer, bed shear stress is much higher, and grains are likely to roll down flow. Thus, more turbulent flow (with a thinner boundary layer) results in more sediment transport. Bed shear stress increases with increasing fluid density, slope, and turbulence (water depth and flow speed). For example, water is better at moving sediment than air because it has a higher density and exerts a larger bed shear stress than air can. Deep, fast rivers move more sediment than shallow, slow rivers because of more turbulence and higher flow speeds in the boundary layer in fast rivers.
Next Time: The Bernouli Effect, which causes grains move, the Hjulstrom Diagram, and sediment transport. Read Chapter 4 again.
The Principle of Uniformitarianism – the processes that formed ancient deposits are the same as those that form modern deposits.
The Principle of Original Horizontality - strata (or sedimentary rock layers) are deposited in a nearly horizontal position. If they are no longer horizontal, later deformation much have changed their orientation.
The Law of Superposition - younger sediments overlie older sediments.
Walther’s Law
Key Concept: (Walther’s Law) Depositional environments vary in space and time such that “The facies [rock types] that occur conformably next to one another in a vertical section of rock will be the same as those found in laterally adjacent depositional environments” (Johannes Walther, 1894).
One of the most important implications of Walther’s Law is that rocks of the same type are not necessarily deposited at the same time. There is a BIG difference between correlating rocks based on having the same lithology and rock being deposited at the same time. This is a critical conceptual idea that we will focus on throughout the class.
Let’s look at an alluvial fan in Gale Crater, Mars: http://tinyurl.com/be39pmv
Where are there differences in environment laterally? If the fan grew through time, how would you predict the deposits to change vertically?
For more information on ancient stream flows on Mars, see:
http://mars.jpl.nasa.gov/msl/news/whatsnew/index.cfm?FuseAction=ShowNews&NewsID=1360
Summary of Walther’s Law: http://www.youtube.com/watch?v=ZSsULiPouTo
Sediment Transport
Most sediment transport is due to gravity. Things fall down hill in slumps, debris flows, and mudflows, and are transported downhill by fluids, like water, ice, and air. In some cases, processes like waves, currents, and wind transport sediment up a slope such as a beach or up mountain sides. This transport goes against gravity and is driven by the processes of fluid dynamics. Fluid dynamics is the main topic of today's and Monday’s lectures. We will come back to mass wasting processes when we talk about erosion. Mass wasting is important for transporting large volumes of sediment short distances, but fluid transport is required to move sediments long distances and is responsible for most sediment transport. To understand sediment transport, it is essential to understand the mechanics of fluid flow.
Fluid Flow
There are two end member ways fluids flow: 1) laminar flow and 2) turbulent flow. There is a wide gradation between these two end members, specifically "transitional" flows.
Laminar Flow - In laminar flow, water molecules move in straight, parallel lines down current. If you add a dye to water that is in the laminar flow regime, the dye would not mix into the water; it would streak out in an approximately straight line. Laminar flow is characteristic of very slow moving, shallow water, which is uncommon in nature. It is also characteristic of flows in "fluids" that are very viscous, like glacial ice or mud flows that have little water.
Turbulent Flow - In contrast, turbulent flow is characterized by complex motion of water (or other) molecules. Molecules move in all directions in bursts of upward, downward, and forward motion, and even some backward movement. There is abundant mixing in the flow because neighboring molecules move in different directions, and an added dye mixes into the water very quickly. Most water and air flows are turbulent, at least to some degree. Turbulence is important for sediment transport in water and air because it makes grains easier to transport and tends to keep them moving longer.
Transitional Flow – Transitional flows have some characteristics of laminar flow and some of turbulent flow. For example, dye may take some time to mix into the flow, but it does mix.
Movies of Laminar and Turbulent Flow: YouTube Fluid Dynamics Playlist
Image of rivers mixing: http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/L3/CostaRicaRiver.jpg
Images of glaciers: http://mygeologypage.ucdavis.edu/sumner/gel109/SedStructures/Lg/GlacierTrails.jpg
Is the flow in glaciers laminar or turbulent? How can you tell? What properties of ice make it behave differently than water in terms of the amount of turbulence?
Reynolds Number - The Reynolds number predicts the extent of turbulence in a fluid based on how fast the fluid is flowing, the geometry of the flow (how deep and wide it is, etc.), and the density and viscosity the of the fluid.
[Viscosity is a measure of the resistance of a material to flow, i.e. how “thick” and easily deformed it is. Viscosity is sort-of like the amount of friction within a substance. Walking through air is easy, because there is not much friction between air molecules. Air has a low viscosity. Swimming is more difficult because the water drags on your body. This is due to the “friction” between adjacent water molecules, i.e. higher viscosity. Ice is more viscous and impossible to move through because of the crystal bonds between the water molecules. It flows, but it does so slowly. It has a high viscosity relative to water and air (but low compared to most rock).]
Back to the Reynolds number. The variables for the Reynolds number (Re) are: flow velocity (u), characteristic length (l) which represents flow geometry, say river depth, fluid density (ρ), and fluid viscosity (µ). The book uses µ/ρ = v (kinematic viscosity). Re = (fluid inertial forces)/(fluid viscous forces) = l*u*ρ/µ. The units for this equation are typically (length)*(length/time)*(mass/length3)/(mass/(length*time)). These all cancel out to form a unitless number, if you choose the same set of units for each variable, which you should always do.
Re can be viewed as inertial forces divided by viscous forces. Inertia is the resistance to change in motion, and inertial forces tend to make a bit of the fluid keep flowing in its own direction if it is misdirected from the main flow direction. Thus, high inertial forces tend to cause more turbulence. In contrast, viscous forces tend to suppress turbulence by damping out variations in motion through friction. Thus, a flow with a high viscosity (ice) tends to have less turbulence than a low viscosity flow (air).
The magnitude of Re gives an idea of whether the flow is turbulent or laminar. Turbulent flow has Re greater than 2000 and laminar flow has Re less than 500. Flow with Re between 500 and 2000 is transitional and has some characteristics of laminar flow, but some turbulence as well. In most cases, water and air flows have high Re because l is large, u is high and µ is low. Rivers and wind storms are good examples of turbulent flow. In contrast, ice has a high µ and flows slowly (u is low), so it is usually laminar. Also, very thin, slow flows of water, such as water flowing off a smooth cement parking lot, have low Re because l and u are small. Thus, it can be laminar. Laminar flow also occurs locally in turbulent flows right at the contact between the fluid and a smooth surface because u becomes very slow. This is really important for sediment transport, and we'll talk more about it in a few minutes.
It is useful to think about which variables are important for different comparisons. When comparing ice and water, the main difference is viscosity; the viscosity of ice ranges from about 103 kg/(m*s) up to more than 1020 kg/(m*s) depending on temperature. In contrast, the viscosity of water is ~10-3 kg/(m*s). The density of both is very close to 1000 kg/m3. Thus, ice is almost always laminar but water is usually turbulent, although it can be laminar. When considering water flows, the flow speed and water depth are both very important. The viscosity and density change a little bit with temperature, but variations in flow speed and water depth are typically much larger effects.
Images of glaciers:
high ice viscosity: http://tinyurl.com/yhyrob9
For air, both the density and viscosity are low, so does Re tend to be high or low? The density of dry air at 1 atm at 15°C is 1.225 kg/m3, and its viscosity is 1.8x10-5 kg/(m*s), giving an inverse “kinematic viscosity” of p/µ=6.8x105 s/m2 for air versus 1.0x106 s/m2 for water. Thus, air would have a slightly lower value for Re than water for the same flow depth and speed. However, the thickness of typical air flows (meters to 100’s of meters) promotes turbulence. p/µ for ice is 1 to 10-17 s/m2, which is why it is essentially always in a laminar flow regime.
Here is a video of a gust of wind that probably has a maximum u somewhere around 40 m/s: http://www.youtube.com/watch?v=iXlYEJaJ66A That’s me putting rocks on the fly of the tent. Note the turbulence and the snow transport.
Boundary Layer
There is boundary layer at the edge of every flow, and it is illustrated in the video above. Flows have an average speed in the middle, but friction with immobile surfaces slows down the speed of the flow right at the surface. This creates a boundary layer that has different flow characteristics than the rest of the flow. Right at the surface, the water does not move, but as you go higher into the flow it starts to move more like the average flow. The area of the flow that has a reduced speed is called the boundary layer. The thickness of the boundary layer depends on Re (i.e. the amount of turbulence) and the roughness of the surface the flow is moving past. If the main water flow is very turbulent, it changes the velocity distribution because more of the high speed water is mixed down into the lower speed areas. Thus, the boundary layer tends to be thin. In less turbulent flow, there is little mixing of water from the center of the flow toward the edge of the flow, so the boundary layer tends to be thicker.
Viscous/Laminar Sublayer - Within the boundary layer, right next to the surface, there is a laminar sublayer. Re=u*l*ρ/µ - remember this defines the difference between laminar and turbulent flow. Because u (water speed) is very low at the base of the boundary layer, the Re is low there and the flow is laminar. The laminar flow part of the boundary layer is called the viscous or laminar sublayer, “viscous” because the viscous properties of the fluid are more important than the inertial effects. The fluid is NOT more viscous here; rather, the inertia of the fluid is lower because u is lower, and the viscous properties dominate the behavior of the fluid. Farther up in the flow, u is higher, so the inertial properties of the flow dominate, and the flow is typically turbulent. If grains do not extend above the top of the laminar sublayer, they do not “see” much turbulence, and they are less likely to be transported. If they do stick up beyond the laminar sublayer because the laminar sublayer is thin or the grains are large, the grains feel the force of the turbulent flow.
Bed roughness or the characteristics of the surface also affect the boundary layer by affecting the amount of water that interacts with the surface. A very smooth bed, say one made of mud, does not deflect the water at all, so there is less mixing and less turbulence. There is a well developed laminar sublayer. In contrast, a bed with pebbles or boulders disrupts the direction of water flow in the boundary layer. The water gets deflected around the pebbles. Water from above tends to take its place. Since it is moving faster, the average water speed in the boundary layer increases. Thus, a rough bed reduces the thickness of the boundary layer much like a more turbulent flow does. A rough bed also disrupts the laminar sublayer by forcing the flow to move around objects. The laminar sublayer is developed locally, but in general, rough beds increase the amount of turbulence in a flow.
Sediments and Flow
Key Concept: The boundary layer strongly affects the amount of “Bed Shear Stress” which corresponds to the forces that tend to roll particles along the bed and the pressure differences above and below grains, which tend to lift them off the bed.
Bed Shear Stress - Sediments are affected by the difference in flow speeds from the bottom to the top of the boundary layer, gravity, and friction with the ground. Bed shear stress is a measure of these differences; it is the differential force that a grain feels from top to bottom. In a thick boundary layer, the speed of water flow at the top of the grains is not much different from the bottom, so bed shear stress is lower, and sediment is less likely to move. In a thin boundary layer, bed shear stress is much higher, and grains are likely to roll down flow. Thus, more turbulent flow (with a thinner boundary layer) results in more sediment transport. Bed shear stress increases with increasing fluid density, slope, and turbulence (water depth and flow speed). For example, water is better at moving sediment than air because it has a higher density and exerts a larger bed shear stress than air can. Deep, fast rivers move more sediment than shallow, slow rivers because of more turbulence and higher flow speeds in the boundary layer in fast rivers.
Next Time: The Bernouli Effect, which causes grains move, the Hjulstrom Diagram, and sediment transport. Read Chapter 4 again.
Wednesday, January 18, 2012
Fluid Flow II
Lecture 3: Fluid Flow and Sediment Transport
Key Concepts from Lecture 2
Reynolds Number - Reynolds number predicts the extent of turbulence in a fluid based on how fast the fluid is flowing, the geometry of the flow (how deep and wide it is, etc.), and the density and viscosity the of the fluid. Re = (fluid inertial forces)/(fluid viscous forces) = l*u*r/µ where the variables are flow velocity (u), characteristic length (l) which represents flow geometry, say river depth, fluid density (r), and fluid viscosity (µ). Turbulent flow has Re is greater than 2000 and laminar flow has Re is less than 500. Flow with Re between 500 and 2000 is transitional and has some characteristics of laminar flow, but some turbulence as well.
Boundary Layer and Laminar Sublayer - There is boundary layer at the edge of every flow where flow speed decreases due to friction. Within the boundary layer, right next to the surface, the flow speed is very low, creating a laminar sublayer.
Sediment Transport
Bed Shear Stress: The boundary layer determines the amount of “Bed Shear Stress” which corresponds to the forces that tend to roll particles along the bed and the pressure differences above and below the grain which tend to lift them off the bed. Bed shear stress is related to the thickness of the laminar sublayer. The narrower it is, the more bed shear stress. It also depends on the slope. If the slope is steep, gravity helps pull grains down the slope, increasing bed shear stress. Also, the roughness of the bed is a factor. A rough bed deflects flows and increases turbulence, which increases the bed shear stress, particularly in places where flow is directed into the sediment and the boundary layer is compressed.
The Bernoulli Effect
A pressure difference “pulls” grains off the bed. The pressure difference comes from a difference in water (or air) speed above and below the grain. As water flows faster, there are fewer collisions between the water and a surface it flows over than there are between standing water and a similar surface. Pressure is due to collisions. Thus, fewer collisions means lower pressure. The upstream side of a grain experiences the most collisions because the water is flowing into it. The downstream side experiences the fewest collisions, and the sides of the grain experience fewer collisions where flow is faster and more where the flow is slower. The net result is a low pressure zone above and slightly downstream of a grain. If the force exerted by this pressure difference is larger than the force of gravity, the grain will lift off the bed. This lift due to the pressure difference is the Bernouli Effect.
Which Grains Move? Which grains get entrained in the flow depends on their size and density (how much they weigh) because that determines the force of gravity holding them down. It also depends on the shape of the grain. One with a large area to experience the low pressure (like a plate) will be more susceptible to being picked up than a round grain of the same mass (although flat grains may see a smaller flow difference from top to bottom if the boundary layer is thick, and flat grains may experience a lower Bernoulli Effect per unit area.) The other thing that really matters is a grain's position relative to surrounding grains. If a grain is sandwiched between larger grains, i.e. in their flow shadows, it will not experience as big a pressure difference. Also, if a grain is upstream of a big grain, it has to be lifted over it, so a larger pressure difference is needed. Thus, things can get complicated if you are trying to predict the behavior of a specific grain. However, we have some general guidelines based on experiments and theory that nicely predict how grains behave on average.
Bedload and Suspended Load Transport
Two things can happen once a grain is lifted into the flow: 1) it can fall back down or 2) it can stay there. It depends on how quickly the grain settles out versus how turbulent the water is (back to Re...). Bedload refers to the grains that are transported along the sedimentary bed, e.g. grains that are rolling and being lifted off the bed, but they fall back quickly. The name bedload comes from the fact that the grains moving by traction and saltation never get too far from the bed and “load” is an engineering term for the amount of sediment transported by a river. Rolling grains are in traction. Grains that are pulled off the bed with the Bernoulli effect but are large enough that gravity causes them to fall “quickly” back to the bed are said to be saltating. (The word saltating refers to the way salt from a salt shaker bounces when it is shaken onto a hard surface. The word is derived from a Latin word meaning dance.) Bedload grains are the ones that form sedimentary structures in flowing water.
Here is a playlist with movies related to sediment transport: Sumnerd’s Sed Transport Playlist and an extra movie at
http://faculty.gg.uwyo.edu/heller/SedMovs/bedload.htm (7.8 Mb)
Suspended sediment consists of grains that are light enough that they do not settle out of the water; the turbulent bursts of water keep them in the flow. The more turbulence in the water, e.g. the higher the Reynolds number, the larger the grains in suspension will be. The upward motions of turbulent flow are faster than the rate these grains settle, so gravity is counteracted and they stay “floating” in the water even though they are denser than the water. Very small grains do not settle out of flows unless the Reynolds number is low, which means that the flows need to be standing or very shallow.
Photo of suspended sediment in a Costa Rica River:
http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/L3/CostaRicaRiver.jpg
YouTube video of white clay in a turbulent flow in a flume: http://tinyurl.com/78kg3z The pulsing in the flow is (probably) due to the pump that is making the water flow.
Hjulstrom Diagrams
The flows that are required to pick up grains of certain sizes have been extensively studied in experiments and the results are plotted in Hjulstrom diagrams. Hjulstrom diagrams show grain entrainment on a plot of log grain size versus log flow speed. This diagram shows the areas where grains of different sizes are left on the bed, where they get moved sometimes (this is the gray zone), and where they get lifted up often and eroded away. Note that larger grains require higher flows - in general. The water speed that is required to transport a grain is call the critical velocity. This is important. If there is gravel in a sedimentary deposit, you can say that the water flow had to be above the critical threshold for it to get there! That might require a fast flowing river or strong wave action, thus, a large part of narrowing down the depositional environment has already been done!
A copy of the Hjulstrom Diagram from the book: http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/L3/Hjulstrom.jpg
Deeper flows can move larger grains at the same flow velocity because they are more turbulent: Re=u*l*r/µ and l is larger. This is because deeper flows can have larger variations in flow speed and the laminar flow layers are very thin. They can have bursts of very rapid flow relative to the average flow speed and these bursts can pick up larger grains. Actual flow characteristics are much more complex in detail than just Hjulstrom diagrams, which summarize a lot of characteristics into two axes. However, like a lot of people, we will use the diagram anyway, because it is very useful as a rule of thumb. Just remember that it is not a completely accurate representation of what will happen - it represents a reasonable guess.
Silt and Clay - Notice that for the small end of grain size, the speed of flow required for erosion actually increases. One reason small grains are hard to erode is that they tend not to stick up through the laminar sublayer; they are just too small. Thus, thinner boundary layers are necessary to roll them or for the pressure differences to pick them up off the bed. Also, the surfaces of clay minerals tend to be charged and the grains stick together. This is most obvious when big clumps of mud stick to your shoes. That just does not happen with sand (unless there is something gross in it). The stickiness of the clay grains makes them difficult to erode, so faster water flows (a greater pressure difference or larger turbulent burst down to the sediment surface) are required to move them. The smaller the grains, the more surface charges stick the grains together, thus the stronger the flow needed to erode them. The stickiness of the clay grains also depends on the amount of water between them and the mineralogy, so there is a big gray zone where a clay may or may not erode.
In the Hjulstrom diagram, there is an interesting area where the flow is not strong enough to move any of the particles on the bed, but those that are in the suspended load do not settle out either. This zone includes many of the waters on the surface of the earth. In flows with low velocity or that are very deep, Re is high enough to keep some clay in suspension. Clay deposition usually occurs very slowly, e.g. when the rate of settling is just slightly faster than the average rate at which turbulence moves clay particles upward or when the clays clump together to form larger grains (which is common when fresh and salty waters mix).
A few more words about saltation: Saltation is a very interesting and important process in sediment transport, because the force of the impact when the grains land tends to knock new grains up into the flow even if the flow is not fast enough to lift them with the Bernoulli Effect. These new grains can kick up more grains when they land, etc. This increases the rate of sediment transport above the amount the flow can lift grains off of the bed. This is one of the causes of the gray zone in the Hjulstrom diagram at larger grain sizes. Once saltation starts, it can trigger sediment transport that would not otherwise occur.
Watch grains transported by saltation and traction in these movies: http://faculty.gg.uwyo.edu/heller/SedMovs/Dietrich.htm (11 Mb)
http://faculty.gg.uwyo.edu/heller/SedMovs/sand_sheet.htm (14 Mb)
Deposition: Deposition is the accumulation of grains. If a flow starts slowly and gains speed, it will start to move larger and larger grains. As it slows down, it can only move the smaller ones. Deposition happens when a flow slows down and starts to leave grains on the bed. The combination of changing average flow speeds and local variations in flow speed caused by topography on the bed give rise to very informative sedimentary structures – including cross stratification - which are extremely useful for interpreting depositional environments.
Ripples and Other Bedforms
Structures form on the surface of a bed when topography influences the strength of the flow (and thus the strength of the Bernouli Effect). Erosion occurs where flow is strongest and directed into the bed. Deposition occurs where flow is slower. Deposition almost always creates laminae that are parallel to the depositional surface. Thus, laminae preserved in rocks reflect the shape of the ancient depositional surface. Small ripples have small laminae that dip downstream because that is where deposition occurs; flat beds have flat laminae; large dunes have coarser laminae that dip downstream.
Next Time: We will talk about the details about sedimentary structures. Homework is due on Monday.
Key Concepts from Lecture 2
Reynolds Number - Reynolds number predicts the extent of turbulence in a fluid based on how fast the fluid is flowing, the geometry of the flow (how deep and wide it is, etc.), and the density and viscosity the of the fluid. Re = (fluid inertial forces)/(fluid viscous forces) = l*u*r/µ where the variables are flow velocity (u), characteristic length (l) which represents flow geometry, say river depth, fluid density (r), and fluid viscosity (µ). Turbulent flow has Re is greater than 2000 and laminar flow has Re is less than 500. Flow with Re between 500 and 2000 is transitional and has some characteristics of laminar flow, but some turbulence as well.
Boundary Layer and Laminar Sublayer - There is boundary layer at the edge of every flow where flow speed decreases due to friction. Within the boundary layer, right next to the surface, the flow speed is very low, creating a laminar sublayer.
Sediment Transport
Bed Shear Stress: The boundary layer determines the amount of “Bed Shear Stress” which corresponds to the forces that tend to roll particles along the bed and the pressure differences above and below the grain which tend to lift them off the bed. Bed shear stress is related to the thickness of the laminar sublayer. The narrower it is, the more bed shear stress. It also depends on the slope. If the slope is steep, gravity helps pull grains down the slope, increasing bed shear stress. Also, the roughness of the bed is a factor. A rough bed deflects flows and increases turbulence, which increases the bed shear stress, particularly in places where flow is directed into the sediment and the boundary layer is compressed.
The Bernoulli Effect
A pressure difference “pulls” grains off the bed. The pressure difference comes from a difference in water (or air) speed above and below the grain. As water flows faster, there are fewer collisions between the water and a surface it flows over than there are between standing water and a similar surface. Pressure is due to collisions. Thus, fewer collisions means lower pressure. The upstream side of a grain experiences the most collisions because the water is flowing into it. The downstream side experiences the fewest collisions, and the sides of the grain experience fewer collisions where flow is faster and more where the flow is slower. The net result is a low pressure zone above and slightly downstream of a grain. If the force exerted by this pressure difference is larger than the force of gravity, the grain will lift off the bed. This lift due to the pressure difference is the Bernouli Effect.
Which Grains Move? Which grains get entrained in the flow depends on their size and density (how much they weigh) because that determines the force of gravity holding them down. It also depends on the shape of the grain. One with a large area to experience the low pressure (like a plate) will be more susceptible to being picked up than a round grain of the same mass (although flat grains may see a smaller flow difference from top to bottom if the boundary layer is thick, and flat grains may experience a lower Bernoulli Effect per unit area.) The other thing that really matters is a grain's position relative to surrounding grains. If a grain is sandwiched between larger grains, i.e. in their flow shadows, it will not experience as big a pressure difference. Also, if a grain is upstream of a big grain, it has to be lifted over it, so a larger pressure difference is needed. Thus, things can get complicated if you are trying to predict the behavior of a specific grain. However, we have some general guidelines based on experiments and theory that nicely predict how grains behave on average.
Bedload and Suspended Load Transport
Two things can happen once a grain is lifted into the flow: 1) it can fall back down or 2) it can stay there. It depends on how quickly the grain settles out versus how turbulent the water is (back to Re...). Bedload refers to the grains that are transported along the sedimentary bed, e.g. grains that are rolling and being lifted off the bed, but they fall back quickly. The name bedload comes from the fact that the grains moving by traction and saltation never get too far from the bed and “load” is an engineering term for the amount of sediment transported by a river. Rolling grains are in traction. Grains that are pulled off the bed with the Bernoulli effect but are large enough that gravity causes them to fall “quickly” back to the bed are said to be saltating. (The word saltating refers to the way salt from a salt shaker bounces when it is shaken onto a hard surface. The word is derived from a Latin word meaning dance.) Bedload grains are the ones that form sedimentary structures in flowing water.
Here is a playlist with movies related to sediment transport: Sumnerd’s Sed Transport Playlist and an extra movie at
http://faculty.gg.uwyo.edu/heller/SedMovs/bedload.htm (7.8 Mb)
Suspended sediment consists of grains that are light enough that they do not settle out of the water; the turbulent bursts of water keep them in the flow. The more turbulence in the water, e.g. the higher the Reynolds number, the larger the grains in suspension will be. The upward motions of turbulent flow are faster than the rate these grains settle, so gravity is counteracted and they stay “floating” in the water even though they are denser than the water. Very small grains do not settle out of flows unless the Reynolds number is low, which means that the flows need to be standing or very shallow.
Photo of suspended sediment in a Costa Rica River:
http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/L3/CostaRicaRiver.jpg
YouTube video of white clay in a turbulent flow in a flume: http://tinyurl.com/78kg3z The pulsing in the flow is (probably) due to the pump that is making the water flow.
Hjulstrom Diagrams
The flows that are required to pick up grains of certain sizes have been extensively studied in experiments and the results are plotted in Hjulstrom diagrams. Hjulstrom diagrams show grain entrainment on a plot of log grain size versus log flow speed. This diagram shows the areas where grains of different sizes are left on the bed, where they get moved sometimes (this is the gray zone), and where they get lifted up often and eroded away. Note that larger grains require higher flows - in general. The water speed that is required to transport a grain is call the critical velocity. This is important. If there is gravel in a sedimentary deposit, you can say that the water flow had to be above the critical threshold for it to get there! That might require a fast flowing river or strong wave action, thus, a large part of narrowing down the depositional environment has already been done!
A copy of the Hjulstrom Diagram from the book: http://mygeologypage.ucdavis.edu/sumner/gel109/Lectures/L3/Hjulstrom.jpg
Deeper flows can move larger grains at the same flow velocity because they are more turbulent: Re=u*l*r/µ and l is larger. This is because deeper flows can have larger variations in flow speed and the laminar flow layers are very thin. They can have bursts of very rapid flow relative to the average flow speed and these bursts can pick up larger grains. Actual flow characteristics are much more complex in detail than just Hjulstrom diagrams, which summarize a lot of characteristics into two axes. However, like a lot of people, we will use the diagram anyway, because it is very useful as a rule of thumb. Just remember that it is not a completely accurate representation of what will happen - it represents a reasonable guess.
Silt and Clay - Notice that for the small end of grain size, the speed of flow required for erosion actually increases. One reason small grains are hard to erode is that they tend not to stick up through the laminar sublayer; they are just too small. Thus, thinner boundary layers are necessary to roll them or for the pressure differences to pick them up off the bed. Also, the surfaces of clay minerals tend to be charged and the grains stick together. This is most obvious when big clumps of mud stick to your shoes. That just does not happen with sand (unless there is something gross in it). The stickiness of the clay grains makes them difficult to erode, so faster water flows (a greater pressure difference or larger turbulent burst down to the sediment surface) are required to move them. The smaller the grains, the more surface charges stick the grains together, thus the stronger the flow needed to erode them. The stickiness of the clay grains also depends on the amount of water between them and the mineralogy, so there is a big gray zone where a clay may or may not erode.
In the Hjulstrom diagram, there is an interesting area where the flow is not strong enough to move any of the particles on the bed, but those that are in the suspended load do not settle out either. This zone includes many of the waters on the surface of the earth. In flows with low velocity or that are very deep, Re is high enough to keep some clay in suspension. Clay deposition usually occurs very slowly, e.g. when the rate of settling is just slightly faster than the average rate at which turbulence moves clay particles upward or when the clays clump together to form larger grains (which is common when fresh and salty waters mix).
A few more words about saltation: Saltation is a very interesting and important process in sediment transport, because the force of the impact when the grains land tends to knock new grains up into the flow even if the flow is not fast enough to lift them with the Bernoulli Effect. These new grains can kick up more grains when they land, etc. This increases the rate of sediment transport above the amount the flow can lift grains off of the bed. This is one of the causes of the gray zone in the Hjulstrom diagram at larger grain sizes. Once saltation starts, it can trigger sediment transport that would not otherwise occur.
Watch grains transported by saltation and traction in these movies: http://faculty.gg.uwyo.edu/heller/SedMovs/Dietrich.htm (11 Mb)
http://faculty.gg.uwyo.edu/heller/SedMovs/sand_sheet.htm (14 Mb)
Deposition: Deposition is the accumulation of grains. If a flow starts slowly and gains speed, it will start to move larger and larger grains. As it slows down, it can only move the smaller ones. Deposition happens when a flow slows down and starts to leave grains on the bed. The combination of changing average flow speeds and local variations in flow speed caused by topography on the bed give rise to very informative sedimentary structures – including cross stratification - which are extremely useful for interpreting depositional environments.
Ripples and Other Bedforms
Structures form on the surface of a bed when topography influences the strength of the flow (and thus the strength of the Bernouli Effect). Erosion occurs where flow is strongest and directed into the bed. Deposition occurs where flow is slower. Deposition almost always creates laminae that are parallel to the depositional surface. Thus, laminae preserved in rocks reflect the shape of the ancient depositional surface. Small ripples have small laminae that dip downstream because that is where deposition occurs; flat beds have flat laminae; large dunes have coarser laminae that dip downstream.
Next Time: We will talk about the details about sedimentary structures. Homework is due on Monday.
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