Shear Stress, Shear Velocity, and Turbulence
Shear within flow creates turbulent eddies.
Learning Goals
- Know that (and why) turbulence exists across a range of scales bounded by viscous dampening (smallest eddies) and the size of the container holding the flow (e.g., a river channel)
- Be able to visualize how shear within fluids drives the formation of eddies (and at least imagine how this could cause erosion or sediment transport when exerted on the bed of a river)
- Understand the depth–slope product for basal shear stress and how it is derived.
- Know the definition of the shear velocity and understand its importance in scaling turbulent intensity and its relationship to flow velocity.
Scales of turbulence
Turbulence exists at many scales in a river.
- The smallest eddies are at what we call the “Kolmogorov scale” – the length scale at which viscous dampening removes eddies from the flow. Fluid viscosity prevents eddies smaller than this from forming.
- The largest eddies exist at the distance across the flow. When considering vertical mixing, as we do when considering velocitgy and shear stress in natural rivers, this is typically the flow depth. There is not enough space available for larger eddies to form.
If we think of eddies as approximately circular, then they have a diameter and we can state that:
Kolmogorov scale < eddy diameter < flow depth
All of these scales of turbulence respond to shear within the flow, and they all in turn affect the flow velocity profile by mixing fluid up and down in the stream.
When watching this video, try to think about what scales you see by following the neuturally buoyant white tracer particles. You might want to watch more than once to train your eye to pick up both small and large whirls in the flow:
Shear driving turbulent intensity
Next, I want you to rewatch this video from the previous lecture. This time, the video will start at the comparison between the scenarios with pay special attention to how fast the top plate moves in the cases with the lower and higher Reynolds numbers.
The plate for the higher Reynolds number – and therefore more turbulent – flow was moving faster. This plate was shearing across the surface of the flow. Therefore, we know that there must be a relationship between velocities of layers in the flow, shear stress, and turbulence.
Deriving basal shear stress and defining shear velocity
Here, I go through scales of turbulence, continue on to derive shear stress (and show the importance of the steady-flow assumption), and then define shear velocity.
Course notes
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