(Mostly Turbulent) Boundary Layers

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(Mostly Turbulent) Boundary Layers

• Vertical structure in flows

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The No-Slip Condition
Flow over a flat plate
u
What happens to velocity right here at the plate?
The layer of liquid molecules right on the
surface does not move!
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So what develops at low Re ?
A viscous, laminar boundary layer
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But higher and(or) faster?
When you consider a thicker region of the bottom
or when the flow gets faster
Things get turbulent.
?
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How about in a pipe, aka Poiseuille flow?
Comparison of laminar (i) and turbulent (ii)
velocity profiles in a pipe for (a) the same mean
velocity and (b) the same driving force (pressure
difference). Figure 22.16 from Tritton, D.J.
1977. Physical Fluid Dynamics. Van Nostrand
Reinhold, NY. p. 277
Note change in du/dz.
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Vertical Structure of a Bottom Boundary Layer
u

• Outer flow (u uinf)
• Top of the bottom boundary layer (u 0.99 uinf)
• Log layer (plot of u vs log z is linear)
• Viscous sublayer (momentum)
• Diffusive sublayer (mass)

z
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Vertical Structure of a Bottom Boundary Layer
Mann and Lazier (1996)
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Vertical Structure of a Bottom Boundary Layer
Middleton and Southard (1984)
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A summary BBL diagram
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Log(arithmic) Layer
u
Ln z
u
z
u
ln

u
k
z0
u
Why is this line dashed?
Ln(z0)
k
What does this intercept mean?
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Log(arithmic) Layer
For rough bottoms
d-zero-plane displacement. z0-roughness
length-adjusts the steepness of the velocity
profile
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What is u?

• Dimensions? L T-1, a velocity
• Name? Shear velocity (u star)
• Significance? It and the roughness height (z0),
  tell you a lot about the structure of the bottom
  boundary layer
• Utility? Also is a shear stress in disguise as
  u Sqrt (t0/r)

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Possible regimes for a flat seabed (grain
roughness only)
Jumars Nowell. 1984. Am. Zool. 24 45-55
VSL-laminar velocity/stress relation.
DSL-unstirred layer adjacent to a layer
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Data for sand tracked by an epifaunal bivalve
Nowell, A.R.M., P.A. Jumars and J.E. Eckman.
1981. Effects of biological activity on
the entrainment of marine sediments. Mar.
Geol. 42 155-172.
Notice that velocities are all shifted
lower after tracking. Why?
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Other bits of information

• One velocity is not enough to characterize flow
  in a boundary layer
• At a minimum, you need hydraulic roughness (z0)
  and one (shear) velocity or velocities at two
  heights in the log layer
• A good roughness Re for bottom boundary layers
  (r u z0)/m

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Boundary layers

• Form with flow over any object
• Complicated by the topography of the bottom
• Despite turbulence have well characterized mean
  properties