1. (Mostly Turbulent) Boundary Layers
Vertical structure in flows

2. The No-Slip Condition u Flow over a flat plate What happens
to velocity right
here at the plate?
The layer of liquid molecules right on the surface does not move!

3. So what develops at low Re ?
A viscous, laminar boundary layer

4. But higher and(or) faster?
When you consider a thicker region
of the bottom or when the flow gets faster
Re =
r u l m
Things get turbulent. ?

5. 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
Physical Fluid Dynamics. Van
Nostrand Reinhold, NY. p. 277
Laminar flow
profile

6. Vertical Structure of a Bottom Boundary Layer
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

7. A summary BBL diagram

8. Log(arithmic) Layer u Log z u* z u = ln + u’ k z0
Why is this line dashed? z0
What does this intercept mean?

9. 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)

10. Possible regimes for a flat seabed (grain roughness only)
P.A. Jumars &
A.R.M. Nowell.
1984. Fluid and
sediment dynamic
effects on marine
benthic community
structure. Am. Zool.
24: 45-55

11. Data for sand tracked by an epifaunal bivalve
Nowell, A.R.M., P.A. Jumars
and J.E. Eckman Effects
of biological activity on the
entrainment of marine
sediments. Mar. Geol.
42:
Notice that velocities
are all shifted lower
after tracking. Why?

12. 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

13. Boundary layers Form with flow over any object
Thinner than flat-plate formulas for convex surfaces
Thicker than flat-plate formulas for concave surfaces, but watch for reattachment points