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? Re =  u l u l  Things get turbulent. When you consider a thicker region of the bottom or when the flow gets faster ?

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. 1977. Physical Fluid Dynamics. Van Nostrand Reinhold, NY. p. 277 Note change in du/dz.

6. Vertical Structure of a Bottom Boundary Layer Outer flow ( u = u inf ) Outer flow ( u = u inf ) Top of the bottom boundary layer ( u = 0.99 u inf ) Top of the bottom boundary layer ( u = 0.99 u inf ) Log layer (plot of u vs log z is linear) Log layer (plot of u vs log z is linear) Viscous sublayer (momentum) Viscous sublayer (momentum) Diffusive sublayer (mass) Diffusive sublayer (mass) u z

7. Vertical Structure of a Bottom Boundary Layer Mann and Lazier (1996)

8. Vertical Structure of a Bottom Boundary Layer Middleton and Southard (1984)

9. A summary BBL diagram

10. Log(arithmic) Layer Ln z u Ln(z 0 ) u = u*u*  ln z z0z0 +u’ Why is this line dashed? What does this intercept mean? u*u* 

11. Log(arithmic) Layer d-”zero-plane displacement”. z 0 -roughness length-adjusts the steepness of the velocity profile For rough bottoms:

12. What is u * ? Dimensions? L T -1, a velocity Dimensions? L T -1, a velocity Name? Shear velocity (“u star”) Name? Shear velocity (“u star”) Significance? It and the roughness height ( z 0 ), tell you a lot about the structure of the bottom boundary layer Significance? It and the roughness height ( z 0 ), tell you a lot about the structure of the bottom boundary layer Utility? Also is a “shear stress in disguise” as u * = Sqrt (  0 /  Utility? Also is a “shear stress in disguise” as u * = Sqrt (  0 / 

13. 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:

14. 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?

15. Other bits of information One velocity is not enough to characterize flow in a boundary layer One velocity is not enough to characterize flow in a boundary layer At a minimum, you need hydraulic roughness ( z 0 ) and one (shear) velocity or velocities at two heights in the log layer At a minimum, you need hydraulic roughness ( z 0 ) and one (shear) velocity or velocities at two heights in the log layer A good “roughness” Re * for bottom boundary layers = (  u * z 0 )/  A good “roughness” Re * for bottom boundary layers = (  u * z 0 )/ 

16. Boundary layers n Form with flow over any object n Complicated by the topography of the bottom n Despite turbulence have well characterized ‘mean’ properties