Transcript Turbulent Boundary Layers

(Mostly Turbulent) Boundary
Layers
Vertical structure in flows
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!
So what develops at low Re ?
A viscous, laminar boundary layer
But higher and(or) faster?
When you consider a thicker region
of the bottom or when the flow gets faster
rul
Re = m
Things get turbulent.
?
How about in a pipe, aka
Poiseuille flow?
Laminar flow
profile
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
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
A summary BBL diagram
Log(arithmic) Layer
u
Log z
z0
u*
z
u=
ln z + u’
k
0
Why is this line dashed?
What does this intercept mean?
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)

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
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?
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

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
