Coherent Wall Structures: Dynamics and Contribution to Turbulent Activity - Transport and Coherent Structures in Wall Turbulence - page 252

decelerations of the fluid particles under the influence of the
pressure gradient and viscosity.

Figure 4. 31. T he distribution in t he inner lay er of the terms in eq uation
[4.54] . a: u b v a

( )

; b: gradient term v a ; c: Θ

1 ; d:

Θ

2 ; e: uv . This

U a − U b

figure is adapted from [BER 90a]

Figure 4.31, adapted from Bernard and Handler
[BER 90a], shows the distribution of the different terms
making up equation [4.54]. To begin wit h, we can see that
the contribution made by the term u b v a is negligible. The
gradient-driven transport term plays a predominant role,
but, at the same time, Θ 1 and Θ 2 are significant in the buffer

sublayer.

Bernard and Handler [BER 90a] propose a model based
on the probability densi ty of move ment of the particles for
the gradient correlation

( )

. Consider the probability

vU U −

a b a

() Δ r that a fluid particle will arrive at a point y out of all
the points in its vicinity r

p y r

r 2 during the time t *

. For

()

− y <Δ

y

all of these particles, U b

() − U y ()

and

− U a = U r

ry − ry −

() ()

v ∝− =−

ty γ

r

()

a * *

ty