Coherent Wall Structures: Dynamics and Contribution to Turbulent Activity - Transport and Coherent Structures in Wall Turbulence - page 254

h
∫

1

( ) γ () ()

0 v a =− r − y r p y r dr =

()

t * y

0

Figure 4.32 illustrates the distribution of the function
F y r

for different positions y + , according to [BER 90a]. Note
the non-lo cal nature of the Reynolds shear stress, in that
v a U b

()

at a given y + depends on a broad spatial domain,
by way of F y r

( )

− U a

()

.

Figure 4.32. Distribution of the function F y from
equation [4.60], according to [BER 90a]. The values of y +
are 3.8 a); 7.3 b); 12.0 c); 17.8 d); 24.6 e); and 36.6 f).

The trajectories of the particles beginning or ending in a
given plane y + can be determined with no major difficulty
[BER 89, BER 90a]. Calculation of the trajectories of the
specific events by dividing them into quadrants, and study of
the trajectories of the particularly intense ejections and
sweeps, provide us with invaluable information about the
dynamics of the Reynolds shear stress.