Transport Phenomena in Wall Turbulence - Transport and Coherent Structures in Wall Turbulence - page 126

Let us first consider Figure 2.2 9, which shows the
evolution of the structural parameter

uv 2 K as a function of −

, o n the basis of data taken from [MAX 82]. We can see that α

uv 2 K first increases in an almost linear fashion with
increasing strain, then reaches a local maximum bef ore
beginning to fall off. Figure 2.30 shows the profiles

−

uv 2 K −

stemming from the closure k -

with and w it hout viscous
damping near to the wall. The maximum

ω

uv 2 K attained
corresponds, in both cases, to the response of an
axisymmetrical

−

turbulence whose initial anisotropy

parameter is s

1.2 (Figure 2.29). The strain is null at the
center of a channel, and increases as we approach the wall. A
correspondence can thus be establi sh ed by determining the
distribution

=

()

uv 2 K at a given position
y + with the results found by the RDT. The effective
strain

+

, which links

α y −

eff

()

+ is qualitatively linked to the distortion of an
initially homogeneous and axisymmetrical turbulence whose
evolution was halted by the nonlinearity and which,
therefore, led to an equilibrium distribution.

α y

eff

Figure 2.30. Profile of Reynolds shear stress generated by the closure
k

Re = 440 . The solid line corresponds to the
profile obtained without taking viscous damping into account; the crosses
indicate the results arising from standard k

in a channel where

− ω

τ

with viscous damping.
This figure is adapted from [TAR 05]

− ω