Transport Phenomena in Wall Turbulence - Transport and Coherent Structures in Wall Turbulence - page 103

to the nonlinear terms, which cont rol the rapid comp onent
[KIM 89]. Of the six groups

( )( )

, the

∂∂ ∂ ∂ ux u x

i j j i

∂ v

∂ z ∂

w
∂

contribution is dominant and is typically four times

y

greater than the other terms. This correlation reaches a peak
value at y + =

20 . Note that the intensity of the streamwise
vorticity component is

2 2

2

( ) ( ) ( ) ∂ w ( )

ω = ∂ w ∂ y + ∂ v ∂ z − 2 ∂ v ∂ z ∂ y

x

Thus, Kim [KIM 89] suggested that ∂

v

z ∂

w
∂

would also be

∂ y

maximal at the centers of the quasi-streamwise vortices,
which are located mainly in the median zone of the buffer
sublayer. 15

Figure 2.20. Distribution of the slow and rapid terms and the Stokes
component in the pressure fluctuations in inner variables in a fully
turbulent channel flow at Re = 180 , according to [KIM 89]

τ

15 The local maximum of the norm of the vorticity vector need not
necessarily be an ideal criterion for detecting structures, as we will show
in Chapter 3.