General Points - Transport and Coherent Structures in Wall Turbulence - page 36

Figure 1.15. Distributions of the maximum value of the Reynolds stress in
external (boundary layer) flows. This figure is adapted from [FER 96]. The
estimation is based on relation [1.49]. See [TAR 11b] for further detail

Approaches based on the spectral behaviors and the
effects of the attached structures found by Townsend
[TOW 76] are in agreement, yieldi ng the logarithmic
distributions of the intensities uu and ww in the constant
stress sublayer. Readers are invited to consult Chapters 3
and 4 of [TAR 11a] and [TAR 11b] for the details and the
many references related to these aspects. In summary, the
turbulent intensities in the fully turbulent zone are
expressed as:

uu y

()

y

+

=− A ln + B

uu uu

2

u
vv

Λ

τ 0

()

+

[1.51]

y B =

vv

2

u
ww

τ

y

()

+

y =− A ln + B

2 ww ww

u Λ

τ 0