Large- and Very Large-scale Structures - Transport and Coherent Structures in Wall Turbulence - page 410

and O u , in which case the effect of the triple correlation
arising from the modulation is relatively insignificant.
These arguments are valid in the inner sublayer. Indeed, the
effect of the large- and very large-scale structures in the
outer layer may be significant, as we will see in the next
section.

These trains of thought certainly need to be compared
against the simultaneous measurements of u and v , which
are painstaking and difficult at large Reynolds numbers.
DNS at large Re
τ

can also be a great help, but at present
they are still costly to perform. A simple argument in the
same vein as the discussion given in the previous section is
based on the behavior of the Reynolds shear stress via Re τ .

We have briefly discussed this behavior in Chapter 1,
pointing out that the maximum of uv + − in the inner layer is

expressed by

⎛ ⎞
−

uv 2

∝ 1 − , for Re ∞

⎜ ⎟
⎝ ⎠

τ

2

u

κ Re τ

τ

max

The sensitivity of the distribution of the Reynolds shear
stress to the Reynolds number is significantly less than the
streamwise turbulent intensity, the maximum of which is
affected considerably more by by way of Re

τ

( )

( )

2

. The role played by the correlations

uu u ∝ ln Re

τ τ

max

++ + , which come into play in equation
[6.8], therefore, is probably negligible in relation to the
similar terms in relation [6.7], if only in the inner layer.

++

and

*

− α O uv β uvu

OM

6.8. Dynamic role of very large-scale motions

The characteristic length scale of the structures, which
contribute to the fluctuations in wall-normal velocity, is