Regeneration and Self-Maintaining of Coherent Structures - Transport and Coherent Structures in Wall Turbulence - page 301

linear superposition of the events. For example, the
conditional average of the unsteady component given by
equation [5.33] is

+∞ +∞ ∞

1 1 1

⎛ ⎞

( )

[5.42]

∫ ∫ ∫

v =− dx dz Q ξ ,, y z dy

RR

−

⎜ ⎟ tr 1 1 n n 1 1 1

4 π '

⎝ ⎠

−∞ −∞ 0

The key problem is the modeling of the nonlinear forcing
( )

. [LAN 90] supposes that the nonlinearity is
essentially caused by an inflectional instability mechanism,
and combines the classic theories of linear hydrodynamical
stability and wave kinematics. Skewness in the plane x

n Qy

ξ ,, z

11

− z

( )

is also assumed, by way of , so as to represent

the sinuous nature of the streaks near the wall. 9
Figure 5.14(a) shows one of the typical results obtained by
Landahl [LAN 90], corresponding to an asymmetrical initial
disturbance. The stretching of the local contours, and the
oscillating nature of the streaks, are clearly visible in this
figure. These results are qualitatively similar to the
experimental observations and the DNS results. Thus, the
conditional averages obtained by DNS and VISA detection
are surprisingly close to those deduced using the model given
in [LAN 90] (Figure 5.14 . (b)).

n Qy

ξ ,, z

11

The model advanced in [LAN 90] can be interpreted as a
modern, elaborate version of the pioneering Prandtl mixing
length model. We can also see a strong resemblance between
the mechanism proposed by Landahl and that of bypass
transition. The process proposed for regeneration of the
streaks is essentially linear. Nonlinearity is imposed by the
forcing

( )

, which is a key element and is
therefore crucial to choose wisely. However, the idea of
exploiting the highly intermittent nature of the velocity at

n Qy

ξ ,, z

11

9 According to the model, those structures which are initially symmetrical
remain so indefinitely.