Regeneration and Self-Maintaining of Coherent Structures - Transport and Coherent Structures in Wall Turbulence - page 297

a) b)

Figure 5.13. Instantaneous streamlines in the plane of symmetry y-x at the
time when the separation takes place (t=5.67 in this particular case) for a
structure with the parameters indicated in the text, (a) at z=0 and (b) at
z=1. This figure is adapted from [ATI 04]

5.4. Generation of streaks and inner shear layers:
simplified theoretical models

The regeneration of the structures and of the high- and
low-velocity streaks associated therewith is a phenomenon
which is intermittent in terms of time and space. Landahl
[LAN 90] developed a simple model whereby nonlinear
activity acts locally in space over short periods of time, and
gives the initial conditions for the linear, non-viscous
evolution of the initial disturbance. 7 His analysis, which
yields a satisfactory description of the regeneration of
streaky wall structures, is based on the transport equation
for the instantaneous wall-normal velocity which, after
manipulation of the Navier-Stokes equations and
elimination of the pressure, can be expressed as

2 2

Dv ∇ ∂∂ v U 4

[5.26]

− − ∇ ν vq =

2

Dt ∂∂ x y

7 The model resembles the rapid distortion theory (RDT) [TOW 76], but is
different in nature in that it takes account of intermittent nonlinearity,
whereas the RDT overlooks it and can only yield a steady-state solution.