Regeneration and Self-Maintaining of Coherent Structures - Transport and Coherent Structures in Wall Turbulence - page 364

Figure 5.43. Bypass of the “streak instability” part of the regeneration
cycle in the mechanism proposed by Tardu et al. [TAR 08a]

The part of the classic cycle analyzed above and
illustrated in Figure 5.43 involving regeneration by streak
instability is no longer entirely necessary. Thus, this part is
short-circuited by a bypass-type mechanism.

The suggested mechanism is based on a proposition made
in [TAR 95a]. Figure 5.44 shows a spanwise plane containing
two CRVPs A and B . Remember that a quasi-streamwise
vortex gives rise to high- and low-velocity streaks against the
wall,

respectively, corresponding to the ejections

( ). The joining of the

high- and low-velocity streaks induces a spanwise gradient of
the streamwise velocity

, ) and sweeps ( ,

u < 0 v > 0 u > 0 v < 0

in a near-wall zone. However,
this gradient is one of the components of the wall-normal
vorticity

∂∂ uz

. Therefore, the streaks are
delimited by thin layers of vorticity

ω =∂ uz wx ∂ − ∂ ∂

y

, directly beneath the
vortex, as stated many times in this chapter [JIM 91,
JIM 94]. The sign of

ω

y

is positive if the direction of rotation
of the mother structure

ω

y

is positive, and vice versa . The
signs of the layers of vorticity engendered by the structures

ω

x