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z
, deduced from the POD
analysis with five modes independent of
x
, presented in [AUB 88]. Time
progression is represented first top to bottom, and then left to right
Figure 4.35.
Velocity field in the plane
y
−
Aubry
et al.
[AUB 88] analyzed a severely truncated
system, with only five modes in the spanwise direction. The
analysis covered the very first modes of the dynamic flow
induced by the quasi-streamwise structures in the
plane
y
,
z
, but did not take into account the mechanism of
regeneration of QSVs, because the dependence in direction
x
is omitted. The authors [AUB 88] showed that the dynamical
system resulting from these approximations has a stable
fixed point when it is highly dissipative. The effect of
pressure fluctuations at the boundaries of the truncated
domain is neglected in this study. This fixed point
corresponds to the streamwise rollers. The least diffusive
system becomes intermittent with the appearance of a
bifurcation between a stable fixed point and an unstable
node point. The mechanism observed is classic in
the dynamical systems theory. The solution - which, it
should be remembered, is independent of
x
and is reproduced
by a limited number of modes - stays for a long time around
a fixed point, then oscillates with an amplitude that
increases over time, and “jumps” intermittently at the
unstable saddle point. Figure 4.35 shows that this severe
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