Civil Engineering Reference
In-Depth Information
Chaotic phase synchronization results from the
adjustment of the timescales when the chaotic trajectories
enter the different unstable orbits. Phase synchronization
coincides with a saddle-point-node bifurcation, and is
characterized by a type-I intermittence [BOC 02]. In t
he
case
of perfect phase synchronization, the mean time
T
l
, or
similarly the spatial occupation of the constant phase
regions
, is governed by a relation such as
Θ
C
ps
−γ
T
l
∝
C
−
In the above relation,
C
corresponds to the coupling
intensity, or to the frequency (the wavenumber) of the signal
driving the system. The parameter
C
ps
corresponds to the
maximum coupling. It is natural to identify
C
by
k
, and
C
ps
by
k
*
in our case. The intermittence is “on/off” if
1
, and is
γ =
type-I when
1 / 2
. The synchronization of the wall
turbulence has type-I intermittence, as shown in
Figure 4.40.
γ =
Figure 4.40.
Mean occupation of constant phase zones as a function of the
wavenumber. Open symbols: DNS at
Re
180
and
y
+
=
20
. Closed
τ
=
symbols: experiments at
y
+
=
10
and
Re
913
. This figure is adapted
θ
=
from [TAR 10c]
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