Civil Engineering Reference
In-Depth Information
sublayer. These interactions will be analyzed in Chapter 6.
The development of reduced-dimension dynamical system
models is certainly interesting for the understanding and
modeling of wall turbulence. However, we cannot content
ourselves with the first modes which are most energetic. We
also need to take account of certain significant modes which
then propagate in the streamwise direction in order to reveal
the mechanisms of regeneration of the coherent structures
(which, as previously discussed in detail, is very closely
linked to the dependencies in direction
x
). Figure 4.36, which
is adapted from [ALF 10], shows the type of modes which
propagate in the streamwise direction. These authors
decomposed the fields obtained by DNS in a channel flow at
Re
180
. Figure 4.36 shows the contours of
u
emanating
from the first four modes of the decomposition [4.69] with
m
,
n
,
q
τ
=
(
)
=
()
. We
can see “bean”-shaped structures extending toward the
center of the channel. The role of this type of structures and
their dynamic importance in the mechanism of regeneration
of the QSVs have yet to be clarified.
1,1,1
and averaged over time for
T
+
=
1,800
4.11.3.
Chaotic synchronization
Chaotic synchronization is a process in which coupled
systems subjected to an external force adjust their
timescales to give us a common spatiotemporal dynamic
[BOC 02]. Synchronization can also be defined as the locking
of the instantaneous phase of a variable of state of the
system and the phase of a periodic external force. There are
various sorts of synchronization, such as identical
synchronization, phase synchronization or generalized
synchronization [BOC 02].
Let us begin by giving a simple example of phase
synchronization between two coupled Rösller oscillators
[ROS 96]. The system is defined by
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