Civil Engineering Reference
In-Depth Information
Readers can easily verify that the equation governing the
local streamwise velocity
(
)
uyzt
then becomes linear and is
reduced to a simple transport equation for a passive scalar,
with
,;
∂
u
∂
u
∂
u
⎛
∂
2
u
∂
2
u
⎞
[5.47]
+
v
+
w
=
ν
+
⎜
⎟
2
2
∂
t
∂
y
∂
z
∂
y
∂
z
⎝
⎠
because
for a Couette flow. The streamwise
structures reform streaks identical to those obtained by
complete simulation. However, the reformed streaks are
completely different when we consider the modes
∂∂=
px
0
uk yk
(,,)
x
z
with
, which rather tends to support the hypothesis
whereby the vortices independent of
x
are essentially
responsible for the formation of the streaky structure of wall
turbulence. It should once again be stressed that a
dependency in direction
x
is essential for the regeneration of
the vortex structures, which, once they are established, are
stretched in the streamwise direction, induce a flow that is
generally independent of
x
in their close vicinity and
generate streaks.
k
≠
0
x
5.6. Regeneration of vortex structures. Observations
deduced from direct numerical simulations
In this section, we present qualitative observations based
on DNS, in particular those reported by Brooke and
Hanratty [BRO 93], who agree with Berkooz
et al.
[BER 93b]
on various points. [BRO 93] use visualizations to analyze a
DNS database at
+
==
in a fully developed turbulent
channel flow.
They describe a series of events leading to the
generation of “baby” structures from a generating “mother”
vortex. This image-rich terminology offers a good depiction of
the process of regeneration, and will therefore be adopted
from here onward.
Re
h
150
τ
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