Civil Engineering Reference
In-Depth Information
We can easily develop a spatial version of VITA, which
can be applied to data gleaned from DNS at fixed times .
The variable-interval space averaging (VISA) technique with
acceleration of time (deceleration in the streamwise
direction) is expressed thus by Kim [KIM 85]
t
=
t
0
2
L
⎛
L
⎞
v
v
x
+
x
+
2
2
1
⎜
1
⎟
(
)
(
)
(
)
∫
2
∫
[3.8]
σ
x yzt
,,;
=
u xyzt dx
,,;
−
u xyzt dx
,,;
⎜
⎟
VS
0
0
0
L
L
⎜
⎟
L
L
V
V
v
v
x
−
x
−
⎝
⎠
2
2
where the detection function is
⎧
∂
u
(
)
()
1, if
σ
xyzt
,
, ;
>
H uu y
, and
<
0
⎪
VS
0
VS
[3.9]
Dx
()
=
∂
x
⎨
⎪
⎩
0, else.
Figure 3.14.
Four possible scenarios linked to the events detected by VITA.
The shear layers caused in cases 2V1 (bottom left) and 2V4 (bottom right)
are predominant. This figure is adapted from [SPI 91]
The conditional averages are found in the usual way, but
this time in the spatial rather than temporal dimension.
Thus, the conditional means obtained can be linked to the
temporal means by way of Taylor's hypothesis. Figure 3.15
shows the conditional averages of streamwise vorticity in
the plane at the point of detection , obtained in a
turbulent channel flow with a low Reynolds number by
ω
xc
(
y
,
z
)
x
=
0
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