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Turbulence
Lecture 9
If the process has too much memory (long correlation time scales) then the time average doesn’t
give independent samples and will not converge.
Statistical Homogeneity
A random process is statistically homogeneous if its statistical properties are invariant under
arbitrary transtations in space.
Analagous to statistically stationary.
E.g]
B.L. over a flat plate.
JJG
0
U
Statistical properties don’t change in
y
direction.
Expect statistically homogeneous in
y
, not homogeneous in
x
or
z
directions.
(
;
Pu
)
,,,
xyzt
=
(
;
)
,,
,
x
yz
t
ζ
+=
(
;
)
xzt
(
12
,;
Pu u
)
,
xyyz
t
=
(
)
21
,
x
yy
z
t
−
We can define correlations, integral scales, microscales, ergodic theorem, and etc. for
homogeneous statistics.
Isotropic Turbulence – the turbulence has no preferred direction (not close to a boundary, not
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This note was uploaded on 06/07/2011 for the course EGM 6341 taught by Professor Mei during the Spring '09 term at University of Florida.
 Spring '09
 MEI

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