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Turbulence lecture 9 - Turbulence Lecture 9 If the process...

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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. ( ; P u ) , , , x y z t = ( ; P u ) , , , x y z t ζ + = ( ; P u ) , , x z t ( 1 2 , ; P u u ) 1 2 , , , , x y y z t = ( 1 2 , ; P u u ) 2 1 , , , x y y z t We can define correlations, integral scales, microscales, ergodic theorem, and etc. for homogeneous statistics.
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