Turbulence lecture 9

Turbulence lecture 9 - Turbulence Lecture 9 If the process has too much memory(long correlation time scales then the time average doesn't give

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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.

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Turbulence lecture 9 - Turbulence Lecture 9 If the process has too much memory(long correlation time scales then the time average doesn't give

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