Turbulence lecture 5-B

# Turbulence lecture - Turbulence Lecture 5-B If we have some function of u say G u x t 4 e.g G u = u,sin u G u x t = G(u P(u x t du The most

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Turbulence Lecture 5-B If we have some function of , say u ( ) , Guxt ± e.g. Gu () 4 ,sin u u = , =   ± G ;, uPuxtd u ± The most common (popular) probability distribution function that occurs in turbulence studies is the Gaussian (normal) p.d.f. 1 2 Puxt πσ = ± exp 2 2 2 uu σ  −−    , x t = - Mean, average, expectation ± 1 2 2 , xt u u σσ == ± - Standard deviation 2 - variance u is the center measures the width. Note that if the process is known to be Gaussian distributed, u & completely define the statistical properties of the random variable ( ) , uxt ± for fixed , x t ± . In turbulence the velocity field is approximately a Gaussian random variable. An important theorem – the Central Limit Theorem- says many random variables are Gaussian. 1

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Area = Probability () { } , uux t u u ≤< + ± ( ) ;, Puxt u ± Properties of random variables f , constant a , averaging is a linear operator.
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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 - Turbulence Lecture 5-B If we have some function of u say G u x t 4 e.g G u = u,sin u G u x t = G(u P(u x t du The most

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