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

Info iconThis preview shows pages 1–3. Sign up to view the full content.

View Full Document Right Arrow Icon
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
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Area = Probability () { } , uux t u u ≤< + ± ( ) ;, Puxt u ± Properties of random variables f , constant a , averaging is a linear operator.
Background image of page 2
Image of page 3
This is the end of the preview. Sign up to access the rest of the document.

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.

Page1 / 4

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

This preview shows document pages 1 - 3. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online