This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Turbulence Lecture 8 If the dependence on x is suppressed, and let u = , assume stationarity. Then ( ) ( ) ( ) ( ) ( ) 2 u t u t u t + = = . This is the auto correlation coefficient (normalized autocovariance). ( ) ( ) = only depends on . From above, CauchySchwartz inequality ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1 2 2 2 1 2 1 2 2 1, 1 u t u t u t u t u t u t u t = + = Nondimensional We can now define a power spectral density. ( ) ( ) ( ) ( ) 1 2 i i S e S e d d = = A Fourier Transform pair Now simpler, since ( ) is real and symmetric. Complex Conjugate ( ) ( ) ( ) * 1 2 i S e d S = = Since ( ) is an even function 1 ( ) ( ) ( ) ( ) ( ) * 1 1 2 2 i i S e d e d S S = = = = ( ) ( ) * , is real , is symmetric...
View
Full
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.
 Spring '09
 MEI

Click to edit the document details