Turbulence lecture 19

# Turbulence lecture 19 - Turbulence Lecture 19 Wake Scaling...

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Turbulence Lecture 19 Wake Scaling Similarity () ( ) max , sy Ux y =∆ \ y () , , s Uxy f xy = 0 U s U y x A Usually similarity occurs when there is just one length and one velocity scale. , s y f x  =   A Flows like this are called self similar or self preserving. Reynolds stress is also self similar. 2 s uv y g x = A 1

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How to determine & f g functions Consider {} s U UU xx x ∂∂ =− ∆=− f 2 ss y Uf Uf ′′ + A A product and chain rules y + A AA Let () y x η = A ,, xy x + A A Plugging into x -momentum equation from above, 0 U Uu v x y with 2 1 s uv U x g y A gives 2 0 0 s g fU f U  −+ + =   A multiply through by 2 s U A . N N N N 00 2 s x x U gU f ηη    A A ±²³ / / x terms must be constant to get similar solution. 1 2 , s s U C U = A 2 s C U = A Reduced a PDE in ( x,y ) to an ODE in n m s x x Ux x A assumptions 1 1 2 mn m x x C x == const 0 x = 12 mnm −+ − = 0 2
1 mn =− Other coefficient gives same result.

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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 19 - Turbulence Lecture 19 Wake Scaling...

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