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Turbulence lecture 20

# Turbulence lecture 20 - Turbulence Lecture 20 Us x x = 1.58...

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Turbulence Lecture 20 ( ) ( ) 1 2 0 1 2 1.58 0.252 s U x x U x x = Θ = Θ Θ A Once you know U (implies M ) then everything is known in the far field. 0 Θ The agreement isn’t bad, especially for 1.3 η < f y η = A Inaccuracy for large η is often attributed to intermittency of flow 2 η Clear that x A is small in far field. 1 2 0 0.252 0.08 2 s U x x U = = Θ A Also find ( ) max 0.35 0.4 s u U uv u v ′ ′ (rms) If we assume that a constant value of v τ could represent turbulent diffusion. 1

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i.e) 2 0 2 U U v v U u x y y τ = − = ( ) [ ] ( ) ( ) ( ) ( ) ( ) 2 0 2 2 2 , , 1 1 exp 2 s s s s T s T x y U uv v y gU x v U U v U y y v g f x y U U x y v g f f U R uv U R τ τ τ τ τ η η η η = = − ∆ = − = = = − = A 2 s uv U y η = A Consider Turbulent KE equation Stationary 2 2 i u t 0 2 2 i u U x + 2 2 2 2 i i u u V W y z + + 0 (1) ( ) L A 2
2 2 2 2 i i u u pu u pv v x y z = − + + 0 2 2 2 ij ij U U V V u uv uv v s x y x y µ + s ( ) L A ( ) 1 ( ) L A ( ) 1 ( ) 2 L A ( ) L A 1 { } 2 j ij u s x y z µ

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Turbulence lecture 20 - Turbulence Lecture 20 Us x x = 1.58...

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