Turbulence lecture 10

Turbulence lecture 10 - Turbulence Lecture 10 Mean Flow...

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Turbulence Lecture 10 Mean Flow Dynamics Start with N-S equations Make Reynolds decomposition Totals Tennekes & Lumley Notation \ ii i uUu TTT pPp ρ ρρ =+    ± ± ± ± Imcompressible flow, no body forces not variable density. 4 equations, 4 unknowns becomes 1. () [] 2 j j i ji j j Uu Pp S s tx x µ ∂∂ x ++ + += + 2 i u ij S is deformation rate tensor 1 2 1 2 j i ij j i ij U U S x x u u s xx    2. 0 jj j x Continuity Average (ensemble or time) the momentum equation 1

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3. 2 iji i j i ji j P UU U S u u tx x x ρρ µ ρ ∂∂ j += +− Average Continuity 4. 0 0 i ii U xx =→ = i u By subtracting 4 from 2 Note i jj uu u = j u i=1 is x -momentum equation ˆ ij j uuvuwu u u uu uv uw i u u u v u w x xyz y yzz uvw u  ∂ ∂ =+ + = + + + + +    ∂∂∂ ++   = 0 j uu u uvwuu xy z x ∂∂ ∂ +++ = ∂∂ ∂ ∂
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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 10 - Turbulence Lecture 10 Mean Flow...

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