Turbulence lecture 16

# Turbulence lecture 16 - Turbulence Lecture 16 Vorticity...

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Turbulence Lecture 16 Vorticity Equation N N 2 uu v t ω ωω +∇= ∇+∇ ±± ± ± ± ± ii ± ²³³´ ³³µ / / / Time derivative Vortex Viscous following fluid tube diffusion element turning & stretching If a fluid element initially has no vorticity, then 0 u = ±± i initially, it can only gain vorticity by diffusion. U Entrainment: process by which a turbulent flow grows into a non-turbulent irrotational flow. j I j I j I ji j i j j j us x =+ i j r can easily show j I 0 j r = I I I j I I 2 2 ij i j i j jj v tx x i ∂∂ += + I iii =Ω+ mean and fluctuating Plug-in and average closure problem for 2 circled terms / N N 2 2 i j i i j Uu S s v xx x ∂∂∂ Ω+ Ω=− +Ω + + ∂∂ ∂ ²³³´³³ µ² ³´ ³ ³´³µ i j / / / \ \ time derivative following turbulent turning production molecular mean flow. diffusion and by turning diffusion of ω i . stretching and of mean due to stretching. Vorticity. mean flow. 1

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This is the Mean Vorticity Equation i 2 1 2 i ω - enstrophy Subtract equation for from that for i i i , gives equation for i .
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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 16 - Turbulence Lecture 16 Vorticity...

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