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Unformatted text preview: Turbulence Lecture 15 The K Model Relate v to , K v 2 K units 4 2 3 u m Lu u s L 2 3 j i i j ij j i U U u u K v x x = + + (Discussion of will follow later) First have to consider turbulent energetics. We previously derived an equation for the energetics of the mean flow. Want an equation for the turbulent energy 1 2 i j K u u = i i i u U u = + i Derive an equation for u by subtracting equation for U from equation for i i i i u i ( ) i i u U t t = + i u i .... 2 i i i i j i j i j i j j j i u U u t t t u p U u u U u u t x x x x x = + + + + = + ij j s Result: equation for fluctuations Coupling with mean flow non-linear Then take the inner product with u and average: contract on i ....
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- Spring '09