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A question about vortex stretching

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Old   February 18, 2012, 07:51
Default A question about vortex stretching
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H.S.Tan
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Dw/Dt = w.grad u, w= curl(u)
where does w.grad u come from?
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Old   February 18, 2012, 17:52
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Filippo Maria Denaro
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you just have to take curl of each term of the momentum equation, then the curl of the non linear term produces one of the parts which is the stretching term. You just need to work carefully on curl [div (vv)]
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Old   February 18, 2012, 22:43
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Quote:
Originally Posted by FMDenaro View Post
you just have to take curl of each term of the momentum equation, then the curl of the non linear term produces one of the parts which is the stretching term. You just need to work carefully on curl [div (vv)]
thank you, I got it with your help! but,is there something wrong with your "curl [div (vv)]"? should it be curl [(curl v)\times v]?
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Old   February 19, 2012, 06:08
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if div v=0, div (vv) = v.div v = grad (|v|^2/2) + (curl v) ^ v

then curl [(curl v) ^ v], owing to a well known tensor identity, opens in further terms, one of those is the stretching term
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