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 kobe February 18, 2012 07:51

A question about vortex stretching

Dw/Dt = w.grad u, w= curl(u)
where does w.grad u come from?

 FMDenaro February 18, 2012 17:52

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)]

 kobe February 18, 2012 22:43

Quote:
 Originally Posted by FMDenaro (Post 345143) 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) v]?

 FMDenaro February 19, 2012 06:08

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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