A question about vortex stretching

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 February 18, 2012, 07:51 A question about vortex stretching #1 New Member   H.S.Tan Join Date: Feb 2012 Posts: 5 Rep Power: 7 Dw/Dt = w.grad u, w= curl(u) where does w.grad u come from?

 February 18, 2012, 17:52 #2 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 3,638 Rep Power: 41 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 likes this.

February 18, 2012, 22:43
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H.S.Tan
Join Date: Feb 2012
Posts: 5
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Quote:
 Originally Posted by FMDenaro 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]?

 February 19, 2012, 06:08 #4 Senior Member   Filippo Maria Denaro Join Date: Jul 2010 Posts: 3,638 Rep Power: 41 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 kobe likes this.

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