A question about vortex stretching
 

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

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]?

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