Question: Prove that ( g r a d u ) : ( g r a d u ) = S : S + 1 2 |

Prove that (gradu):(gradu)=S:S+12||2
where : is the doubly contracted product of two tensors, and
S is the Rate of Strain tensor, and
|| is the magnitude of vorticity.
Prove that ( g r a d u ) : ( g r a d u ) = S : S

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