# B Vector Calculus Identity proof?

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1. Jun 15, 2016

### FluidStu

The following identity is found in a book on Turbulence:

Can someone provide a proof of this identity? It isn't listed in the list of vector calculus identities on Wiki.

Thanks

2. Jun 15, 2016

### RUber

3. Jun 15, 2016

Apparently $\omega$ is defined as $\omega=\nabla \times u$. This one is actually a variation of a well-known E&M vector identity (i.e. a vector calculus identity used quite often in E&M coursework): $\nabla (a \cdot b)=a \cdot \nabla b +b \cdot \nabla a + \ a \times \nabla \times b + \ b \times \nabla \times a$ $\$ where $a=b=u$. (This one is found on the cover of J.D. Jackson's E&M textbook as well as other E&M textbooks.)