Vector Calculus Identity proof?

  • #1
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Main Question or Discussion Point

The following identity is found in a book on Turbulence:

upload_2016-6-15_19-33-17.png


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

Thanks
 

Answers and Replies

  • #3
Charles Link
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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.)
 
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