Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

B Vector Calculus Identity proof?

  1. Jun 15, 2016 #1
    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
     
  2. jcsd
  3. Jun 15, 2016 #2

    RUber

    User Avatar
    Homework Helper

  4. Jun 15, 2016 #3

    Charles Link

    User Avatar
    Homework Helper

    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.)
     
    Last edited: Jun 15, 2016
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?
Draft saved Draft deleted



Similar Discussions: Vector Calculus Identity proof?
Loading...