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Vector calculus

  1. Oct 18, 2009 #1
    1. The problem statement, all variables and given/known data
    For a fluid flow of velocity u and vorticity w=∆ x u, show that:

    (u. ∆ )u=-u x w + ∆(1/2|u|²)

    Sorry the triangles should be the other way up!

    2. Relevant equations

    ∆(u.v)=(u.∆)v + (v.∆)u +u x (∆ x v) + v x (∆ x u )

    3. The attempt at a solution
    I need to show this using subscipt notation, but am really stuck, any help?
  2. jcsd
  3. Oct 18, 2009 #2


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    Homework Helper

    here's how you write it correctly in tex - click it on the tex to see the expression
    [tex] (u \cdot \nabla )u=-u \times w + \nabla (\frac{1}{2}|u|^2) [/tex]

    i would start by trying to expanding one of the expressions in your equation, use the equations and product rule expansions

    by subscript notation do you mean like:
    [tex] \textbf{u} \cdot \textbf{w} = u_i v_i [/tex]

    [tex] \textbf{u} \times \textbf{w} = u_i v_j \epsilon_{ijk} [/tex]
    Last edited: Oct 19, 2009
  4. Oct 18, 2009 #3
    I don't know how to expand the expression....Sorry im really not very good at this area of maths.

    but yes that is what i mean by subscript notation.
  5. Oct 19, 2009 #4


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    Homework Helper

    have a crack, i'm not just going to do it for you - how about starting with u x w?
    Last edited: Oct 19, 2009
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