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Vector identity

  1. Oct 20, 2009 #1
    1. The problem statement, all variables and given/known data

    Could someone please tell me how to expand:

    ∆ x [(u.∆)u]

    2. Relevant equations



    3. The attempt at a solution
    thankyou
     
  2. jcsd
  3. Oct 20, 2009 #2

    lanedance

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    Homework Helper

    do you mean nabla again, and i assume u is a vector? so
    [tex] \nabla \times ((u \bullet \nabla) u) [/tex]

    start first with finding the expression
    [tex] (u \bullet \nabla) u [/tex]

    i think for teh expression in the brackets, you consider it as an operator, so transforming to the subscript notation, where x_i is the ith coordinate, and we sum over repeated indicies to perform the dot product
    [tex] u \bullet \nabla = u_i \frac{\partial}{\partial x_i} = u_x \frac{\partial}{\partial x} + u_y \frac{\partial}{\partial y} + u_z \frac{\partial}{\partial z} [/tex]
     
    Last edited: Oct 20, 2009
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