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I Order of Operations for Tensors

  1. Nov 3, 2016 #1
    Hey so probably a really simple question, but I'm stumped. How do you simplify:

    ν∇⋅(ρν), where
    ν is a vector
    ∇ is the "del operator"
    ⋅ indicates a dot product
    ρ is a constant.

    I want to say to do the dyadic product of v and ∇, but then you would get (v_x)*(d/dx) + .... which would be meaningless, so I'm thinking you do the dot product first, but I can't find an order of operations for algebra involving tensors of any order (except zero order of course).

    Thanks in advance.
     
  2. jcsd
  3. Nov 3, 2016 #2

    TeethWhitener

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    It's kind of like a product rule for vector calculus:
    $$\nabla \cdot (\rho \vec{\nu}) = \rho \nabla \cdot \vec{\nu} + \vec{\nu} \cdot \nabla \rho$$
    gives you a scalar. ##\vec{\nu} \nabla \cdot (\rho \vec{\nu}) ## just multiplies the vector ##\vec{\nu}## by that scalar.
     
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