Order of Operations for Tensors

[echandler]

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.

 

[TeethWhitener]

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.