Homework Help: Vector identity

1. Oct 20, 2009

Fairy111

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. Oct 20, 2009

lanedance

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

start first with finding the expression
$$(u \bullet \nabla) u$$

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
$$u \bullet \nabla = u_i \frac{\partial}{\partial x_i} = u_x \frac{\partial}{\partial x} + u_y \frac{\partial}{\partial y} + u_z \frac{\partial}{\partial z}$$

Last edited: Oct 20, 2009