Expanding Vector Identity: ∆ x [(u.∆)u]

[Fairy111]

Homework Statement

Could someone please tell me how to expand:

∆ x [(u.∆)u]

Homework Equations

3. The Attempt at a Solution
thankyou

 

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