The convective acceleration (u ⋅ ∇) u can be thought of as the advection operator u ⋅ ∇ acting on the velocity field u. This contrasts with the expression in terms of tensor derivative ∇ u, which is the component-wise derivative of the velocity vector defined by [∇ u ] mi = ∂ m v i, so that [ u ⋅ ⋅ ( ∇ ∇ u ) ] i = ∑ ∑ m v m ∂ ∂ m v i = [ ( u ⋅ ⋅ ∇ ∇ ) u ] i .