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Let $\mathbf{\omega }=\nabla \times \mathbf{u}$ be the vorticity. In component notation, contracting two Levi-Civita symbols givesThe first term is ${\partial }_i(|\mathbf{u}{|}^2/2)$ and the second is the $i$th component of the convective acceleration. Rearranging proves the velocity identity

In steady flow, the velocity and other relevant flow fields are independent of time in the chosen reference frame. Streamlines then coincide with the paths of moving particles, while convective acceleration can still be nonzero.