= Convective acceleration identity
{title2=$(\mathbf u\cdot\nabla)\mathbf u=\nabla(|\mathbf u|^2/2)-\mathbf u\times\boldsymbol\omega$}
The local vector-calculus identity
$$
(\mathbf u\cdot\nabla)\mathbf u=\nabla(\tfrac12|\mathbf u|^2)-\mathbf u\times(\nabla\times\mathbf u)
$$
separates the convective <acceleration> into a kinetic-energy gradient and a <vorticity> cross-product contribution. Substitution into the steady <Euler equations for an inviscid fluid> yields the vorticity form of the <Bernoulli equation>.
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