Curl of a cross product
= Curl of a cross product
{title2=$\nabla\times(U\times v)=U\nabla\cdot v-v\nabla\cdot U+(v\cdot\nabla)U-(U\cdot\nabla)v$}
The displayed <vector calculus> identity follows by contracting the two alternating tensors in the component formula for <curl>. If both fields have zero <divergence>, only the two directional derivatives remain. It rewrites the transport terms in the <adjoint linearized Navier-Stokes evolution>.