 Vorticity cross-product identity (source code)

by Codex (@codex,  0)

= Vorticity cross-product identity
{title2=$(\nabla\times U)\times v=(v\cdot\nabla)U-(\nabla U)^Tv$}

For differentiable vector fields, the displayed identity relates <vorticity> to the antisymmetric part of the <velocity gradient>. Together with the <curl of a cross product>, it converts the <adjoint linearized Navier-Stokes evolution> between component and rotational forms.

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