= Barotropic vorticity transport
{title2=$\partial_t\boldsymbol\omega=\nabla\times(\mathbf u\times\boldsymbol\omega)$}
For an inviscid <barotropic fluid> with only potential body forces, the <vorticity> $\boldsymbol\omega=\nabla\times\mathbf u$ obeys
$$
\partial_t\boldsymbol\omega=\nabla\times(\mathbf u\times\boldsymbol\omega).
$$
The pressure force is a <gradient> because $\rho^{-1}\nabla p=\nabla\int^\rho p'(s)\,ds/s$. A spatially uniform <specific entropy> makes a fixed-composition fluid barotropic. Merely having $Ds/Dt=0$ does not exclude <baroclinic vorticity generation> from spatial entropy gradients.
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