= Inertial-wave vorticity equation
{title2=$\partial_t(\nabla\times\mathbf u)=2(\boldsymbol\Omega\cdot\nabla)\mathbf u$}
Linearize the <Euler equation in a uniformly rotating frame> about rest and impose <incompressible flow>, $\nabla\cdot\mathbf u=0$. Taking the <curl> eliminates the reduced <pressure>. For constant $\boldsymbol\Omega$, $\nabla\times(\boldsymbol\Omega\times\mathbf u)=-(\boldsymbol\Omega\cdot\nabla)\mathbf u$, giving the displayed <vorticity> equation. Taking another curl and time derivative yields $\partial_t^2\nabla^2\mathbf u+4(\boldsymbol\Omega\cdot\nabla)^2\mathbf u=0$. These equations describe the restoring influence of background rotation on small disturbances without buoyancy or viscosity.
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