= Group velocity and polarization of an inertial wave
{title2=$\mathbf v_g=\sigma(2\Omega/k)(\widehat{\mathbf z}-k_\parallel\mathbf k/k^2)$}
For $\omega=\sigma2\Omega k_\parallel/k$, differentiating the <dispersion relation> gives the displayed <group velocity>. It is perpendicular to the <wavevector>. If $|k_\parallel|\ll k_\perp$, <energy> propagates almost along the rotation axis while the <phase velocity> is almost horizontal. In an orthonormal basis $\mathbf e_1,\mathbf e_2$ normal to $\mathbf k$, with $\mathbf e_2=\widehat{\mathbf k}\times\mathbf e_1$, the complex <velocity> is $A(\mathbf e_1-\sigma i\mathbf e_2)$ and its real oscillation is circular. In the anisotropic limit the vertical and transverse-horizontal <velocity> amplitudes are comparable, while the horizontal component parallel to $\mathbf k_\perp$ is smaller by $|k_\parallel|/k_\perp$.
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