Polar gamma-plane Rossby wave
= Polar gamma-plane Rossby wave
Near a north pole, $f=2\Omega-\gamma r^2/2$ with $\gamma=2\Omega/a^2$. If a <quasi-geostrophic streamfunction> satisfies $\nabla_h^2\psi-\psi/L_d^2=-\alpha^2\psi$, then $Q=f-\alpha^2\psi$. Its nonlinear self-advection cancels because $J(\psi,\psi)=0$, leaving $-\alpha^2\psi_t+\gamma\psi_\phi=0$. An azimuthal mode $\cos(\omega t-n\phi)$ therefore has $\omega=-n\gamma/\alpha^2$ at any amplitude consistent with the underlying balanced model.