= Resonant topographic quasi-geostrophic wave
A stationary boundary corrugation can resonate with a <Rossby wave> whose intrinsic propagation cancels the background current. For constant $N$, rigid upper height $H$, and $m=\pi/H$, define $\kappa^2=k^2+\ell^2+f_0^2m^2/N^2$. When $U=\beta/\kappa^2$, a lower corrugation proportional to $e^{ikx}\sin(\ell y)$ admits a disturbance proportional to $e^{ikx}\sin(\ell y)[Bt\cos(mz)+C(z-H)\sin(mz)]$, with $B=2ikf_0U^2/\beta$ and $C=N^2/(f_0m)$. Its <wave activity> grows quadratically with time while the upward <Eliassen–Palm flux> grows linearly. The linear prediction applies only while the disturbance remains small.
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