= Forced Eady edge wave
{title2=$\dot A+i\omega A=C e^{-i\omega_0t}$}
With uniform <thermal wind> $U=\Lambda z$ above a plane boundary, write the zero-interior-<potential vorticity> response as $\psi'=\operatorname{Re}\{Ae^{-\mu z+i(kx+ly)}\}$, where $\mu=N\sqrt{k^2+l^2}/f$ and $f>0$. Boundary vertical <velocity> $\epsilon\cos(kx+ly-\omega_0t)$ gives $C=N^2\epsilon/(f\mu)$ and natural <angular frequency> $\omega=\Lambda k/\mu$. An initially zero response has $A=C(e^{-i\omega_0t}-e^{-i\omega t})/[i(\omega-\omega_0)]$. Its continuous resonant limit is $Ct e^{-i\omega t}$: forcing in phase with the boundary mode supplies <energy> every cycle, and linear undamped theory predicts secular growth.
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