Phase of a resonantly forced topographic edge wave (${\psi }_t^{\prime }=ikϵN^2{U}_0{e}^{-Kz}\cos (\ell y)e^{ikx}/(Kf)$)

For constant stratification and $U=U_0+\Lambda z$, a decaying zero-interior-PV mode has vertical structure $e^{-Kz}$. Its topographic boundary condition gives $A^{\prime }+ik(U_0+\Lambda /K)A=ikϵN^2{U}_0/(Kf)$. Resonance requires $K{U}_0+\Lambda =0$ and nonzero forcing $kϵU_0$. With zero initial disturbance, $A$ grows linearly and is imaginary relative to cosine topography. Its meridional velocity is therefore opposite in phase to the relief for positive $f,U_0,ϵ$. A zero zonal wavenumber or zero boundary current removes the forcing and invalidates an unconditional claim of secular growth.