 Step-trapped topographic Rossby wave

A depth discontinuity between two constant-depth rotating layers supports an exponentially trapped Rossby wave. Continuity of surface height and cross-step volume flux gives $\omega (H_{+}{\kappa }_{+}+H_{-}{\kappa }_{-})=fk(H_{+}-H_{-})$, where ${\kappa }_{\pm }^2=k^2+(f^2-{\omega }^2)/(g{H}_{\pm })$ and positive roots give decay. For $H_{\pm }=H_0\pm d$ with $|d|\ll H_0$, the low-frequency branch has $\omega \simeq (fd/H_0)k/\sqrt{k^2+R_D^{-2}}$. In the Northern Hemisphere it propagates with the shallow side on its right.