= Step-trapped topographic Rossby wave
{title2=$\omega=\dfrac{f k(H_+-H_-)}{H_+\kappa_++H_-\kappa_-}$}
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 $\kappa_\pm^2=k^2+(f^2-\omega^2)/(gH_\pm)$ 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.
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