= Quasi-geostrophic wave at a stratification interface
Two vertically unbounded regions with <buoyancy frequencies> $N_1,N_2$ and <thermal wind> shears $\Lambda_1,\Lambda_2$ support a localized wave if pressure and normal velocity are continuous at their common material interface. With decays $\phi_1=Ae^{\mu_1z}$ below and $\phi_2=Ae^{-\mu_2z}$ above, $\mu_j=N_jK/|f_0|$, matching gives
$$
c-U_I=\frac{\Lambda_2/N_2^2-\Lambda_1/N_1^2}{\mu_1/N_1^2+\mu_2/N_2^2}.
$$
When $N_1/N_2\to\infty$ with bounded shear, the lower layer becomes effectively rigid and the upper-layer <Eady edge wave> speed $\Lambda_2/\mu_2$ is recovered.
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