= Eady edge wave
{c}
For a semi-infinite fluid above a rigid horizontal boundary, constant <buoyancy frequency> $N$, and <thermal wind> $U=\Lambda z$, a zero-interior-<potential vorticity> perturbation has vertical dependence $e^{-\mu z}$, where $\mu=NK/|f_0|$ and $K=(k^2+l^2)^{1/2}$. Material conservation of boundary buoyancy gives $c\phi'(0)+\Lambda\phi(0)=0$. Thus its <phase velocity> relative to the boundary flow is $c=\Lambda/\mu$. The wave's time dependence resides in its boundary condition; the interior field follows by potential-vorticity inversion. https://ocw.mit.edu/courses/12-803-quasi-balanced-circulations-in-oceans-and-atmospheres-fall-2009/d6bf75cb60b05018230aefa5c315584d_MIT12_803F09_lec12.pdf[MIT's Eady-edge-wave notes] develop this boundary-wave interpretation.
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