Eady edge wave

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 $c{\varphi }^{\prime }(0)+\Lambda \varphi (0)=0$. 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. MIT's Eady-edge-wave notes develop this boundary-wave interpretation.

For a semi-infinite stratified fluid with thermal wind $U=\Lambda z$ above a gently sloping boundary $z=\alpha y$, a zero-interior-potential vorticity perturbation decays as $e^{-\mu z}$, where $\mu =N|k|/|f_0|$. The boundary buoyancy perturbation obeys a single oscillatory equation with phase velocity $c=(\Lambda -\alpha N^2/f_0)/\mu$. The topographic and thermal-wind contributions cancel when the boundary follows a background isopycnal.