= Decaying vertical structure of a semi-infinite Eady edge wave
{title2=$\widehat\psi=C e^{-mz},\quad m=NK/|f_0|$}
A smooth zero-interior-<potential vorticity> mode has
$$
\widehat\psi''-m^2\widehat\psi=0,\qquad m=NK/|f_0|,\qquad K=\sqrt{k^2+l^2}.
$$
Decay for $z\to\infty$ gives $\widehat\psi=C e^{-mz}$. Its penetration depth $1/m$ increases with horizontal wavelength and decreases with <buoyancy frequency>. Singular neutral interior sheets are a distinct continuous-spectrum class.
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