Decaying vertical structure of a semi-infinite Eady edge wave ($\hat{\psi }=C{e}^{-mz},m=NK/|f_0|$)

A smooth zero-interior-potential vorticity mode hasDecay for $z\to \infty$ gives $\hat{\psi }=C{e}^{-mz}$. Its penetration depth $1/m$ increases with horizontal wavelength and decreases with buoyancy frequency. Singular neutral interior sheets are a distinct continuous-spectrum class.