 Eady model with parallel sloping boundaries

When both rigid boundaries of a constant-shear Eady model have the same small slope $\alpha$, define $a=N^2\alpha /(f_0\Lambda )-1$, $M=N|k|D/|f_0|$ and $C=c/(\Lambda D)$. Zero-interior-PV modes have vertical structure $A\cosh (Mz/D)+B\sinh (Mz/D)$. The boundary conditions $(z/D-C){\hat{\psi }}_{z/D}+a\hat{\psi }=0$ at both endpoints give the displayed dispersion relation. For $a\ge 0$ its square root is real and there is no exponential baroclinic instability. The same-sign boundary-pseudomomentum criterion is necessary, not sufficient.