= Eady model with parallel sloping boundaries
{c}
{title2=$C=\tfrac12\pm\sqrt{\tfrac14+a\coth M/M+a^2/M^2}$}
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> $(z/D-C)\widehat\psi_{z/D}+a\widehat\psi=0$ at both endpoints give the displayed <dispersion relation>. For $a\ge0$ its square root is real and there is no exponential <baroclinic instability>. The same-sign boundary-pseudomomentum criterion is necessary, not sufficient.
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