Absence of exponential instability in the semi-infinite Eady model

A growing complex phase speed cannot equal the real basic velocity. The linear interior potential-vorticity equation then forces zero anomaly everywhere, decay fixes one exponential, and the wall fixes the real speed $c=\Lambda /m$. Thus there is no growing smooth decaying edge-wave eigenmode. This excludes exponential normal-mode instability without claiming that every initial disturbance lacks transient amplification or a singular neutral component.