On the Non-Existence of Critical Wavelengths in a Continuous Baroclinic Stability Problem

The baroclinic stability problem relating to a Couette west-wind profile over a flat topography and extending to infinite height on the rotating earth is treated in the β-plane formulation, as presented by Charney and Kuo. It is shown by analytical methods that the concept of a critical wavelength, separating unstable from neutral waves, is not applicable in this case, and that, with the exception of a finite number of isolated wavelengths, all wavelengths have an exponentially unstable mode associated with them, together with no or a finite number of neutral regular modes. A limiting procedure for vanishing friction, using Wasow's singular perturbation theory, establishes that all unstable solutions are relevant to the problem.