New phenomena in the Eckhaus instability of thermal Rossby waves

Abstract

An analytical study on the Eckhaus instability of moderately nonlinear thermal Rossby waves is developed. A solvability condition of the lowest order is derived. The condition not only produces results that agree reasonably well with the earlier Galerkin formulation, but also leads to some new findings that are otherwise difficult to discover by the previous method. Over a wide range of parameters, this paper reports the existence of a branch of the stability limit that corresponds to a pair of disturbances with a finite, rather than an infinitesimal wavenumber modulation. As the Prandtl number tends to a small value, the asymmetry between the two branches of the stability limit becomes very pronounced, which is manifested as a severely distorted stability region.