On the impossibility of solitary Rossby waves in meridionally unbounded domains

Abstract

Evolution of weakly nonlinear and slowly varying Rossby waves in planetary atmospheres and oceans is considered within the quasi-geostrophic equation on unbounded domains. When the mean flow profile has a jump in the ambient potential vorticity, localized eigenmodes are trapped by the mean flow with a non-resonant speed of propagation. We discuss amplitude equations for these modes. Whereas the linear problem is suggestive of a two-dimensional Zakharov-Kuznetsov equation, we found that the dynamics of Rossby waves are effectively linear and confined to zonal waveguides of the mean flow. This eliminates even the ubiquitous Korteweg-de Vries equations as the underlying model for spatially localized coherent structures in these geophysical flows.