G.A. Gottwald and D.E. Pelinovsky

On the impossibility of solitary Rossby waves in meridionally unbounded domains

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 address 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 is effectively linear and moreover confined to zonal waveguides of the mean flow. This eliminates even the ubiquitous Korteweg-de Vries equations as underlying models for spatially localized coherent structures in these geophysical flows.

quasi-geostrophic equation; Rayleigh–Kuo eigenvalue problem; Korteweg-de Vries equation; mod- ified Korteweg-de Vries equation; Zakharov-Kuznetsov equation; Rossby waves