G.A. Gottwald and D.E. Pelinovsky

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 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.

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