On the impossibility of solitary Rossby waves in meridionally unbounded domains

TL;DR

This paper demonstrates that in unbounded planetary atmospheres and oceans, Rossby waves cannot form solitary structures due to their linear and confined dynamics, challenging previous assumptions about localized wave solutions.

Contribution

It shows that Rossby wave dynamics in unbounded domains are effectively linear and confined, ruling out the existence of solitary wave solutions like KdV solitons.

Findings

Rossby waves are confined to zonal waveguides.

Localized eigenmodes are trapped by mean flow with non-resonant speeds.

Spatially localized coherent structures are not supported by these flows.

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.