From Gulf Stream rings in the ocean to split-flow blocks in the atmosphere, large-scale isolated anomalies play a prominent role in the dynamics of Earth's geophysical fluid systems. Although these isolated anomalies are among the most observed features in the oceans and atmosphere, their theoretical underpinnings remain poorly understood.

Here we carry out a theoretical study of the weakly nonlinear dynamics of isolated anomalies in the form of solitary waves (SWs) propagating in a zonally varying baroclinic flow. Among our goals is to determine the characteristics of the zonally varying background flow that create, maintain and destroy isolated anomalies. Our work is an important and significant extension of work carried out by Helfrich and Pedlosky (1993; hereafter HP), who derived a Boussinesq equation for the SW amplitude. This nonlinear equation supports two types of instability processes: 1) “fission” and 2) “implosion.” The former is characterized by splitting of the initial SW and the latter by a rapid amplitude increase with commensurate scale decrease of the SW.

To what extent HP's results change as a result of a zonally varying background flow will be a central focus of our study. Our preliminary work shows that, in contrast to HP, the zonally varying background flow yields a Boussinesq equation with variable coefficients. These variable coefficients are manifestations of localized supercritical and subcritical flow regions that result from the zonally varying background flow. Several important questions immediately arise. How do these supercritical and subcritical flow regions affect the "fission" and "implosion" characteristics of the SWs? Can these background flow regions introduce new modes of behavior other than fission and implosion? And how does the zonal extent of the supercritical region, for example, affect the various modes of behavior? In order to address these questions and provide new insights into the dynamics of isolated anomalies in large-scale atmospheric flow, new conservation laws are derived and the amplitude evolution equation is solved numerically. These results will be compared with observations of isolated anomalies in the atmosphere.