Hetonic Quartet: Exploring the Transitions in Baroclinic Modons

Abstract

The notions of a heton and baroclinic modon had been brought into use in geophysical find dynamics more than two decades ago; the concept of a hetonic quartet is a new one. A heton is a two-layer quasigeostrophic (generally, translating) point-vortex pair. Two aligned hetons with properly fitted circulations and separations form a steadily translating collinear ensemble of four discrete vortices, termed a hetonic quartet. Baroclinic modons, i.e., localized regular steady-state solutions to the nonlinear equations of potential vorticity (PV) conservation in a (differentially) rotating stratified fluid, represent a paradigm for coherent structures in geophysical flows. Hetons and hetonic quartets share some traits with baroclinic modons and, therefore, offer a finite-dimensional model for exploring the modon stability and transitions. A baroclinic modon appears as two oppositely signed PV chunks that reside at different depths (one in the upper layers and the other in the lower layers) and are shifted relative to each other in the north-south direction. A hetonic quartet is a discrete counterpart of a two-layer modon whose upper- and lower-layer PV chunks overlap considerably, while a heton models a nonoverlapping modon. The phenomenon of transition of baroclinic modons from overlapping to nonoverlapping states (observed in numerical simulations) is explained in terms of stability of hetonic quartets and their breakdown into two noninteracting hetons.