On the dynamics and interactions of coherent magnetic dipolar structures in a magnetohydrodynamic rotating shallow water model

In this study, we explore the evolution of instabilities in magneto-quasi-geostrophic (MQG) modons on the $f$ -plane using a magnetohydrodynamic rotating shallow water model. The numerical experiments have been conducted using a recently proposed second-order flux-globalisation-based path-conservative central-upwind scheme. Our focus is on the evolution and interactions of three key configurations: singular, regular and hollow MQG modons, which represent cases where the magnetic field is confined within the separatrix, evenly distributed inside and outside the separatrix and localised outside the separatrix, respectively. The singular MQG modon emerges as the most stable configuration, demonstrating the greatest resilience to destabilising forces. A notable observation is its transition from a quadrupolar to a tripolar magnetic field structure before reverting to a quadrupole adjusted magnetic modon, accompanied by a clockwise rotation of the system. In terms of stability, singular modons are the most stable ones, while hollow modons are the least stable. As instabilities develop, southward or northward displacements become significantly more pronounced than eastward or westward movements, primarily due to the Coriolis force. Among the configurations, the hollow (singular) modons experience the biggest (smallest) displacements. Additionally, we investigate modon collisions and highlight three scenarios: interactions between cyclonic and anticyclonic components that form a composite modon with meridional bifurcation; collisions of cyclonic vortices that produce a tripolar structure with counterclockwise rotation; and collisions between anticyclonic components that result in a stable, quasi-stationary tripolar configuration. The resulting magnetic poles exhibit a checkered pattern, with their amplitude decreasing with increasing distance from the central vortex.