We study the Euler equations on the rotating unit sphere, focusing on the dynamics of vortex caps, i.e. piecewise constant absolute vorticity. Leveraging the area stability of monotone, longitude-independent profiles, we demonstrate that certain ill-prepared initial data within the vortex cap class exhibit an instability characterized by the growth of the interface perimeter. These configurations are nearly equivalent in area to a zonal vortex cap but are perturbed by a localized latitudinal bump. By comparing the longitudinal flows at points along the zonal interface and within the bump region, we track the induced stretching and capture the underlying instability mechanism.
By Geoffrey Vallis
By Luca Melzi
By Beatrice Pelloni
