Mathematics

We provide an analytical proof for the existence of periodic vortex cap solutions for the homogeneous and incompressible Euler equations on the rotating unit 2-sphere. These solutions are piecewise constant absolute vorticity distributions, subject to the Gauss constraint and rotating uniformly around the vertical axis (rotation axis of the sphere). The emergence of such structures was numerically conjectured in the atmospheric community by Dritschel-Polvani in the 90s. Our proof is based on the bifurcation from zonal solutions given by spherical caps. This is a joint work with Claudia García (Granada) and Zineb Hassainia (NYUAD).