Filamentation near monotone zonal vortex caps

Gian Marco Marin; Emeric Roulley

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arXiv · 2505.12197

Filamentation near monotone zonal vortex caps

Gian Marco Marin·Emeric Roulley

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Abstract

We study the Euler equations on a rotating unit sphere, focusing on the dynamics of vortex caps. Leveraging the $L^1$-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.

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Gian Marco Marin, Emeric Roulley. 2025-05-18. Filamentation near monotone zonal vortex caps. https://arxiv.org/abs/2505.12197

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