Geodesic interpretation of the global quasi-geostrophic equations

Klas Modin; Ali Suri

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arXiv · 2504.10226

Geodesic interpretation of the global quasi-geostrophic equations

Klas Modin·Ali Suri

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Abstract

We give an interpretation of the global shallow water quasi-geostrophic equations on the sphere $\Sph^2$ as a geodesic equation on the central extension of the quantomorphism group on $\Sph^3$. The study includes deriving the model as a geodesic equation for a weak Riemannian metric, demonstrating smooth dependence on the initial data, and establishing global-in-time existence and uniqueness of solutions. We also prove that the Lamb parameter in the model has a stabilizing effect on the dynamics: if it is large enough, the sectional curvature along the trade-wind current is positive, implying conjugate points.

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BibTeX RIS

Klas Modin, Ali Suri. 2025-04-14. Geodesic interpretation of the global quasi-geostrophic equations. https://arxiv.org/abs/2504.10226

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