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arXiv · 2310.03403

Curvature and stability of quasi-geostrophic motion

Ali Suri
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Abstract

This paper outlines the study of the curvature of the quantomorphism group and its central extension, as well as the quasi-geostrophic equation. By utilizing spherical harmonics and structure constants, a formula for computing the curvature of the $L^2$ metric on the central extension $\hat{\cg}=\cg\ltimes_\Omega\mathbb{R}$ is derived, where $\cg$ represents the Lie algebra of $\cD^s_\mu(\mathbb{S}^2)$. The sectional curvatures of the planes containing $Y_{10}$ and the tradewind current are calculated as special cases. The impact of the Rossby and Froude numbers, as well as the Coriolis effect, on the (exponential) stability of these quasi-geostrophic motions is highlighted. Finally, a lower bound for weather prediction error in a simplified model governed by the tradewind current and the Coriolis effect on a rotating sphere is suggested.

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Ali Suri. 2023-10-05. Curvature and stability of quasi-geostrophic motion. https://doi.org/10.1016/j.geomphys.2024.105109

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