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- W4387432942 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 $hat{cg}=cgltimes_Omegamathbb{R}$ 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." @default.
- W4387432942 created "2023-10-09" @default.
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- W4387432942 date "2023-10-05" @default.
- W4387432942 modified "2023-10-09" @default.
- W4387432942 title "Curvature and stability of quasi-geostrophic motion" @default.
- W4387432942 doi "https://doi.org/10.48550/arxiv.2310.03403" @default.
- W4387432942 hasPublicationYear "2023" @default.
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