Curvature and stability of quasi-geostrophic motion

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 L2 metric on the central extension gˆ=g⋉ΩR is derived, where g represents the Lie algebra of Dμs(S2). The sectional curvatures of the planes containing Y10 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 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.