Hyper-Kähler geometry and semi-geostrophic theory | Zendy

Sylvain Delahaies | Zendy; Ian Roulstone | Zendy

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Hyper-Kähler geometry and semi-geostrophic theory

Author(s) -

Sylvain Delahaies,

Ian Roulstone

Publication year - 2009

Publication title -

proceedings of the royal society a mathematical physical and engineering sciences

Language(s) - English

Resource type - Journals

eISSN - 1471-2946

pISSN - 1364-5021

DOI - 10.1098/rspa.2009.0139

Subject(s) - geostrophic wind , formalism (music) , legendre polynomials , legendre transformation , duality (order theory) , mathematics , mathematical physics , geometry , physics , mathematical analysis , classical mechanics , pure mathematics , mechanics , art , musical , visual arts

We use the formalism of Monge–Ampère operators to study the geometric properties of the Monge–Ampère equations arising in semi-geostrophic (SG) theory and related models of geophysical fluid dynamics. We show how Kähler and hyper-Kähler structures arise, and the Legendre duality arising in SG theory is generalized to other models of nearly geostrophic flows.

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