Abstract
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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