Monge-Ampere Geometry and the Eady Problem

Abstract

Chynoweth and Sewell proposed a mathematical model for an atmospheric front based on the singularities of the Legendre transformation between different pairs of dual variables. Drawing inspiration from their work, we formalize the idea of a Chynoweth-Sewell front and illuminate its geometrical meaning from the viewpoint of Monge-Ampere geometry. This extends our previous work on the semigeostrophic model to dynamically-forming singularities. We use the notion of a Chynoweth-Sewell front to characterize the classical Eady problem and its known solutions in geometrical terms.