Monge-Ampere Geometry and the Eady Problem

TL;DR

This paper explores the geometrical structure of atmospheric fronts using Monge-Ampere geometry, extending previous models to include dynamically-forming singularities and providing a new geometric perspective on the classical Eady problem.

Contribution

It formalizes the concept of Chynoweth-Sewell fronts within Monge-Ampere geometry, linking atmospheric front models to advanced geometric frameworks.

Findings

Characterization of the Eady problem using Monge-Ampere geometry

Extension of semigeostrophic models to dynamic singularities

Geometric interpretation of classical solutions

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.