Generalised Lagrangian Solutions for Atmospheric and Oceanic Flows (original) (raw)

SIAM Journal on Applied Mathematics, 1991

Abstract

ABSTRACT Atmospheric or oceanic flows strongly constrained by rotation and stratification can be described by a set of Lagrangian partial differential equations called the semigeostrophic equations. In these equations the trajectories must be determined implicitly. Generalized solutions of these equations are defined as a sequence of rearrangements of the fluid, which need not be smooth. These solutions are closely related to generalized solutions of the Monge-Ampere equation. Existence and uniqueness of such solutions is proved. The evolution is shown to be a sequence of minimum-energy states of the fluid, giving strong physical plausibility to the solutions.

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