Generalised Lagrangian Solutions for Atmospheric and Oceanic Flows
M. J. P. Cullen, J. Norbury, R. J. Purser
Source 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. Generalised 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 generalised 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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