Large-Scale Atmosphere-Ocean Dynamics: Volume 1: Analytical Methods and Numerical Models

The complex flows in the atmosphere and oceans are believed to be accurately modelled by the Navier-Stokes equations of fluid mechanics together with classical thermodynamics. However, due to the enormous complexity of these equations, meteorologists and oceanographers have constructed approximate models of the dominant, large-scale flows that control the evolution of weather systems. The simplifications often result in models that are amenable to solution both analytically and numerically. This volume and its companion explain why such simplifications to Newton's second law produce accurate, useful models and, just as the meteorologist seeks patterns in the weather, mathematicians seek structure in the governing equations. They show how geometry and analysis facilitate solution strategies.

This book and its companion describe, in a language accessible to both mathematicians and meteorologists, the mathematics underpinning our understanding of large-scale atmosphere and ocean dynamics. Meteorologists understand 'weather' by identifying the dominant controlling mechanisms, and so mathematicians are deducing how such features can be described mathematically. They are discovering that geometry plays a key role in this process. These developments promise an important spin-off--improving numerical models by incorporating, using a geometric language, constraints that govern the optimal use of observational data and the development of typical weather systems.