Large-Scale Atmosphere-Ocean Dynamics I Analytical Methods and Numerical Models

About this book

Numerical weather prediction is a problem of mathematical physics. 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 and that describe, for example, the dynamics of cyclones and ocean eddies. The simplifications often result in models that are amenable to solution both analytically and numerically. The lectures in these volumes examine and 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, such as groups of transformations, Hamiltonian structure and stability. This book and its companion show how geometry and analysis facilitate solution strategies.

Contents

Introduction J. C. R. Hunt, J. Norbury and I. Roulstone; 1. A view of the equations of meteorological dynamics and various approximations A. A. White; 2. Extended-geostrophic Euler-Poincare models for mesoscale oceanographic flow J. S. Allen, D. D. Holm and P. A. Newberger; 3. Fast singular oscillating limits of stably stratified three-dimensional Euler-Boussinesq equations and ageostrophic wave fronts A. Babin, A. Mahalov and B. Nicolaenko; 4. New mathematical developments in atmosphere and ocean dynamics, and their application to computer simulations M. J. P. Cullen; 5. Rearrangements of functions with applications to meteorology and ideal fluid flow R. J. Douglas; 6. Statistical methods in atmospheric dynamics: probability metrics and discrepancy measures as a means of defining balance S. Baigent and J. Norbury.

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