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

Cambridge University Press, 8/15/2002
EAN 9780521806817, ISBN10: 052180681X

Hardcover, 402 pages, 24.7 x 17.4 x 2.2 cm
Language: English

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 2002 book and its companion show how geometry and analysis facilitate solution strategies.

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-Poincaré 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.

'The book is a rich source of novel ideas and open research problems as well as up-to-date references. I shall want to refer back to it again and again.' Contemporary Physics