Large-Scale Atmosphere-Ocean Dynamics

by Edited by John Norbury , Ian Roulstone

• ISBN13: 9780521807579
• ISBN10: 0521807573
• Format: Hardcover
• Copyright: 2002-09-09
• Publisher: Cambridge University Press

Summary

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.

Table of Contents

Contributors	ix
Preface	xi
J.C.R. Hunt
J. Norbury
I. Roulstone
Introduction and Scientific Background	xiii
Balanced models in geophysical fluid dynamics: Hamiltonian formulation, constraints and formal stability	1	(63)
O. Bokhove
The swinging spring: a simple model of atmospheric balance	64	(45)
P. Lynch
On the stationary spectra for an ensemble of plane weakly nonlinear internal gravity waves	109	(8)
P. Caillol
V. Zeitlin
Hamiltonian description of shear flow	117	(26)
N.J. Balmforth
P.J. Morrison
Some applications of transformation theory in mechanics	143	(81)
M.J. Sewell
Legendre-transformable semi-geostrophic theories	224	(27)
R. James Purser
The Euler--Poincare equations in geophysical fluid dynamics	251	(50)
D.D. Holm
J.E. Marsden
T. Ratiu
Are there higher-accuracy analogues of semi-geostrophic theory?	301
M.E. McIntyre
I. Roulstone