A Mathematical Theory of Large-scale Atmosphere/ocean FlowWorld Scientific, 2006 - 259 pages This book counteracts the current fashion for theories of ?chaos? and unpredictability by describing a theory that underpins the surprising accuracy of current deterministic weather forecasts, and it suggests that further improvements are possible. The book does this by making a unique link between an exciting new branch of mathematics called ?optimal transportation? and existing classical theories of the large-scale atmosphere and ocean circulation. It is then possible to solve a set of simple equations proposed many years ago by Hoskins which are asymptotically valid on large scales, and use them to derive quantitative predictions about many large-scale atmospheric and oceanic phenomena. A particular feature is that the simple equations used have highly predictable solutions, thus suggesting that the limits of deterministic predictability of the weather may not yet have been reached. It is also possible to make rigorous statements about the large-scale behaviour of the atmosphere and ocean by proving results using these simple equations and applying them to the real system allowing for the errors in the approximation. There are a number of other titles in this field, but they do not treat this large-scale regime. |
Table des matières
1 Introduction | 1 |
2 The governing equations and asymptotic approximations to them | 11 |
3 Solution of the semigeostrophic equations in plane geometry | 57 |
4 Solution of the semigeostrophic equations in more general cases | 117 |
5 Properties of semigeostrophic solutions | 163 |
6 Application of semigeostrophic theory to the predictability of atmospheric flows | 201 |
7 Summary | 243 |
| 245 | |
| 255 | |
Autres éditions - Tout afficher
A Mathematical Theory of Large-scale Atmosphere/ocean Flow Michael J. P. Cullen Aucun aperçu disponible - 2006 |
Expressions et termes fréquents
analysis aspect ratio assume boundary conditions Brunt-Väisälä frequency calculated conservation constant convex function coordinates Cullen defined derived discussed in section displacement dual variables energy integral energy minimisation equation of 2.83 evolution finite fluid forecasting geostrophic wind given gives gradient hand side horizontal Hoskins hydrostatic hypersurface incompressible inertia-gravity wave initial data kinetic energy Lagrangian Legendre transform matrix Q Mawson Met Office momentum Navier-Stokes equations optimal map perturbations physical space positive definite potential density potential temperature potential vorticity predictability problem proof qsat quasi-geostrophic rearrangement ridge Rossby number Rossby waves Royal Meteorological Society satisfying scales semi-geostrophic equations semi-geostrophic model semi-geostrophic solutions semi-geostrophic theory shallow water equations shown in Fig shows Shutts slow manifold solved Theorem tions two-dimensional variations velocity weather systems zero θα θο θυ ду Јг