Recent advances in asymptotic modelling of tangent atmospheric motions

Abstract

The main objective of this study is to present an asymptotic theory of the modelling of various atmospheric motions. By asymptotic modelling we mean the process by which starting from a given, well set. Navier-Stokes “exact” model equations, in the β-plane approximation, we take advantage of the existence of one or more small parameters in order to derive simpler mathematical models by some appropriate limiting process leading to a hierarchy of approximations ruled, in turn, at each step by a set of equations and appropriate boundary and initial conditions. But, when we simplify the basic Navier-Stokes model, for “tangent” atmospheric flows, more often than once we are faced with singular perturbation problems. This is due, in particular, to the fact that the limiting process, which leads to approximate models, niters out some time derivatives. And it is necessary to elucidate the problem of the adjustment of the initial set of data to the asymptotic structure of the model under consideration. Here we consider the following basic models: hydrostatic and primitive equation models, quasigeostrophic and ageostrophic models, Boussinesq and deep convection equation models, models for the environmental prediction.