Chapter 2 Asymptotic Methods with Applications to the Fast–Slow Splitting and the Geostrophic Adjustment

Abstract

Publisher Summary This chapter discusses asymptotic methods with applications to the fast–slow splitting and the geostrophic adjustment. The one- and multi-layer rotating shallow water models, as well as their parent primitive equation model, possess a gap in the spectrum of linear excitations that separate the fast inertia–gravity wave (IGW) motions and slow vortex motions. The vortex motions at small Rossby numbers are in geostrophic balance—for example, close to the equilibrium between the Coriolis force and the pressure force. Under hypothesis of splitting—in particular, noninteraction of fast and slow motions, useful balanced models may be derived from the full dynamical equations by using exclusively slow time-scales. This coupling at the level of initial conditions becomes dramatic in the non-localized initial conditions at the boundary in the case of laterally bounded domains, where initial conditions of the fast component (Kelvin wave) enter explicitly in the evolution equation of the slow component.