Chapter 5 Nonlinear Wave Phenomena in Rotating Shallow Water with Applications to Geostrophic Adjustment

Abstract

Publisher Summary This chapter discusses nonlinear wave phenomena in rotating shallow water with applications to geostrophic adjustment. The inspection of the dispersion curve for inertia–gravity waves (IGW) in the rotating shallow water (RSW) model on the f -plane shows that IGW are dispersionless in the short-wave limit and dispersive in the long-wave limit. Therefore, at the heuristic level, the short IGW behave such as acoustic waves, as in the absence of rotation the model is equivalent to the acoustics of a two-dimensional (2D) barotropic gas. The use of Lagrangian variables turns to be advantageous because of the quasi one-dimensional character of the model and allows to treat the fully nonlinear adjustment process and to prove that rotation cannot prevent breaking for a large class of initial conditions. The chapter explains that for periodic boundary conditions, exact solutions in the form of finite-amplitude propagating waves of special form appear in the model thus proving that rotation does equilibrate nonlinearity for some sets of initial conditions.