The Role of Variable Coriolis Parameter in the Propagation of Inertia-Gravity Waves During the Process of Geostrophic Adjustment

Abstract

Abstract This analysis treats the transient inertia-gravity wave response of a shallow fluid to an impulsive addition of momentum. The Coriolis parameter varies with latitude, but Rossby waves are not considered. The square of the Coriolis term is approximated by a constant term plus a term linear in the northward coordinate. In this approximation, monochromatic waves, which reach a turning point at the latitude where the wave frequency equals the local Coriolis frequency, are given by Airy functions. A contour integral solution to the initial value problem is expressed as a Fourier integral over wave frequency with an Airy function argument and is evaluated approximately using the stationary phase technique. The solution at a given latitude is first dominated by waves from the source and then waves reflected from turning points poleward of the source. The results are applied to give a qualitative description of the wake of a hurricane moving over a stratified ocean.