Linear unsteady mountain waves

Abstract

The object of this paper is to describe the generation of mountain gravity waves when the incident wind is transient. The incident flow is a stably stratified fluid which velocity starts from zero at a given time and returns to zero after a finite time. For the mountain, both a single harmonic and a single ridge topography are considered. The nature of transient effects on the disturbance is discussed according to the value of the parameter, ε = U₀t_f/L, which measures the ratio between the time scale t_f of the temporal variation of the incident wind and the advective time scale L/U₀. L and U₀ characterize the horizontal extension of the mountain and the incident wind intensity, respectively. Situations for which ε ≫ 1 are referenced as quasi-steady and the wavefield can be conveniently described using ray-tracing techniques. Situations for which ε ≪ 1, are referenced as very unsteady, and essentially reduce to a ground vibrating disturbance generated in a fluid at rest. In this paper, we consider both limit configurations as well as intermediate ones. This allows us to describe various mechanisms of generation of unsteady mountain waves. The incidence of the unsteadiness on the amplitude of the gravity wave momentum flux and on the location of the mountain wave breaking level are also discussed.