Topographic waves generated by a transient wind

The concept of linear mountain waves is generally equated with steady-state stationary waves. This essentially means that the absolute horizontal phase velocity of mountain waves is zero and that their momentum flux profile is independent of height and time in the absence of dissipation and zero-level wind. This paper investigates the generation of linear unsteady mountain gravity waves. The incident flow is transient, starting from zero at a given time and returning to zero after a finite time. The topography is a single horizontal harmonic. The unsteadiness of the waves is due partly to the temporal change of their phase velocity, which takes place during their propagation in the time-dependent mean flow. When the wind ceases, most of the waves present have a phase velocity nearly opposite to the maximum wind. For this reason, mountain waves can propagate through levels of zero mean wind. The transient structure of the wave field also comes from the temporal change of the amplitude of the ground forcing. Moreover, it is the result of the interference between the waves generated while the wind increases and those generated while it decreases. These transient effects naturally lead to z-dependent momentum flux profiles that are analyzed in detail. This paper deals with an analytical model, when the unsteady incident flow is uniform in the vertical direction. When the incident wind varies slowly in time, a comprehensive picture of the wave field is given by an asymptotic expansion of the wave solution. When the mean flow changes rapidly in time and when it varies in the vertical direction, the solution is obtained with a numerical model.