The linear problem of rotating, stratified, adiabatic, hydrostatic, Boussinesq airflow over a mountain ridge is solved analytically for the case where the spatially uniform, normally incident airflow is the sum of a steady and sinusoidally varying component. The mountain generates a response at the fundamental frequency of the wind and all higher harmonics.
During flow acceleration, the evanescent (vertically decaying) modes deepen and broaden the high-low pressure asymmetry across the ridge and increase the mountain drag. In contrast, the evanescent modes for steady airflow product only a symmetric mountain anticyclone that generates no drag. The influence of the acceleration is more pronounced for mesoscale and synoptic-scale ridges (i.e., ridges whose Rossby number is order unity or smaller) and when the fundamental period is near the inertial period.
The transience also amplifies the magnitude of the maximum wave drag over its value predicted from steady airflow theory using the instantaneous wind speed. The total acceleration reaction due to both evanescent and wave modes can be larger than this steady airflow drag.