Gravity wave radiation and mean responses to local body forces in the atmosphere

Abstract

The authors determine the spectral linear solutions that arise in response to local 3D body forces and heatings in an idealized environment that turn on and off smoothly but not necessarily slowly over a finite interval in time. The solutions include impulsive through slowly varying body forcings. The forcings result in both a mean response, which is typically significantly broadened spatially in one direction, and a gravity wave response, which allows the fluid to reach this state. The gravity wave field depends on both the spatial attributes of the source and the forcing duration. The frequency of the wave response is the "characteristic" source frequency (formed from the source dimensions) if the forcing frequency is greater than the characteristic frequency and is the forcing frequency otherwise. The radiated gravity waves from zonal forcings have vertical wavelengths, which are approximately twice the vertical extent of the forcing, and horizontal wavelengths, which are at least twice the horizontal extent of the forcing. Wave excitation is increasingly inefficient when the forcing frequency is smaller than the characteristic source frequency. In addition, the mean responses are not confined to the source region; in general, significant spatial broadening of the mean responses occurs. If the source's frequency is high and low, the responses are broadened horizontally and vertically, respectively, with the amount depending on the characteristic scales of the source. If the body forcing is in the eastward direction, then much or all of the ensuing zonal mean wind is eastward. However, for many realistic forcing scenarios, a large percentage of the ensuing zonal wind flows westward. These countersigned jets are displaced meridionally about the source. Thus, spatially confined body forcings create both gravity wave and mean responses if the forcings are fast enough; very slowly varying forcings create only mean responses.