Gravity wave generation by a three-dimensional thermal forcing

Thermal forcing is one of the mechanisms of wave generation in convection. Although it does not account for all the wave generation mechanisms, thermal forcing is a good proxy for estimating the gravity wave spectrum forced by convection. This work presents a linear theory of gravity wave generation by a three-dimensional thermal forcing assuming constant mean wind conditions in the forcing region. Relationships are derived linking the amplitude and spectral characteristics of the generated gravity waves to the properties of the thermal forcing. It is shown that the three-dimensional problem can be viewed as a multiple two-dimensional problem by means of a squire transformation and that the gravity wave properties in a given azimuthal direction depend on the projection of the heating and environmental mean wind in that direction. Shown in detail is the sensitivity of the gravity wave characteristics in three dimensions to varying heating parameters, and it is concluded that the knowledge of both horizontal and vertical scales of the heating (at least statistical), and of the environmental wind distribution, is necessary to properly parameterize convectively generated gravity waves in GCMs.