## Abstract

A mathematical theory was recently developed on the relationship between the dominant and gravity wave components of the slowly varying in time solutions (solutions varying on the advective timescale) corresponding to midlatitude mesoscale motions forced by cooling and heating. Here it will be shown that slowly varying in time equatorial motions of any length scale satisfy the same balance between the vertical velocity and heating as in the midlatitude mesoscale case. Thus any equatorial gravity waves that are generated will have the same time- and depth scales and the same size of pressure perturbations as the corresponding dominant component, a horizontal length scale an order of magnitude larger than that of the heat source, and an order of magnitude smaller velocity than the corresponding dominant component. In particular, in the large-scale equatorial case, when the heating has a timescale *O*(1 day), horizontally propagating gravity waves with a timescale *O*(1 day) and a length scale *O*(10 000 km) can be generated. But in the large-scale equatorial case when the heating has a timescale *O*(10 days), balanced pressure oscillations with a timescale *O*(10 days) are generated. It is also shown that if a solution of the diabatic system describing equatorial flows (and hence equatorial observational data in the presence of heating) is written in terms of a series of the modes of the linear adiabatic system for those flows, then a major portion of the dominant solution is projected onto gravity wave modes, and this result can explain the confusion over the relative importance of equatorial gravity waves.

* Additional affiliation: Cooperative Institute for Research in the Atmosphere, Colorado State University, Fort Collins, Colorado.

*Corresponding author address:* Dr. Gerald Browning, Cooperative Institute for Research in the Atmosphere, David Skaggs Research Center #3B906, 325 Broadway, Boulder, CO 80303.

Email: browning@fsl.noaa.gov