A cloud resolving model (CRM) is used to conduct a 15-day simulation of radiative convective equilibrium in a two-dimensional, basin-scale domain with a spatially uniform sea surface temperature and a spatially uniform radiative cooling profile. Results show that large-scale [O(1000 km)] convectively coupled gravity waves, with phase speeds (~ 16 m/s) and dynamical structures broadly matching observations of convectively coupled Kelvin waves, spontaneously develop from random initial conditions, even in the absence of a mean flow.

What are the mechanisms responsible for the development and maintainance of the simulated waves? Also, what determines their speed? In an effort to address these questions, a vertical normal mode transform algorithm is used to analyze output from the simulation. Results show that the “boomerang”-like stucture of the waves is primarily due to the superposition of two pairs of vertical normal modes that are phase shifted with respect to one another: a pair of relatively slow-moving modes with “free” gravity wave phase speeds of 16 and 18 m/s and a pair of relatively fast-moving modes with free gravity wave phase speeds of 35 and 45 m/s. Deep convection associated with the waves is found to be in phase with geopotential anomalies of the slow-modes, while being in quadrature with those of the fast-modes. Stratiform heating processes, which tend to lag deep convection by roughly two hours, play an important role in maintaining the energy of the slow-modes. Shallow convective heating processes, on the other hand, strongly remove energy from these modes. The energy of the fast-modes is primarily maintained by deep convective heating processes.

The results of this study broadly support the stratiform instability theory of Mapes. Two important exceptions, however, are as follows. First, the simulated large-scale waves arise through an unstable interaction between convection and vertical modes with phase speeds in the range, 16-18 m/s, rather than 23-25 m/s. Second, deep convective heating processes, as well as stratiform heating processes, play an important role in the maintaining the energy of the slow modes.