A new model of tropical waves incorporating momentum mixing by cumulus convection

A comparison is made between the magnitudes of observed large-scale weather waves over the tropical Pacific and the magnitudes of the corresponding waves, predicted by wave-CISK theories, which are driven by the observed amount of latent heating (i.e., precipitation). The theoretical wave fields of meridional velocity, vorticity, and temperature rate are shown to exceed the observed quantities by an order of magnitude. An attempt is made to simulate the observed balance between the diabatic heating and adiabatic cooling within the context of the inviscid theories. For a broad class of heating profiles, geometries and basic states, it is found that this compensation without temperature change cannot be satisfactorily modelled, regardless of the vertical shape of the heating, when the vertical wavelength of the disturbance exceeds about 6 km.Scale analysis demonstrates that an important dynamical term has been neglected in the inviscid models, viz., the vertical transport of horizontal momentum by cumulus clouds. When this process is included in the wave model, velocities, relative vorticity, and the time rate of temperature change are all comparable to the observed values. The general behavior of a system where both forcing and cumulus “friction” are proportional to each other has not been previously examined. We find the behavior of such a system to have several novel features. For example, we find that for a wide range of precipitation amplitudes (from 1/4 to 4 times the precipitation amplitudes of waves in the western Pacific) we get essentially constant amplitudes for wind. The implications of this and other features for various aspects of tropical wave modelling are discussed.