Baroclinic and Barotropic Instability with Cumulus Heating and Tropical Cyclogenesis.

To better understand the problem of tropical cyclogenesis, baroclinic and barotropic instability with parameterized cumulus heating is studied with an emphasis on basic zonal flows with easterly shear. As a prelude, a discussion of the symmetry or asymmetry of the baroclinic instability problem to the sign of the vertical shear is presented. The sensitivity of the conditional instability of the second kind (CISK) to variations in the basic thermodynamic structure is studied, using a three-level model with the Arakawa-Schubert cumulus parameterization. The model is then used to study the stability properties for various basic states with non-zero vertical shear. It is found that cumulus heating has an enormous influence on the instability. For low relative humidities, the Charney modes for westerly as well as easterly shears are destabilized. For high relative humidities, however, the Charney mode for easterly shear is stabilized, while, the enhanced heating due to the increased relative humidity leads to the destabilization of longer waves for easterly shear. The wavelength of these unstable waves in easterly shear decreases and their growth rate increases with the relative humidity. An energy analysis shows that the baroclinic conversion of the unstable modes can be enhanced by the cumulus heating in addition to its direct effect on the generation of eddy available potential energy. The mechanism of baroclinic instability with cumulus heating is further studied using a seven-level model. In this model, both the Arakawa-Schubert parameterization and a simpler parameterization, in which the heating is proportional to the vertical velocity at the top of the lowest model layer ((eta)-model), are used. The results are similar to those of the three-level model, except that the Charney mode as well as the Green mode for westerly shear are destabilized with Arakawa-Schubert parameterization. Instability analyses of the basic zonal flows similar to the monsoon situations are performed using the seven-level model with the Arakawa-Schubert parameterization. The structure, wavelength and phase speed of the fastest growing wave are in close agreement with those of observed monsoon depressions. The study using the three-level model is further extended to include horizontal shear of the basic zonal flow in a (beta)-plane channel. An initial-value approach is used to obtain the growth rates and the structures of the unstable waves. The results are similar to those without the y-variation of the basic zonal flow, though with a strong horizontal shear the contribution of the barotropic energy conversion in the energetics is also significant.