Stability of Symmetrical Motions Driven by Latent Heat Release by Cumulus Convection under the Existence of Surface Friction

Abstract

To obtain a theoretical basis for the numerical simulation of tropical cyclones, the stability properties of symmetrical disturbances driven by the latent heat of condensation released in deep cumulus clouds under the existence of surface friction are discussed by solving a system of primitive thermohydrodynamic equations applied to a three-layer model including the friction layer. The processes of heat generation and transfer by cumulus clouds are incorporated by assuming that the total amount of latent heat released in any vertical column of air is proportional to the horizontal convergence in the friction layer.
An analysis of linear perturbation equations shows that a typhoon-scale disturbancesimilar to those obtained by Ooyama (1963), Charney and Eliassen (1964) and Ogura (1964)using the balanced model is also found in the unbalanced (or primitive) model. Without surface friction the disturbance would be in geostrophic (or gradient wind) balance. Under some conditions unstable gravity waves as discussed by Haque (1952) and Syono (1953) still exist even in our model in spite of a different treatment of condensational heating. Moreover, under some conditions gravity oscillations are amplified with a large amplification rate and short period. These unstable gravity waves are found to be filtered out by use of the assumption that the pressure gradient force is balanced with the Coriolis force and the frictional force in the friction layer, as adopted by Ooyama (1963) and others. At the same time the use of this assumption modifies the growth rate of the typhoon-scale disturbance. Furthermore this assumption alters the condition under which the typhoon-scale disturbance exists. The analysis further shows that the vertical partition of the released latent heat as well as the amount of water vapor in the ascending air and the static stability of the atmosphere are important factors which determine properties of the disturbance.