We examine here the convection in a conditionally unstable atmosphere as an eigenvalue problem. If we take account of the effect of evaporation in a downdraft of liquid water which has condensed in the updraft in a convection, we have various types of convection. One of them has an updraft only in the cloud body and the others have both an updraft and a downdraft.
We deal with these convections as an open system, that is, the air-mass flow through lateral boundaries is taken account of. The stability properties are discussed in connection with the mean vertical motion associated with the air-mass flow.
It is shown that the convection followed by mean upward motion has a smaller lowest Rayleigh number, wider preferred cloud area and smaller compensating downdraft area while the convection followed by mean downward motion has a larger lowest Rayleigh number and smaller preferred cloud area than those for a closed convection. These results may explain the fact that the activity of cumulus convections increases in the low level convergence field or the upper level divergence field.
Furthermore we discuss the energy conversion process of convection with mean vertical motion and the heating effect of convection on the large scale field.