A dynamical study is made of properties of cumulus convection and its preferred mode in a conditionally unstable atmosphere based on numerical experiments. The preferred mode of cumulus convection is determined as the steady convection cell which consists of an ascending saturated region and a descending unsaturated one attained eventually after random temperature disturbances are imposed initially. It is shown that the preferred cell size and the area ratio of the ascending region to the descending one depend on the mean vertical velocity and the static stability of the atmospheric layer in which the connections are imbedded. Inspection of each term of energy equations indicates that the preferred convection is of the mode for which the potential energy of the layer is at the lowest. Since the potential energy represents the static stability of the layer, the minimum value of the mean temperature lapse-rate can be observed when the preferred convection is realized.

The cumulus model proposed by Asai (1967) is applied to cellular cumulus convection in a moist atmospheric layer uniformly heated below and cooled above. The governing system of equations derived has a steady state solution of cumulus convection independent of initial input disturbances. A preferred mode of steady cumulus convection can be expressed in terms of an amount of heat supply, employing the selection principle that a preferred mode is one for which the lapse rate of temperature is the lowest. An examination of the results shows a coincidence with the feature of cumulus clouds in colder air over warmer water. However, tall vigorous cumulus convection is hardly expected to develop by uniform heating even with a large amount of heat supply.

No abstract