The numerical experiments are tried in a simple two dimensional atmospheric model in order to investigate the evolution of a cumulus convection from a dynamical aspect.
In the first place, a system of the equations governing a thermal convection in cumulus scale is derived by making use of the perturbation method. It is suggested, especially, that the assumption of non-divergent motion is appropriate and the introduction of eddy exchange is inevitable.
Secondly, a non-linear system of the equations designed on the basis of the perturbation analysis is integrated numerically for some cases during several tens of minutes. An isolated convection 5 km thick and 10 km wide is investigated assuming the pseudo-adiabatic process in some conditionally unstable layers at rest. The convection is further assumed to be without supply of energy through the boundary of rectangular domain.
In general, a lifetime of convection ranges from 20 to.30 min. The development in an early stage of the convection is characterized by the intensification of convective circulation associated with narrowing an updraft region. Immediately after the convection attains the mature stage with maximum upward velocity and rate of condensation, it plunges into the decaying stage with damping oscillation.
Finally a great difference between the co n vections in warm and cold layers is illustrated.
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