Some dynamical aspects of atmospheric convection

Abstract

Some dynamical characteristics of atmospheric convection are investigated by obtaining an analytical solution for a most simplified set of difference equations which represent a two-layer model of an incompressible buoyant fluid. Several invariants are obtained as a function of initial values of vertical and horizontal potential temperature differences and kinetic energy. Then the analytical solution is obtained in using these invariants. One of the major advantages of using such a simplified model is to make it possible to discuss the nonlinear processes based on an analytical solution. The major disadvantage is caused by the low resolution in the space derivatives (time derivatives are exact). However, invariant quantities obtained for this simple model are equivalent to those obtained for the original differential equations, so that the important characteristics of convection are probably described in the present simplified model. Major results obtained from the model are presented.