On the dynamics in evaporating cloud envelopes

Cowie and McKee (1977) have conducted an analytical study of the case of an isolated, spherical cloud at rest in an infinite, hot medium. The present investigation is concerned with the theoretical model considered by Cowie and McKee for a thermally evaporating cloud. An analysis is conducted under the same conditions of inviscid flow with temperature equipartition. The current analysis allows for a continuous change in the saturation of the conductivity, rather than abrupt transitions from a classical to a fully saturated regime and back again, as in the model employed by Cowie and McKee. By suitable variable transformations, the momentum and energy equations can be reduced in the inviscid limit to a single equation for the Mach number in terms of a modified radius, and the solutions represented in a phase plane. An analytic model for the structure of the shock layer is developed.