Penetrative Convection Due to a Field of Thermals

Abstract

A model of a field of thermals is presented to describe the observed behavior of high-Rayleigh-number convection. It is assumed that the response time of thermals within the convection layer is much less than the time scale over which the bulk properties of the layer vary. Hence the depth of the layer does not affect the mechanics of the thermals. The interaction between the thermals is taken into account implicitly by imposing similarity conditions, and it is found that the thermals grow by entrainment at a rate much less than that of an isolated thermal. Thermals reaching the top of the convection layer tend to penetrate into the stable fluid above, causing the layer depth to increase and producing a net downward heat flux into the layer. This process is modeled so that the overall behavior of a convection layer is predicted in terms of parameters associated with the generation of thermals at the base of the layer.