A Plume Theory for the Convective Field in Clear Air

Abstract

In this paper the equations for a field of convective plumes are non-dimensionalized. These were derived in an earlier paper by formulating a model which included turbulence as an independent property with a specific kinetic energy. The numerical solutions previously discussed are extended so as to cover all conditions. It is shown that two non-dimensional parameters fully determine the solutions obtained. The field consists of plumes rising up to a level where the stability of the overlying air forces the air to turn about and descend again between the plumes to the surface. The model uses the beat flux, the layer depth, and the surface turbulence intensity (rms turbulent velocity) as parameters and does not include the wind specifically. The previous cases of the field solutions showed properties similar to those observed in atmospheric convection, as then discussed, and this paper extends the number of solutions so the general behavior becomes clear. These results show how there is likely to be a limit to the maximum depth of the layer and suggest that a different form of convection may be expected when heating continues after this depth is reached. The variation of this depth is discussed in terms of changing surface turbulence and heat flux or rate of temperature increase.