Analysis and modeling for a turbulent convective plume

Asymptotic and scaling analyses are applied to develop a simple model for a turbulent convective plume at high Rayleigh number R in a high Prandtl number fluid layer whose lower boundary surface maintains steady local buoyant sources. The convective plume is assumed to be axisymmetric and conical whose radius b is small compared to the depth of the layer. Under statistically steady conditions, the dependence of the mean components, to the leading order terms, of axial velocity, radial velocity, pressure and temperature of the plume, as well as the vertical volume flux in the plume, on R and b are determined. The main results are in satisfactory agreement with available experimental observations. The results are equally applicable to the case where any finite number of such plumes are present under similar conditions, provided no interactions between the individual plumes take place.