Three-dimensional numerical experiments on thermal convection in a very viscous fluid: Implications for the dynamics of a thermal boundary layer at high Rayleigh number

In this study we present results from three-dimensional numerical experimen ts on thermal convection in a volumetrically heated, infinite Prandtl numbe r fluid cooled from above. At high Rayleigh number, a thin thermal boundary layer forms adjacent to the cold top boundary. On the basis of our numeric al results we study the thermal structure and dynamics of this boundary lay er and the population of plumes that it creates. Cold thermal plumes that d evelop by boundary layer instability form continuous nearly vertical column s that migrate horizontally sweeping off the unstable boundary layer. A plu me usually persists until it coalesces with another plume. The average spac ing of plumes, inferred from the variation of the observed number of plumes with Rayleigh number, is proportional to (delta d)(1/2), where delta and d are the thermal boundary layer and fluid layer thicknesses, respectively. Based on a "kinetic theory" of plume populations, we show that this is cons istent with an equilibrium plume population in which the creation of plumes by boundary layer instability and their disappearance by coalescing with o ther plumes are balanced. This scaling of average plume spacing is a conseq uence of the width of velocity plumes in a very viscous (infinite Prandtl n umber) fluid comparable to the fluid layer depth. For finite Prandtl number , the same analysis but with temperature and velocity plumes of comparable width predicts a plume spacing proportional to the boundary layer thickness . (C) 2000 American Institute of Physics. [S1070-6631(00)00103-3].