A stochastic model for high-Rayleigh-number convection

Abstract

A stochastic one-dimensional model for thermal convection is formulated and applied to high-Rayleigh-number convection. Comparisons with experimental data for heat transfer in Rayleigh–Bénard cells are used to estimate two model parameters. Reasonable agreement with experimental results is obtained over a wide range of physical parameter values (six orders of magnitude in Rayleigh number, five orders of magnitude in Prandtl number). Using the model, the statistics of fluctuations in the core of the convection cell are studied. Good agreement with available experimental data is obtained. Two distinct p.d.f. shapes are seen; one at low Prandtl number which matches experimental observations, and another at high Prandtl number for which no experimental data exists. The model results are interpreted in terms of two distinct mechanisms for the production of core fluctuations.