A Numerical Study of Pseudo Three-Dimensional Parallel-Plate Convection

Abstract

A numerical model for the study of three-dimensional, small-scale, horizontally homogeneous turbulence is presented for use with a two-dimensional grid in a vertical plane. The model is called pseudo three-dimensional because all quantities involving one of the horizontal dimensions are obtained by assumption during the calculations. It is applied to the problem of turbulent thermal convection between horizontal plates, with a Rayleigh number of 6.75×10⁵, and Prandtl numbers of 0.71 and 10. It is shown that this model allows turbulent motions to develop, whereas a two-dimensional model yields nearly steady convective rolls. The calculated heat flux is only about 5 per cent larger than experimental values, and the horizontal variances of temperature, vertical velocity and horizontal velocity are in rough agreement with observations at all levels. Terms in the vorticity and temperature variance equations are also evaluated, although experimental values are lacking for comparison.