A Numerical Study of Three-Dimensional Benard Convection

Abstract

The preferred horizontal plan form of Benard convection is examined by a numerical integration of Boussinesq system of equations. We carried out the computations of the cases of R/Rc =2 and 6 for air and water, where R is a prescribed Rayleigh number and Rc is the critical Rayleigh number. The steady rolls are obtained under a nearly random small initial temperature perturbation except the case of R=6Rc for water. In the case of R=6Rc for water we have a steady three-dimensional convection. However the final steady convection with a finite amplitude initial perturbation has a different horizontal plan form from one with the nearly random small initial temperature perturbation.The vertically coherent oscillation whose period is almost the same as that observed in the laboratory experiments by Krishnamurti (1970) and Willis and Deardorff (1970) was found in the case of R=6Rc for air.