A Numerical Study of Three-Dimensional Benard Convection Part III On the Preferred Roll Diameter

Abstract

The preferred roll diameter is examined by a simple three-dimensional numerical model of Bénard convection. We obtained two types of preferred size for the convection roll, which are called the size I and size II. The size I is smaller than the critical size Lc and the size II is larger than Lc, where the critical size Lc is the preferred size at the critical Rayleigh number. The roll with the size I is realized just above the critical Rayleigh number. The roll with the size II is preferable to that with the size I at rather high Rayleigh numbers. The size I corresponds to one predicted in the previous theoretical and numerical works. The preference of the size II to the size I at rather high Rayleigh numbers may explain the discrepancy between the previous theoretical works and experimental works.
Furthermore the energy consideration indicates that the inertial terms tend to decrease the roll diameter and the advective terms in the thermodynamic equation have a controlling influence on the selection of the preferred size of the convection.