Wavenumber Selection in Be´nard Convection

Abstract

The results of three related studies dealing with wavenumber selection in Rayleigh–Be´nard convection are reported. The first, an extension of the power integral method, is used to argue for the existence of multi-wavenumbers at all supercritical wavenumbers. Most existing closure schemes are shown to be inadequate. A thermodynamic stability criterion is shown to give reasonable results but requires empirical measurement of one parameter for closure. The third study uses an asymptotic approach based in part on geometric considerations and requires no empiricism to obtain good predictions of the wavenumber. These predictions, however, can only be used for certain planforms of convection.