Forma, Vol. 8 (No. 1), pp. 99-117, 1993

Pattern Formation in Rayleigh-Bénard Convection

J. Mizushima

Faculty of Engineering, Doshisha University, Kamigyo-ku, Kyoto 602, Japan

(Received April 28, 1993; Accepted June 4, 1993)

Keywords: Pattern Formation, Rayleigh-Bénard Convection, Stability

Abstract. Abstract. An attempt is made to clarify the mechanism of pattern formation in Rayleigh-Bénard convection. A set of model equations, which describe the time development of the amplitudes of Fourier modes, are proposed. It is shown that a hexagonal cellular pattern is a stable steady solution of the set of model equations. Results of numerical simulations for the set of model equations illustrate the mechanism of the pattern formation.