Construction of a dynamical system governing the Rayleigh-Bénard convection in a rectangular box

• Published in: Journal of the Physical Society of Japan 2005-06, Vol.74 (6), p.1750-1761
• Main Author: YAHATA, Hideo
• Format: Article
• Language: English
• Subjects: Buoyancy-driven instability; Exact sciences and technology; Fluid dynamics; Fundamental areas of phenomenology (including applications); Hydrodynamic stability; Nonlinearity (including bifurcation theory); Physics
• ISSN: 0031-9015; 1347-4073
• DOI: 10.1143/jpsj.74.1750

A dynamical system governing the Rayleigh-Bénard convection in a rectangular box is constructed with the aid of the Galerkin method starting from a Boussinesq system consisting of the Navier-Stokes and heat-transport equations. The boundary conditions are such that the velocity satisfies the rigid conditions on all the wall surfaces; and that the temperature satisfies the isothermal and insulating conditions on the horizontal and lateral wall surfaces respectively. The resulting dynamical system is used to evaluate critical Rayleigh numbers for onset of convection and those for oscillatory instability each together with the associated spatial patterns of the emerging convection fields under the conditions of box aspect ratios of Γx=3.5, Γy=2.0 and a Prandtl number of Pr=2.5. The results are shown to be in fairly good agreements with experiments available at present and other computations.