ROTATING RAYLEIGH-BENARD CONVECTION IN CYLINDERS

摘要

This article presents a numerical study of rotating Rayleigh-Benard convection (RBC) in a fluid with Prandtl number 5.3 confined in cylindrical enclosures. Using three-dimensional numerical solutions of the basic equations in the Boussinesq-Oberbeck approximation, we have explored the transition from an initially conductive state to a nonlinear aperiodic regime. The patterns have been investigated in two cylindrical cavities with a circular and annular cross section, respectively. Different aspect ratios have been considered; in the case of the cylindrical box of height d and radius R the aspect ratio, defined as I'(= R/d) = 5 has been considered while in the case of annular channels with radial extent R = R_1 — R_0 (where R_0 and R_1 are the inner and outer radii, respectively); values L(= R/d) < 5 and F1(= R_1/d) = 12 : 5 have been considered. The pseudo-spectral numerical method allows the computation of three dimensional unsteady flows without any restriction on the patterns. Visualizations of the flow reproduce some experimentally observed patterns and agree with the results of linear stability analysis. The primary transition from the conductive state of no motion occurs in the form of processing convection modes. The secondary transitions show interesting dynamical processes, which vary with different boundary conditions. When the cylindrical sidewall is thermally insulating the primary travelling wave coexists with travelling wave convection in the bulk as the Rayleigh number is increased. In the case of a perfect thermally conducting sidewall the primary wave coexist with chaotic convection characterized by breaking rolls. In annular channels, two counter-rotating sidewall travelling waves are observed as predicted by theory. In narrower channels, these sidewall travelling waves interact and lead to a quasi-periodic time behaviour.