Numerical solution and analysis of asymmetric convention in a vertical cylinder: An effect of Prandtl number

Three-dimensional steady flows are simulated with a finite-difference technique in a cylinder of height-to-radius ratio A=4 heated from below. Basic axisymmetric (m=0) and asymmetric (m=1,2) modes are identified in the solutions. The relative contributions of these modes to the supercritical flow are assessed for Rayleigh numbers up to Ra≅10 Rac at Prandtl number Pr=6.7 and Ra≅2.5 Rac at Pr=0.02. At low Rayleigh number the core flow exhibits characteristic features of the m=1 dominant mode. At elevated Rayleigh numbers secondary vortices corresponding to the m=0 mode appear and develop differently in both size and magnitude for the two Prandtl numbers. The Ra dependence of important characteristic variables is analyzed in light of available nonlinear theories and laboratory measurements.