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PATTERN FORMATION IN RAYLEIGH-BENARD CONVECTION IN A RAPIDLY ROTATING CYLINDER

Michael Sprague
Department of Applied Mathematics, University of Colorado UCB 526, Boulder, CO 80309-0526, USA

Keith Julien
Department of Applied Mathematics, University of Colorado, Boulder, CO 80309-0526, USA

Eric Serre
Aix-Marseille Universite, CNRS, Ecole Centrale Marseille, Laboratoire M2P2, Marseille, France

J. J. Sanchez-Alvarez
Departmento Fisica Fundamental, U.N.E.D., Apdo. 60.141,28080 Madrid, Spain

Emilia Crespo del Arco
Departamento de Fisica Fundamental, U.N.E.D., Apdo. Correos 60.141, 28080 Madrid, Spain

Abstract

Pattern formation in a rotating Rayleigh-Benard convection configuration is investigated for moderate and rapid rotation in moderate aspect-ratio cavities. While the existence of Kuppers-Lortz rolls is predicted by theory at the onset of convection (Kiippers and Lortz, 1969; Busse and Clever, 1979), square patterns have been observed in physical (Bajaj et al., 1998) and numerical experiments (Sanchez-Alvarez et al., 2005) at relatively high rotation rates. Direct numerical simulation (DNS) of the Boussinesq equations becomes progressively more difficult as the rotation rate is increased due the presence of increasingly thin Ekman boundary layers and fast inertial waves. In addition to presenting numerical results produced from DNS of the full Boussinesq equations, we derive a reduced system of nonlinear PDEs valid for convection in a cylinder in the rapidly rotating limit. Reduced equations have been of great utility in the investigation of rapidly rotating convection on the infinite plane (Julien et al., 1998, 2005; Sprague et al., 2005)