Rayleigh-Bénard convection with time-dependent boundary conditions

J. B. Swift and P. C. Hohenberg
Phys. Rev. A 39, 4132 – Published 1 April 1989
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Abstract

The 13-mode Lorenz model previously introduced to describe hexagons and rolls in a Rayleigh-Bénard cell with periodic modulation of the lower plate is generalized to arbitrary time dependence of both upper and lower plates. Earlier results of Krishnamurti [J. Fluid Mech. 33, 445 (1968); 33, 457 (1968)] for the case of a linear ramp with constant temperature difference are recovered. The conditions for observing hexagons are derived analytically for periodic modulation with different frequencies, amplitudes, and phases at the two plates.

  • Received 2 November 1988

DOI:https://doi.org/10.1103/PhysRevA.39.4132

©1989 American Physical Society

Authors & Affiliations

J. B. Swift

  • Department of Physics and Center for Nonlinear Dynamics, University of Texas, Austin, Texas 78712

P. C. Hohenberg

  • AT&T Bell Laboratories, Murray Hill, New Jersey 07974

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Vol. 39, Iss. 8 — April 1989

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