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Lyapunov exponents for small aspect ratio Rayleigh-Bénard convection

Scheel, J. D. and Cross, M. C. (2006) Lyapunov exponents for small aspect ratio Rayleigh-Bénard convection. Physical Review E, 74 (6). Art. No. 066301. ISSN 1539-3755.

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Leading order Lyapunov exponents and their corresponding eigenvectors have been computed numerically for small aspect ratio, three-dimensional Rayleigh-Benard convection cells with no-slip boundary conditions. The parameters are the same as those used by Ahlers and Behringer [Phys. Rev. Lett. 40, 712 (1978)] and Gollub and Benson [J. Fluid Mech. 100, 449 (1980)] in their work on a periodic time dependence in Rayleigh-Benard convection cells. Our work confirms that the dynamics in these cells truly are chaotic as defined by a positive Lyapunov exponent. The time evolution of the leading order Lyapunov eigenvector in the chaotic regime will also be discussed. In addition we study the contributions to the leading order Lyapunov exponent for both time periodic and aperiodic states and find that while repeated dynamical events such as dislocation creation/annihilation and roll compression do contribute to the short time Lyapunov exponent dynamics, they do not contribute to the long time Lyapunov exponent. We find instead that nonrepeated events provide the most significant contribution to the long time leading order Lyapunov exponent.

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Additional Information:©2006 The American Physical Society (Received 1 March 2006; revised 12 October 2006; published 4 December 2006) The authors thank Paul Fischer and Anand Jayaraman for the use of their numerical code NEK5000, which was used for all simulations. They would like to thank Mark Paul, Keng-Hwee Chiam, and Henry Greenside for helpful discussions. This work was supported by the Engineering Research Program of the Office of Basic Energy Sciences at the Department of Energy, Grant Nos. DE-FG03-98ER14891 and DEFG02-98ER14892. The numerical code was run on the following supercomputing sites, whom the authors gratefully acknowledge: the National Energy Research Scientific Computing Center which is supported by the Office of Science of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098, the Center for Computational Sciences at Oak Ridge National Laboratory, which is supported by the Office of Science of the Department of Energy under Contract No. DE-AC05-00OR22725, “Jazz,” a 350-node computing cluster operated by the Mathematics and Computer Science Division at Argonne National Laboratory as part of its Laboratory Computing Resource Center, and the IBM “Blue Gene” system at the San Diego Supercomputing Center.
Subject Keywords:chaos; Rayleigh-Benard instability; convection
Issue or Number:6
Record Number:CaltechAUTHORS:SCHEpre06
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:6386
Deposited By: Archive Administrator
Deposited On:06 Dec 2006
Last Modified:02 Oct 2019 23:32

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