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Extensive chaos in Rayleigh-Bénard convection

Paul, M. R. and Einarsson, M. I. and Fischer, P. F. and Cross, M. C. (2007) Extensive chaos in Rayleigh-Bénard convection. Physical Review E, 75 (4). Art. No. 045203(R). ISSN 1539-3755. doi:10.1103/PhysRevE.75.045203.

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Using large-scale numerical calculations we explore spatiotemporal chaos in Rayleigh-Bénard convection for experimentally relevant conditions. We calculate the spectrum of Lyapunov exponents and the Lyapunov dimension describing the chaotic dynamics of the convective fluid layer at constant thermal driving over a range of finite system sizes. Our results reveal that the dynamics of fluid convection is truly chaotic for experimental conditions as illustrated by a positive leading-order Lyapunov exponent. We also find the chaos to be extensive over the range of finite-sized systems investigated as indicated by a linear scaling between the Lyapunov dimension of the chaotic attractor and the system size.

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Additional Information:©2007 The American Physical Society (Received 15 August 2006; published 26 April 2007) We are grateful for many useful interactions with Janet Scheel and Anand Jayaraman. We also acknowledge generous support from Argonne National Laboratory under DOE Contract No. DE-AC02-06CH11357, NSF Teragrid under Grant No. MCA03T028, and Virginia Tech’s Terascale Computing Facility for grants of supercomputing resources. The early stages of this research was supported by the U.S. Department of Energy, Grant No. DE-FT02-98ER14892.
Subject Keywords:Benard convection; Rayleigh-Benard instability; chaos; spatiotemporal phenomena; flow simulation; Lyapunov methods
Issue or Number:4
Record Number:CaltechAUTHORS:PAUpre07a
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:8552
Deposited By: Archive Administrator
Deposited On:20 Aug 2007
Last Modified:08 Nov 2021 20:51

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