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A computational study of Rayleigh–Bénard convection. Part 2. Dimension considerations

Published online by Cambridge University Press:  26 April 2006

Lawrence Sirovich  and
Anil E. Deane
Lawrence Sirovich
Affiliation:
Center for Fluid Mechanics and The Division of Applied Mathematics, Brown University, Providence, RI 02912, USA
Anil E. Deane
Affiliation:
Center for Fluid Mechanics and The Division of Applied Mathematics, Brown University, Providence, RI 02912, USA Present address: Applied and Computational Mathematics, Princeton University, Princeton, NJ 08544, USA
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Abstract

A study is made of the number of dimensions needed to specify chaotic Rayleigh–Bénard convection, over a range of Rayleigh numbers (γ = Ra/Rac < 102). This is based on the calculation of Lyapunov dimension over the range, as well as the notion of Karhunen–Loéve dimension. An argument suggesting a universal relation between these estimates and supporting numerical evidence is presented. Numerical evidence is also presented that the reciprocal of the largest Lyapunov exponent and the correlation time are of the same order of magnitude. Several other universal features are suggested. In particular it is suggested that the intrinsic attractor dimension is $O(Ra^{\frac{2}{3}})$, which is sharper than previous results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 222 , January 1991 , pp. 251 - 265
Copyright
© 1991 Cambridge University Press

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