A computational study of Rayleigh-Bénard convection. II: Dimension considerations. (English) Zbl 0717.76048
Summary: [For part I, see the review above Zbl 0717.76047).]
A study is made of the number of dimensions needed to specify chaotic Rayleigh-Bénard convection, over a range of Rayleigh numbers \((\gamma =Ra/Ra_ c<10^ 2)\). 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 \(O(Ra^{2/3})\), which is sharper than previous results.
A study is made of the number of dimensions needed to specify chaotic Rayleigh-Bénard convection, over a range of Rayleigh numbers \((\gamma =Ra/Ra_ c<10^ 2)\). 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 \(O(Ra^{2/3})\), which is sharper than previous results.
MSC:
| 76E15 | Absolute and convective instability and stability in hydrodynamic stability |
| 76M35 | Stochastic analysis applied to problems in fluid mechanics |
Citations:
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