E Aurell et al 1997 J. Phys. A: Math. Gen. 30 1 doi:10.1088/0305-4470/30/1/003
Predictability in the large: an extension of the concept of Lyapunov exponent
E Aurell
, G Boffetta
, A Crisanti§, G Paladin¶ and A Vulpiani||
We investigate the predictability problem in dynamical systems with many degrees of freedom and a wide spectrum of temporal scales. In particular, we study the case of three-dimensional turbulence at high Reynolds numbers by introducing a finite-size Lyapunov exponent which measures the growth rate of finite-size perturbations. For sufficiently small perturbations this quantity coincides with the usual Lyapunov exponent. When the perturbation is still small compared to large-scale fluctuations, but large compared to fluctuations at the smallest dynamically active scales, the finite-size Lyapunov exponent is inversely proportional to the square of the perturbation size. Our results are supported by numerical experiments on shell models. We find that intermittency corrections do not change the scaling law of predictability. We also discuss the relation between the finite-size Lyapunov exponent and information entropy.
- PACS
- MSC
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76F20 Dynamical systems approach to turbulence (See also 37-XX)
- Subjects
- Dates
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Issue 1 (7 January 1997)
Received 8 July 1996, in final form 10 September 1996
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Predictability in the large: an extension of the concept of Lyapunov exponent
E Aurell et al 1997 J. Phys. A: Math. Gen. 30 1
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