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On using extreme values to detect global stability thresholds in multi-stable systems: the case of transitional plane Couette flow

Faranda, D., Lucarini, V., Manneville, P. and Wouters, J. (2014) On using extreme values to detect global stability thresholds in multi-stable systems: the case of transitional plane Couette flow. Chaos Solitons & Fractals, 64. 26 - 35. ISSN 0960-0779

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To link to this item DOI: 10.1016/j.chaos.2014.01.008

Abstract/Summary

Extreme Value Theory (EVT) is exploited to determine the global stability threshold Rg of plane Couette flow ‚ the flow of a viscous fluid in the space between two parallel plates ‚ whose laminar or turbulent behavior depends on the Reynolds number R. Even if the existence of a global stability threshold has been detected in simulations and experiments, its numerical value has not been unequivocally defined. Rg is the value such that for R>Rg, turbulence is sustained, whereas for R<Rg it is transient and eventually decays. We address the problem of determining Rg by using the extremes - maxima and minima - of the perturbation energy fluctuations. When R >>Rg, both the positive and negative extremes are bounded. As the critical Reynolds number is approached from above, the probability of observing a very low minimum increases causing asymmetries in the distributions of maxima and minima. On the other hand, the maxima distribution is unaffected as the fluctuations towards higher values of the perturbation energy remain bounded. This tipping point can be detected by fitting the data to the Generalized Extreme Value (GEV) distribution and by identifying Rg as the value of R such that the shape parameter of the GEV for the minima changes sign from negative to positive. The results are supported by the analysis of theoretical models which feature a bistable behavior.

Item Type:Article
Refereed:Yes
Divisions:Faculty of Science > School of Mathematical, Physical and Computational Sciences > Department of Mathematics and Statistics
ID Code:71522
Additional Information:Nonequilibrium Statistical Mechanics: Fluctuations and Response
Publisher:Elsevier

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