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Maximal stochastic transport in the Lorenz equations
Stockholm University, Nordic Institute for Theoretical Physics (Nordita). Yale University, USA; University of Oxford, UK.
Number of Authors: 2
2016 (English)In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 380, no 1-2, 142-146 p.Article in journal (Refereed) Published
Abstract [en]

We calculate the stochastic upper bounds for the Lorenz equations using an extension of the background method. In analogy with Rayleigh-Benard convection the upper bounds are for heat transport versus Rayleigh number. As might be expected, the stochastic upper bounds are larger than the deterministic counterpart of Souza and Doering [1], but their variation with noise amplitude exhibits interesting behavior. Below the transition to chaotic dynamics the upper bounds increase monotonically with noise amplitude. However, in the chaotic regime this monotonicity depends on the number of realizations in the ensemble; at a particular Rayleigh number the bound may increase or decrease with noise amplitude. The origin of this behavior is the coupling between the noise and unstable periodic orbits, the degree of which depends on the degree to which the ensemble represents the ergodic set. This is confirmed by examining the close returns plots of the full solutions to the stochastic equations and the numerical convergence of the noise correlations. The numerical convergence of both the ensemble and time averages of the noise correlations is sufficiently slow that it is the limiting aspect of the realization of these bounds. Finally, we note that the full solutions of the stochastic equations demonstrate that the effect of noise is equivalent to the effect of chaos.

Place, publisher, year, edition, pages
2016. Vol. 380, no 1-2, 142-146 p.
Keyword [en]
Lorenz equations, Rayleigh-Benard convection, Heat transport, Stochastic dynamics, Upper bounds
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:su:diva-125635DOI: 10.1016/j.physleta.2015.09.046ISI: 000365365300021OAI: oai:DiVA.org:su-125635DiVA: diva2:895533
Available from: 2016-01-19 Created: 2016-01-15 Last updated: 2016-01-19Bibliographically approved

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Wettlaufer, John S.
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Nordic Institute for Theoretical Physics (Nordita)
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