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Circuit bounds on stochastic transport in the Lorenz equations
KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Yale University, New Haven, United States.
2018 (English)In: Physics Letters A, ISSN 0375-9601, E-ISSN 1873-2429, Vol. 382, no 26, p. 1731-1737Article in journal (Refereed) Published
Abstract [en]

In turbulent Rayleigh–Bénard convection one seeks the relationship between the heat transport, captured by the Nusselt number, and the temperature drop across the convecting layer, captured by the Rayleigh number. In experiments, one measures the Nusselt number for a given Rayleigh number, and the question of how close that value is to the maximal transport is a key prediction of variational fluid mechanics in the form of an upper bound. The Lorenz equations have traditionally been studied as a simplified model of turbulent Rayleigh–Bénard convection, and hence it is natural to investigate their upper bounds, which has previously been done numerically and analytically, but they are not as easily accessible in an experimental context. Here we describe a specially built circuit that is the experimental analogue of the Lorenz equations and compare its output to the recently determined upper bounds of the stochastic Lorenz equations [1]. The circuit is substantially more efficient than computational solutions, and hence we can more easily examine the system. Because of offsets that appear naturally in the circuit, we are motivated to study unique bifurcation phenomena that arise as a result. Namely, for a given Rayleigh number, we find a reentrant behavior of the transport on noise amplitude and this varies with Rayleigh number passing from the homoclinic to the Hopf bifurcation.

Place, publisher, year, edition, pages
Elsevier, 2018. Vol. 382, no 26, p. 1731-1737
Keywords [en]
Chaotic dynamics, Circuit model, Lorenz equations, Stochastic upper bounds
National Category
Physical Sciences
Identifiers
URN: urn:nbn:se:kth:diva-228720DOI: 10.1016/j.physleta.2018.04.035ISI: 000433646600005Scopus ID: 2-s2.0-85046641736OAI: oai:DiVA.org:kth-228720DiVA, id: diva2:1211021
Funder
Swedish Research Council, 638-2013-9243
Note

QC 20180530

Available from: 2018-05-30 Created: 2018-05-30 Last updated: 2018-06-19Bibliographically approved

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Wettlaufer, John S.
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