Mode-locking and chaos in Rayleigh-Bénard convection
type: Item
instance of: scholarly article
title: Mode-locking and chaos in Rayleigh-Bénard convection
zbMATH Open document ID: 0611.76062
DOI: 10.1016/0167-2789(87)90106-0
author: H. Haucke
author: Robert E. Ecke
published in: Physica D
publication date: 1987-01-01T00:00:00Z
review text: We have experimentally studied the transition to chaos in a thermally convecting dilute solution of \({}^ 3He\) in superfluid \({}^ 4He\). Two natural oscillatory instabilities are found in our geometry. Mode-locking is observed over a range of Rayleigh and Prandtl number. The mode-locking steps have a measured fractal dimension in good agreement with theoretical predictions and the larger steps show Farey tree ordering. Far below chaos many features of the measurements are suggestive of the circle map. We produce a one-dimensional map showing a tangent bifurcation to a mode- locked state. An effective phase angle change across a mode-locked step is calculated from the data. Close to chaos, hysteresis and other effects are suggestive of a two-dimensional map. The fractal dimension of the attractor is measured over a range of Rayleigh number close to the chaotic onset. Our Poincaré sections show the fractalization of the torus and are characterized by extremely high resolution.
Mathematics Subject Classification ID: 76E15
Mathematics Subject Classification ID: 76Y05
Mathematics Subject Classification ID: 81V99
Mathematics Subject Classification ID: 76M99
Mathematics Subject Classification ID: 76-04
Mathematics Subject Classification ID: 70K50
zbMATH DE Number: 3988957
zbMATH Keywords: transition to chaos
zbMATH Keywords: thermally convecting dilute solution
zbMATH Keywords: superfluid
zbMATH Keywords: natural oscillatory instabilities
zbMATH Keywords: Mode-locking
zbMATH Keywords: fractal dimension
zbMATH Keywords: Farey tree ordering
zbMATH Keywords: circle map
zbMATH Keywords: tangent bifurcation
zbMATH Keywords: mode-locked state
zbMATH Keywords: phase angle change
zbMATH Keywords: hysteresis
zbMATH Keywords: two-dimensional map
zbMATH Keywords: fractal dimension of the attractor
MaRDI profile type: Publication
full work available at URL: 0167-2789(87)90106-0
OpenAlex ID: W2069282976
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description: scientific article; zbMATH DE number 3988957