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The influence of thermal noise on the onset of travelling-wave convection in binary fluid mixtures: an experimental investigation

Published online by Cambridge University Press:  26 April 2006

Wolfgang Schöpf  and
Ingo Rehberg
Wolfgang Schöpf
Affiliation:
Physikalisches Institut der Universität Bayreuth, 95440 Bayreuth, Germany Present address: Centre for Water Research, University of Western Australia, Nedlands WA 6009, Australia
Ingo Rehberg
Affiliation:
Physikalisches Institut der Universität Bayreuth, 95440 Bayreuth, Germany
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Abstract

When dealing with systems showing a Hopf bifurcation as the first instability from a conductive state leading to travelling waves, the distinction between convective and absolute instability becomes significant. The convectively unstable regime is characterized by the fact that a homogeneous disturbance may have a positive growth rate, while a single localized perturbation cannot trigger the onset of nonlinear convection. In this paper the convective instability occurring in binary fluid mixtures for a negative separation ratio is utilized for amplifying intrinsic thermal fluctuations, which in this way become accessible to quantitative measurements. The experiments are performed in a quasi-one-dimensional convection channel which, by means of subcritical ramps, effectively prevents the reflection of the travelling waves from the sidewalls. Thus, that range of the convective instability within which linear waves can be observed is strongly enhanced. The temperature variations involved in the observed travelling-wave states are quantified by using the shadowgraph method. By resonantly stimulating the system with its linear Hopf frequency, the reflection ability and some coefficients of the amplitude equation appropriate for describing the convection features near onset can be determined. Without stimulation, travelling-wave states of very small amplitudes showing an erratic spatio-temporal behaviour occur spontaneously inside the convectively unstable regime. The temporal correlation function calculated from the measured light intensity caused by these states is compared with a theoretical expression obtained from a Ginzburg—Landau equation containing a noise term. A very good agreement is found for the amplitude if thermal noise is assumed to be the reason for these fluctuating convection rolls, thus supporting the idea that the response of the system to thermal fluctuations is observed.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 271 , 25 July 1994 , pp. 235 - 265
Copyright
© 1994 Cambridge University Press

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