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Measuring the departures from the Boussinesq approximation in Rayleigh–Bénard convection experiments

Published online by Cambridge University Press:  22 July 2011

H. KURTULDU ,
K. MISCHAIKOW  and
M. F. SCHATZ
H. KURTULDU
Affiliation:
Center for Nonlinear Science and School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA
K. MISCHAIKOW
Affiliation:
Department of Mathematics, Rutgers University, Piscataway, NJ 08854, USA
M. F. SCHATZ*
Affiliation:
Center for Nonlinear Science and School of Physics, Georgia Institute of Technology, Atlanta, GA 30332, USA
*
†Email address for correspondence: michael.schatz@physics.gatech.edu
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Abstract

Algebraic topology (homology) is used to characterize quantitatively non-Oberbeck–Boussinesq (NOB) effects in chaotic Rayleigh–Bénard convection patterns from laboratory experiments. For fixed parameter values, homology analysis yields a set of Betti numbers that can be assigned to hot upflow and, separately, to cold downflow in a convection pattern. An analysis of data acquired under a range of experimental conditions where NOB effects are systematically varied indicates that the difference between time-averaged Betti numbers for hot and cold flows can be used as an order parameter to measure the strength of NOB-induced pattern asymmetries. This homology-based measure not only reveals NOB effects that Fourier methods and measurements of pattern curvature fail to detect, but also permits distinguishing pattern changes caused by modified lateral boundary conditions from NOB pattern changes. These results suggest a new approach to characterizing data from either experiments or simulations where NOB effects are expected to play an important role.

JFM classification

Convection: Buoyancy-driven instability Nonlinear Dynamical Systems: Pattern formation

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Papers
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Journal of Fluid Mechanics , Volume 682 , 10 September 2011 , pp. 543 - 557
Copyright
Copyright © Cambridge University Press 2011

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