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Dynamics of fluctuations in a fluid below the onset of Rayleigh-Bénard convection

Jaechul Oh1, José M. Ortiz de Zárate2, Jan V. Sengers3, and Guenter Ahlers1

  • 1Department of Physics and iQUEST, University of California, Santa Barbara, California 93106, USA
  • 2Departamento de Física Aplicada I, Facultad de Física, Universidad Complutense, 28040 Madrid, Spain
  • 3Institute for Physical Science and Technology, and Departments of Chemical Engineering and Mechanical Engineering, University of Maryland, College Park, Maryland 20742, USA

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Phys. Rev. E 69, 021106 – Published 23 February, 2004

DOI: https://doi.org/10.1103/PhysRevE.69.021106

Abstract

We present experimental data and their theoretical interpretation for the decay rates of temperature fluctuations in a thin layer of a fluid heated from below and confined between parallel horizontal plates. The measurements were made with the mean temperature of the layer corresponding to the critical isochore of sulfur hexafluoride above but near the critical point where fluctuations are exceptionally strong. They cover a wide range of temperature gradients below the onset of Rayleigh-Bénard convection, and span wave numbers on both sides of the critical value for this onset. The decay rates were determined from experimental shadowgraph images of the fluctuations at several camera exposure times. We present a theoretical expression for an exposure-time-dependent structure factor which is needed for the data analysis. As the onset of convection is approached, the data reveal the critical slowing down associated with the bifurcation. Theoretical predictions for the decay rates as a function of the wave number and temperature gradient are presented and compared with the experimental data. Quantitative agreement is obtained if allowance is made for some uncertainty in the small spacing between the plates, and when an empirical estimate is employed for the influence of symmetric deviations from the Oberbeck-Boussinesq approximation which are to be expected in a fluid with its density at the mean temperature located on the critical isochore.

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Phys. Rev. E 69, 021106– Published 23 February, 2004
  • Received 1 September 2003

© 2004 American Physical Society

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