Dynamics of fluctuations in a fluid below the onset of Rayleigh-B\'enard convection

TL;DR

This study combines experimental measurements and theoretical analysis to investigate the decay rates of temperature fluctuations in a fluid near the critical point, just below the onset of Rayleigh-Bénard convection, revealing critical slowing-down and matching predictions with data.

Contribution

It provides a new theoretical expression for the exposure-time-dependent structure factor and compares it with experimental data near the convection threshold.

Findings

Decay rates increase as convection onset is approached.

Quantitative agreement achieved with theoretical predictions after accounting for uncertainties.

Critical slowing-down observed in fluctuation decay near bifurcation.

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-B\'enard 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.