Thermal-Noise Effect on the Transition to Rayleigh-Bénard Convection

Abstract

We report measurements of fluctuation and roll patterns near the transition to Rayleigh-Bénard convection which are consistent with a fluctuation-induced first-order transition, as predicted by Swift and Hohenberg. Above onset, we find convection rolls with noise-induced fluctuations, time-dependent amplitude modulation and roll undulation, and homogeneous dislocation nucleation.

Onset of patterns in an oscillated granular layer: Continuum and molecular dynamics simulations

“…The value determined in an experiment for a slightly shallower granular layer at f * = 0.28 was F = 3.5 × 10 −3 [24], which is within the range of noise values obtained in this investigation. The smallest noise strength found for our granular system is comparable to the largest noise strength found thus far in experiments in ordinary fluids, which obtained F = 7.1 × 10 −4 in measurements near the critical point, while values typical for convection are closer to 10 −9 [23]. For f * = 0.4174, the noise is strong enough to delay onset of long range patterns by 10% in MD simulation, and influences strongly the behavior of the system even more than 20% below this onset.…”

“…These fluctuations are described by the addition of terms to the Navier-Stokes equations; this theory is known as fluctuating hydrodynamics [18,19,20]. Recent experiments have shown that fluctuating hydrodynamics theory accurately describes the dynamics of fluids near the onset of convection [21,22,23].…”

Thermal Fluctuations in a Layer of LiquidCS2Subjected to Temperature Gradients with and without the Influence of Gravity

“…Fluctuations below the onset of convection have also been measured [12], but experimental factors limit the accuracy and/or comparison with theory. For such systems, the transition to convection is made first-order by the fluctuations [13], as predicted by Swift and Hohenberg [14]. Recent measurements [15] of the dynamic structure factor S(q,ω ) revealed line shapes consistent with theory, but were not made in absolute terms.…”

Phase diagram of vertically shaken granular matter

“…In both cases the onset of convection is caused by a set of particles in the cluster that are more mobile (higher granular temperature) than the surrounding area, creating an opening in the bed. These particles have picked up an excess of energy from the vibrating bottom (due to a statistical fluctuation) and collectively move upwards, very much like the onset of Rayleigh-Bénard convection in a classical fluid heated from below [37,38,39,40,41,42,43]. This upward motion of the highly mobile beads must be balanced by a downward movement of neighboring particles, leading to the formation of a convection roll.…”