On the role of thermal fluctuations in Rayleigh–Taylor mixing

Abstract

We study the significance of thermal fluctuations in fluid mixing that is induced by the Rayleigh–Taylor instability (RTI) using numerical solutions of the fluctuating compressible Navier–Stokes equations. Our results indicate that thermal fluctuations can trigger the onset of RTI at an initially unperturbed fluid–fluid interface and lead to mixing of multi-mode character with growth rates of αs = 0.035 and αb = 0.023 for the spikes and bubbles, respectively. In addition, we find that whether or not thermal fluctuations quantitatively affect the mixing behavior, depends on the magnitude of the dimensionless Boltzmann number of the system, and not solely on its size. When the Boltzmann number is much smaller than unity, the quantitative effect of thermal fluctuations on the mixing behavior is negligible and the behavior is the average of the outcome from several stochastic instances, with the ensemble of stochastic instances providing bounds on behavior. When the Boltzmann number is of order unity, we find that thermal fluctuations can significantly affect the mixing behavior; the ensemble-averaged solution shows a departure from the deterministic solution at late times. We conclude that for such systems, it is important to account for thermal fluctuations in order to correctly capture their physical behavior.