A model of diffusion in a potential well for the dynamics of the large-scale circulation in turbulent Rayleigh-Benard convection

TL;DR

This paper presents a stochastic model of the large-scale circulation in turbulent Rayleigh-Benard convection, validated by experiments, capturing key dynamics and probability distributions, with some limitations in tail behavior prediction.

Contribution

The paper introduces a coupled stochastic differential equation model for LSC dynamics, validated by experimental data, linking turbulence-induced noise to large-scale flow behavior.

Findings

Model accurately predicts the two main time scales of LSC dynamics.

Scaling law between temperature amplitude and Reynolds number is confirmed.

Probability distributions of flow orientation and amplitude are well described by the model.

Abstract

Experimental measurements of properties of the large-scale circulation (LSC) in turbulent convection of a fluid heated from below in a cylindrical container of aspect ratio one are presented and used to test a model of diffusion in a potential well for the LSC. The model consists of a pair of stochastic ordinary differential equations motivated by the Navier-Stokes equations. The two coupled equations are for the azimuthal orientation theta_0, and for the azimuthal temperature amplitude delta at the horizontal midplane. The dynamics is due to the driving by Gaussian distributed white noise that is introduced to represent the action of the small-scale turbulent fluctuations on the large-scale flow. Measurements of the diffusivities that determine the noise intensities are reported. Two time scales predicted by the model are found to be within a factor of two or so of corresponding experimental measurements. A scaling relationship predicted by the model between delta and the Reynolds number is confirmed by measurements over a large experimental parameter range. The Gaussian peaks of probability distributions p(delta) and p(\dot\theta_0) are accurately described by the model; however the non-Gaussian tails of p(delta) are not. The frequency, angular change, and amplitude bahavior during cessations are accurately described by the model when the tails of the probability distribution of $\delta$ are used as experimental input.