Model for the structure function constant for index of refraction fluctuations in Rayleigh-Benard turbulence

TL;DR

This paper develops a theoretical model for the structure function constant related to index of refraction fluctuations in Rayleigh-Benard turbulence, supported by numerical simulations confirming its predictions.

Contribution

The paper introduces a new model linking the structure function constant to turbulence properties, assuming homogeneity, isotropy, and specific dissipation rates, with validation through simulations.

Findings

The normalized structure function constant is independent of Rayleigh number.

The model's predictions agree with numerical simulation results.

The model relates structure function to geometry, heat flux, and fluid properties.

Abstract

A model for the structure function constant associated with index of refraction fluctuations in Rayleigh-Benard turbulence is developed. The model is based upon the following assumptions: (1) the turbulence is homogeneous and isotropic at or near the mid-plane, (2) the rate of production is in balance with the rate of dissipation, (3) an inertial region exists, and (4) estimates for the rate of dissipation of temperature fluctuations and of turbulent kinetic energy can be made by assuming that the large-scale turbulence is dissipated in one eddy turnover time. From these assumptions, the dependence of the structure function on the geometry, heat flux, and the properties of the fluid is obtained. The model predicts that the normalized structure function constant is independent of the Rayleigh number. To verify the model, numerical simulations of Rayleigh-Benard turbulence were performed using two different approaches: an in-house code based on a pseudo-spectral method, and a finite volume code which employs a model for the smallest scales of the turbulence. The model was found to agree with the results of the simulations, thereby lending support for the assumptions underlying the theory.