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A model for the structure function constant associated with index ofrefraction fluctuations in Rayleigh-Benard turbulence is developed. The modelis based upon the following assumptions: (1) the turbulence is homogeneous andisotropic at or near the mid-plane, (2) the rate of production is in balancewith the rate of dissipation, (3) an inertial region exists, and (4) estimatesfor the rate of dissipation of temperature fluctuations and of turbulentkinetic energy can be made by assuming that the large-scale turbulence isdissipated in one eddy turnover time. From these assumptions, the dependence ofthe structure function on the geometry, heat flux, and the properties of thefluid is obtained. The model predicts that the normalized structure functionconstant is independent of the Rayleigh number. To verify the model, numericalsimulations of Rayleigh-Benard turbulence were performed using two differentapproaches: an in-house code based on a pseudo-spectral method, and a finitevolume code which employs a model for the smallest scales of the turbulence.The model was found to agree with the results of the simulations, therebylending support for the assumptions underlying the theory.

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