  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.
