We start with a brief look at how fluid flow can be described using a hierarchy of models of different complexities. Next, we consider modeling of turbulent flows at two levels of the hierarchy and pose a practical question of how a model of lower complexity can be improved given simulations of the same flow that better resolves some of the relevant processes. The specific context of buoyancy-driven, variable-density turbulence is chosen for illustration. In this context a Reynolds-stress turbulence closure model is considered and analyzed given a few "fully-resolved" Direct Numerical Simulations (DNS) of the flow. The task of improving the closure model is currently the domain of turbulence modeling experts. Are there alternatives? Computational?
There are a number of coefficients in the closure model associated with various turbulent processes. Traditional approaches to calibrating such coefficients are presented and their shortcomings discussed. We then go on to demonstrate the potential of hierarchical Bayesian analysis to uncover previously unanticipated physical dependencies in the closure model---something that point estimates fail to do, and how such insights can then be used to improve the model. In effect parametric dependencies found from the Bayesian analysis are used to improve structural aspects of the model. This idea has wide applicability. Time permitting, related issues and other applications will be considered.