Towards Leveraging Machine Learning and Other Statistical Methods To Improve Turbulence Modeling

Notwithstanding the on-going explosive growth in computational capabilities, coarse-grained
descriptions of turbulent flows such as the Reynolds-Averaged Navier Stokes (RANS) continue
to remain the workhorse for industrial and commercial applications. Nevertheless,
highly-resolved simulations of complex flows and Direct Numerical Simulations (DNS) of a
subset of such flows are increasingly commonplace. As such we are working towards leveraging
machine learning and other statistical tools in the development of coarse-grained models. In one
example, we demonstrate how Bayesian analysis of a Reynolds stress model (RSM) in
conjunction with DNS of a flow driven by (homogeneous) Rayleigh-Taylor instability helped us
identify a deficiency in the RSM. We then proceed to demostrate how such analysis also
provides a means to quantify uncertainty that is inherent in the RANS approach. Time
permitting, other examples and results will be presented.