Ensemble Kalman Methods for Learning Closure Parameters

Reynolds-average Navier-Stokes simulations require closure models to estimate Reynolds stresses. These closure models often contain adjustable model parameters. Estimating these parameters is a key step in implementing accurate and effective closure models in simulations. We demonstrate how techniques in data assimilation can be used to determine the optimal values of these parameters. The test case we use is the minimal flow unit, a channel simulation that is considered to be the smallest domain to sustain turbulent structures. As such, it has become a common test case for algorithmic development. Recent efforts have shown that ensemble Kalman methods can accurately and efficiently estimate system states. These techniques typically utilize observations and an ensemble of model realizations, with the goal of optimally combining these two data streams. Specifically, a method called ensemble Kalman inversion has been developed to iteratively optimize model parameters. This method has primarily been utilized in atmospheric modeling, however, we will demonstrate how this technique can be applied to a Reynolds-stress closure.