Data-enabled discovery of specific and generalizable turbulence closures*

Turbulence closures are critical for the predictive modeling of fluid flows in both natural and engineering contexts. We address this generalizability issue in the context of symbolic regression. A critical aspect of our work is distinguishing between flow physics that is specific to the training data and those that are generalizable, the former of which must be removed or replaced when applying the closure beyond the training dataset. By progressively training on increasingly complex flows, we successively incorporate inner-layer physics, outer-layer physics, and pressure gradient physics into the closures. The resulting models are validated against a wide range of flows, most of which are outside the training dataset, and the results are highly favorable. This work enables the discovery of data-specific and generalizable turbulence closures,  addressing the generalizability issue and leading to truly predictive modeling of fluid flows using machine-learning.