Machine-learning energy-preserving nonlocal closures for turbulent fluid flows and inertial tracers

Alexis-Tzianni Charalampopoulos, Themistoklis Sapsis

Abstract: We formulate a data-driven, physics-constrained closure method for coarse-scale numerical simulations of turbulent fluid flows. Our approach involves a closure scheme that is nonlocal both in space and time, ie, the closure terms are parametrized in terms of the spatial neighborhood of the resolved quantities but also their history. The data-driven scheme is complemented with a physical constraint expressing the energy conservation property of the nonlinear advection terms. We show that the adoption of this physical constraint not only increases the accuracy of the closure scheme but also improves the stability properties of the formulated coarse-scale model. We demonstrate the presented scheme in fluid flows consisting of an incompressible two-dimensional turbulent jet. Specifically, we first develop one-dimensional coarse-scale models describing the spatial profile of the jet. We then proceed to the …