🔹 Title: Data-based approach for time-correlated closures of turbulence models
🔹 Speaker: Julia Domingues Lemos (Federal University of Rio de Janeiro (UFRJ) School of Chemical and Biochemical Process Engineering)
🔹 Abstract:Developed turbulent motion of fluid still lacks an analytical description despite more than a century of active research. Nowadays phenomenological ideas are widely used in practical applications, such as small-scale closures for numerical simulations of turbulent flows. In the present work, we use a shell model of turbulence to construct a closure intended to have a solid theoretical background and to capture intrinsic probabilistic features of turbulence. Shell models of turbulence are dynamical deterministic systems used to model energy cascade and other key aspects of the Navier-Stokes equation. Some, such as the Sabra model, also present intermittency. We rescale the variables of the Sabra model in a way which leads to hidden symmetries and universal distributions. We then use such fine distributions to write closures, i.e., missing expressions for some of the Sabra variables. Our closures rely on approximating probability density functions using a Gaussian Mixture Model, which makes them probabilistic by nature and allows us to write time-correlated closures. We also provide a framework where other Machine Learning tools can be employed with reduced black-box aspects.