Data-based approach for time-correlated closures of turbulence models.

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 paper, 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 such as 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.

Validation and application of the lattice Boltzmann algorithm for a turbulent immiscible Rayleigh-Taylor system.

We develop a multicomponent lattice Boltzmann (LB) model for the two-dimensional Rayleigh-Taylor turbulence with a Shan-Chen pseudopotential implemented on GPUs. In the immiscible case, this method is able to accurately overcome the inherent numerical complexity caused by the complicated structure of the interface that appears in the fully developed turbulent regime. The accuracy of the LB model is tested both for early and late stages of instability. For the developed turbulent motion, we analyse the balance between different terms describing variations of the kinetic and potential energies. Then we analyse the role of the interface in the energy balance and also the effects of the vorticity induced by the interface in the energy dissipation. Statistical properties are compared for miscible and immiscible flows. Our results can also be considered as a first validation step to extend the application of LB model to three-dimensional immiscible Rayleigh-Taylor turbulence. This article is part of the theme issue 'Progress in mesoscale methods for fluid dynamics simulation'.