Data-Driven Low-Order Modeling of the Rayleigh-Taylor Transition to Turbulence

We consider a data-driven, low-order modeling approach to the Rayleigh-Taylor (RT) transition to turbulence. Towards this, a suite of Direct Numerical Simulations (DNS) of low Atwood number RT flows was performed. This dataset was parametrized by four non-dimensional quantities characterizing the initial conditions and emphasizing the inertial and diffusive regimes of growth of the mixing region.

A related talk in this session presents results on a Bayesian approach to inferring the initial conditions (IC) using a neural network trained to map IC and time to a handful of domain-averaged scalars that characterize the instantaneous state of the system---length of the mixing zone, turbulent kinetic energy and dissipation and others.

In this talk, we pursue the analysis further by considering data-driven modeling of the dynamical evolution and transition to turbulence in the suite of RT simulations.

While we are ultimately interested in developing improved mix-models, here we present preliminary results on modeling the dynamical evolution of the same set of domain-averaged scalars using a variety of methods ranging from neural-ODEs to attention mechanisms. We expect that further data-driven modeling of the residual with respect to state of the art RANS models will lead to such improved mix models.