Selecting optimal state variables for the Rayleigh-Taylor transition to turbulence

We propose a state variable identification method relying on a Bayesian approach in order to model the Rayleigh-Taylor (RT) transition to turbulence. Neural networks are used to emulate a large data-set of RT direct numerical simulations determined by their initial conditions. Using this surrogate model and an efficient MCMC algorithm, we infer the perturbed initial interface from the knowledge of several state variable candidates. From the posterior probability distributions, we then assess the ability of given state variables to predict accurately the evolution of the mixing layer. It is shown that a reduced number of variables allows to model efficiently the RT transition to turbulence, enabling extensions of classical mixing models to capture it.