Learning Turbulence Closures with Physics-Informed Neural Networks for the Rayleigh-Taylor Transition to Turbulence

Abstract

Reynolds-averaged Navier-Stokes (RANS) turbulence models are known to perform poorly in predicting the dynamics of Rayleigh-Taylor mixing when turbulence is not fully developed, particularly during the transition from an initially perturbed interface. In this work, we investigate the use of data-driven strategies to enhance a simple $k$-$\varepsilon$-$b$ model for this transitional regime. The turbulence model is first embedded within a surrogate physics-informed neural network (PINN), enabling the calibration of coefficients that account for parametric errors and the identification of corrective terms representing structural errors associated with missing physical processes. The learned corrections are then re-expressed onto the model state variables and relevant flow indicators, leading to explicit analytical modifications of the closure. The resulting fully interpretable corrected model is assessed against an extensive database of direct numerical simulations (DNS) of Rayleigh-Taylor flows. This framework enables improved predictions of the mixing-layer growth during the transition to turbulence.