Modeling late-time sensitivity to initial conditions in Boussinesq Rayleigh–Taylor turbulence

This article sheds light on the influence of initial conditions in Boussinesq Rayleigh–Taylor turbulence. It builds on the related paper from Thévenin et al. (2025), which introduces a physics-informed neural network that effectively extrapolates the dynamics to very late times and unseen initial conditions, beyond the reach of direct numerical simulations. The present paper focuses on the self-similar regime and combines machine learning, variance-based sensitivity analysis and theory to provide a robust understanding of the late-time dependency on initial conditions. Particular emphasis is placed on the virtual time origin, which is shown to strongly vary with the initial Reynolds, perturbation steepness and bandwidth numbers. We develop an analytical model based on the phenomenology of Rayleigh–Taylor mixing layers to explain most of this dependency and give accurate predictions of the virtual time origin. It turns out that when the initial perturbation reaches nonlinear saturation earlier, the mixing layer also re-accelerates earlier, while the virtual time origin is larger.