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

This work sheds light on the influence of initial conditions in Boussinesq

Rayleigh-Taylor turbulence. It builds on the related paper from Thévenin

et al. (Journal of Fluid Mechanics, 2025 [63]), 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 numer-

ical 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 condi-

tions. Particular emphasis is placed on the virtual time origin, which is shown

to strongly vary with the initial Reynolds, perturbation steepness and band-

width 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.