Analysis of nonlocality in turbulent Rayleigh-Taylor instability

Turbulent mixing caused by hydrodynamic instabilities such as Rayleigh-Taylor (RT) instability plays a crucial role in natural and engineering processes, such as supernovae and inertial confinement fusion (ICF). Reynolds-averaged Navier-Stokes (RANS) simulations are often employed to study turbulent mixing, and, in the context of ICF, to aid in the iterative design process. A main challenge with RANS is to determine models for unclosed terms. One such term is the turbulent species flux in the mean scalar transport equation. In this work, we approach this problem by directly measuring the scalar transport closure operator in numerical simulations using the Macroscopic Forcing Method (MFM) (Mani and Park, Phys. Rev. Fluids, 2021). Specifically, MFM allows us to determine the moments of the spatio-temporally nonlocal eddy diffusivity kernel. With this data, we determine the influence of nonlocality in modeling RT mixing and propose ways of incorporating this nonlocality into turbulent mixing models. By examining different Atwood cases, we also examine the effect of Atwood number on nonlocality. Finally, we demonstrate MFM as a tool to assess RANS model forms and assist in model selection.