Multi-scale dynamics of scalar transfer in Rayleigh–Taylor turbulent mixing

Miscible Rayleigh–Taylor (RT) turbulence exhibits a wide range of length scales in both the velocity and density fields, leading to complex deformations of isoscalar surfaces and enhanced mixing due to nonlinear interactions among different scales. Through high-resolution numerical simulations and a coarse-graining analysis, we demonstrate that the variance of the heavy fluid concentration, initially maximised by the unstable stratification, progressively cascades from larger to smaller scales, eventually dissipates at the smallest scale. The transfer of scalar variance, $\Pi ^Y$ , primarily governed by the filtered strain rate tensor, is effectively captured by a nonlinear model that links $\Pi ^Y$ to the isoscalar surface stretching. On the other hand, the backscatter of scalar variance transfer, represented by the negative component of $\Pi ^Y$ , is influenced by the filtered vorticity field. Furthermore, we examine the directional anisotropy of scalar transfer in RT turbulence, enhancing the accuracy of the nonlinear model by separating the horizontal mean of the mass fraction from its fluctuating part.