Two-point description of two-fluid turbulent mixing—I. Model formulation

What is certain and what is not so certain in our knowledge of Rayleigh–Taylor mixing?

“…These models served to quantitatively describe RT mixing and calibrate experimental and numerical data. The other set of modelling efforts is represented by turbulence models [46,50,65,66,[85][86][87][88][89][90][91]. Presuming that RT mixing is a process somewhat similar to isotropic turbulence, these models considered RT mixing within the general context of turbulent flows and served for development of the stateof-the-art numerical methods.…”

Two-point spectral model for variable-density homogeneous turbulence

“…We will follow the development proposed for singlefluid incompressible flow by Besnard et al [20], and subsequently adapted for variable-density flow by [21,22]. We first decompose the flow field variables, i.e., density ρ, velocity u, and pressure p into their mean and fluctuating parts as follows:…”

“…Based on the diffusion approximation model proposed by Leith [28], we model these triple correlation terms as nonlinear advection and diffusion in k space [20,26,28]. We modify Steinkamp's set of equations for statistically homogeneous variable-density flow, keeping the gravity direction same, and arrive at the following set of equations [21,22]:…”

“…The cascade terms for R nn and a y in Eqs. (17) and (18) respectively are written in an analogous manner [21]. The drag between the fluids is described in the mass-flux equation (18) by the second term on the RHS.…”

“…In this paper, we work with a two-point spectral closure model for constant-density turbulent flow originally developed in [20], and modified in [21,22] for variable density flows. The advantage of a model based on twopoint correlations is it's ability to capture the evolution of scales with time.…”