Nonlocality of Mean Scalar Transport in Two-Dimensional Rayleigh-Taylor Instability Using the Macroscopic Forcing Method

TL;DR

This paper investigates the nonlocal effects in mean scalar transport within 2D Rayleigh-Taylor Instability using the Macroscopic Forcing Method, revealing that higher-order moments are essential for accurate modeling.

Contribution

It introduces a novel approach to quantify nonlocality in RTI scalar transport by measuring higher-order moments of the eddy diffusivity kernel with MFM.

Findings

Purely local eddy diffusivity models are inadequate for RTI.

Higher-order moments significantly improve model accuracy.

Implicit operator models outperform explicit Kramers-Moyal expansions.

Abstract

The importance of nonlocality of mean scalar transport in 2D Rayleigh-Taylor Instability (RTI) is investigated. The Macroscopic Forcing Method (MFM) is utilized to measure spatio-temporal moments of the eddy diffusivity kernel representing passive scalar transport in the ensemble averaged fields. Presented in this work are several studies assessing the importance of the higher-order moments of the eddy diffusivity, which contain information about nonlocality, in models for RTI. First, it is demonstrated through a comparison of leading-order models that a purely local eddy diffusivity is insufficient in capturing the mean field evolution of the mass fraction in RTI. Therefore, higher-order moments of the eddy diffusivity operator are not negligible. Models are then constructed by utilizing the measured higher-order moments. It is demonstrated that an explicit operator based on the Kramers-Moyal expansion of the eddy diffusivity kernel is insufficient. An implicit operator construction that matches the measured moments is shown to offer improvements relative to the local model in a converging fashion.