High resolution numerical study of Rayleigh-Taylor turbulence using a thermal lattice Boltzmann scheme

TL;DR

This study uses high-resolution numerical simulations with a thermal lattice Boltzmann method to analyze 2D Rayleigh-Taylor turbulence, focusing on methodological accuracy and physical insights into scaling laws at high Rayleigh numbers.

Contribution

It introduces a high-resolution thermal lattice Boltzmann scheme for simulating 2D Rayleigh-Taylor turbulence and evaluates its stability, accuracy, and physical validity at high Rayleigh and Reynolds numbers.

Findings

Confirmation of Bolgiano-like inertial scaling in 2D turbulence

Identification of intermittency deviations in velocity and temperature scaling

Analysis of gradient flatness dependence on Rayleigh number

Abstract

We present results of a high resolution numerical study of two dimensional (2d) Rayleigh-Taylor turbulence using a recently proposed thermal lattice Boltzmann method (LBT). The goal of our study is both methodological and physical. We assess merits and limitations concerning small- and large-scale resolution/accuracy of the adopted integration scheme. We discuss quantitatively the requirements needed to keep the method stable and precise enough to simulate stratified and unstratified flows driven by thermal active fluctuations at high Rayleigh and high Reynolds numbers. We present data with spatial resolution up to 4096 x 10000 grid points and Rayleigh number up to Ra ~ 10^11 . The statistical quality of the data allows us to investigate velocity and temperature fluctuations, scale-by-scale, over roughly four decades. We present a detailed quantitative analysis of scaling laws in the viscous, inertial and integral range, supporting the existence of a Bolgiano-like inertial scaling, as expected in 2d systems. We also discuss the presence of small/large intermittent deviation to the scaling of velocity/temperature fluctuations and the Rayleigh dependency of gradients flatness.