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

Abstract

We present the results of a high resolution numerical study of two-dimensional (2D) Rayleigh–Taylor turbulence using a recently proposed thermal lattice Boltzmann method. 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 4096×10 000 grid points and Rayleigh number up to Ra∼1011. 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 deviations to the scaling of velocity/temperature fluctuations and the Rayleigh dependency of gradients flatness.