Inter-scale transfer of the large-scale background anisotropy under periodic conditions

C H Wang,J Z Wu,J Zhang

doi:10.1063/1.5055651

Abstract

In numerical simulations of three-dimensional isotropy turbulence, low-wave-number truncation leads to large-scale anisotropy, but little anisotropy is generated at small scales. As the generally accepted energy cascade theory suggests an energy transfer from large to small scale, we phenomenally guess that an inter-scale anisotropy evolution might occur in the energy transfer process. With analyses in Kolmogorov’s equation and DNS validations, we demonstrate that the large-scale anisotropy is effectively transferred by convective effect, but this anisotropy is then diminished at small scales by viscous dissipation. The inter-scale anisotropy transfer process is synchronised with the inter-scale energy transfer. Time evolution of anisotropy distribution is then investigated in free-decaying, forced and non-equilibrium isotropic turbulence. It is shown that the anisotropy distribution remains stationary if the shape of energy spectrum does not change. The objective of this work is to provide a theoretical and numerical support for the further study on anisotropy correction in post-processing results.

Highlights

Nowadays the turbulence communities are tending to study towards more and more complex turbulence flow, homogeneous isotropic turbulence (HIT) still holds a key position in understanding the fundamental mechanism of turbulence and serves as the basic framework for turbulence modeling
The numerical methods for generating three-dimensional homogeneous isotropic turbulence often base on a Fourier-based discretized field with the involvement of three-dimensional periodic conditions.[1,2,3,4,5,6,7,8,9]
With T = 0, 1, 2 denoting three successive time steps, we present in Figs. 2–4 the time evolution of hemispherical surface average and its coefficient of variation representing anisotropy distribution, defined in Eq (2) and Eq (1), for Dii(r, t) in the three cases above

Summary

Introduction

Nowadays the turbulence communities are tending to study towards more and more complex turbulence flow, homogeneous isotropic turbulence (HIT) still holds a key position in understanding the fundamental mechanism of turbulence and serves as the basic framework for turbulence modeling. On the large-scale anisotropy caused by low-wave-number truncation, for example, it is shown that this artificially-involved anisotropy can be about 10% of the mean values,[14] adding non-negligible error into post-processing results. This motivates a recent study on the physical and numerical factors, influencing the intensity of anisotropy at large scales due to low-wave-number truncation by Fang.[15] For a scalar χ(r, θ, φ) under spherical coordinate, the quantitative description of anisotropy can be defined by its coefficient of variation (CV) in a hemispherical surface with radius r

Objectives

Results

Conclusion