One-point and two-point statistics of homogeneous isotropic decaying turbulence with variable viscosity

TL;DR

This study uses DNS to analyze how variable viscosity affects turbulence decay, revealing that viscosity fluctuations increase small-scale intermittency and alter the turbulent cascade, with minimal impact on mean dissipation rates.

Contribution

It provides new insights into the effects of variable viscosity on turbulence decay, especially regarding small-scale intermittency and inter-scale transport mechanisms.

Findings

Mean dissipation rate remains nearly unchanged by viscosity variations.

Variable viscosity enhances small-scale intermittency and modifies turbulent mixing.

Viscosity gradients contribute to inverse inter-scale transport from small to large scales.

Abstract

The decay of homogeneous isotropic turbulence in a variable viscosity fluid with a viscosity ratio up to 15 is analyzed by means of highly resolved direct numerical simulations (DNS) at low Reynolds numbers. The question addressed by the present work is how quantities such as the kinetic energy and the associated dissipation rate, as well as the inter-scale transport mechanism of turbulence are changed by local fluctuations of the viscosity. From the one-point budget equation of the turbulent kinetic energy, it is shown that the mean dissipation rate is nearly unchanged by variable viscosity effects. This result is explained by a negative correlation between the local viscosity and the local velocity gradients. However, the dissipation is a highly fluctuating quantity with a strong level of intermittency. From a statistical analysis it is shown that turbulent flows with variable viscosity are characterized by an enhanced level of small-scale intermittency, which results in the presence of smaller length scales and a modified turbulent mixing. The effect of variable viscosity on the turbulent cascade is analyzed by a budget equation for the velocity structure function. From DNS it is shown that viscosity gradients contribute to the inter-scale transport mechanism in the form of an inverse transport, where information propagates from the small scales to the large scales.