Inviscid Criterion for Decomposing Scales

TL;DR

This paper discusses the importance of the inviscid criterion for scale decomposition in variable-density flows, demonstrating that Favre decomposition satisfies it while others may not, impacting turbulence modeling.

Contribution

It provides numerical evidence that Favre decomposition meets the inviscid criterion, unlike other methods, informing better turbulence analysis and modeling in compressible flows.

Findings

Favre decomposition satisfies the inviscid criterion.

Other common decompositions can violate the inviscid criterion.

Viscous terms in LES can be neglected without modeling.

Abstract

The proper scale decomposition in flows with significant density variations is not as straightforward as in incompressible flows, with many possible ways to define a `length-scale.' A choice can be made according to the so-called \emph{inviscid criterion} \cite{Aluie13}. It is a kinematic requirement that a scale decomposition yield negligible viscous effects at large enough `length-scales.' It has been proved \cite{Aluie13} recently that a Favre decomposition satisfies the inviscid criterion, which is necessary to unravel inertial-range dynamics and the cascade. Here, we present numerical demonstrations of those results. We also show that two other commonly used decompositions can violate the inviscid criterion and, therefore, are not suitable to study inertial-range dynamics in variable-density and compressible turbulence. Our results have practical modeling implication in showing that viscous terms in Large Eddy Simulations do not need to be modeled and can be neglected.