The contribution of dilatational motion to energy flux in homogeneous compressible turbulence

TL;DR

This paper extends an energy flux decomposition method to compressible turbulence, revealing how dilatational motion influences energy transfer through multiple mechanisms and challenging common modeling assumptions.

Contribution

It introduces a generalized decomposition for compressible turbulence and quantifies the role of dilatational motion in energy transfer at moderate Mach numbers.

Findings

Dilatational motion contributes to energy transfer via three physical mechanisms.

The contribution scales with the turbulent Mach number.

Eddy-viscosity models often neglect dilatational interactions, leading to overestimations.

Abstract

We analyze the energy flux in compressible turbulence by generalizing the exact decomposition recently proposed by Johnson (Phys. Rev. Lett., vol. 124, 2020. 104501) to study incompressible turbulent flows. This allows us to characterize the effect of dilatational motion on the inter-scale energy transfer in three-dimensional compressible turbulence. Our analysis reveals that the contribution of dilatational motion to energy transfer is due to three different physical mechanisms: the interaction between dilatation and strain, between dilatation and vorticity, and the self-interaction of dilatational motion across scales. By analyzing numerical simulations of flows at moderate turbulent Mach numbers ($Ma_t \lesssim 0.3$), we validate our theoretical derivations and provide a quantitative description of the role of dilatational motion in energy transfer. In particular, we determine the scaling dependence of the dilatational contributions on the turbulent Mach number. Moreover, our findings reveal that the eddy-viscosity assumption often used in large-eddy simulations, in the spirit of the approach used for incompressible flows, effectively neglects the interaction between solenoidal-dilatational energy transfer and overestimate dilatational effects.