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

Published online by Cambridge University Press:  28 August 2025

Chensheng Luo Open the ORCID record for Chensheng Luo [Opens in a new window] ,
Le Fang Open the ORCID record for Le Fang [Opens in a new window] ,
Jian Fang Open the ORCID record for Jian Fang [Opens in a new window] ,
Haitao Xu Open the ORCID record for Haitao Xu [Opens in a new window] ,
Alain Pumir Open the ORCID record for Alain Pumir [Opens in a new window]  and
Ping-Fan Yang Open the ORCID record for Ping-Fan Yang [Opens in a new window]
Chensheng Luo
Affiliation:
School of Aeronautics and Institute of Extreme Mechanics, Northwestern Polytechnical University, Xi’an 710072, PR China Research Institute of Aero-Engine, Beihang University, Beijing 100191, PR China Laboratory of Complex System, Ecole Centrale de Pékin/School of General Engineering, Beihang University, Beijing 100191, PR China
Le Fang
Affiliation:
Research Institute of Aero-Engine, Beihang University, Beijing 100191, PR China Laboratory of Complex System, Ecole Centrale de Pékin/School of General Engineering, Beihang University, Beijing 100191, PR China
Jian Fang
Affiliation:
LHD, Institute of Mechanics, Chinese Academy of Sciences, Beijing 100190, PR China
Haitao Xu
Affiliation:
Center for Combustion Energy and School of Aerospace Engineering, Tsinghua University, Beijing 100084, PR China
Alain Pumir
Affiliation:
Laboratoire de Physique, Ecole Normale Supérieure de Lyon, CNRS Université de Lyon, Lyon F-69007, France
Ping-Fan Yang*
Affiliation:
School of Aeronautics and Institute of Extreme Mechanics, Northwestern Polytechnical University, Xi’an 710072, PR China Center for Combustion Energy and School of Aerospace Engineering, Tsinghua University, Beijing 100084, PR China National Key Laboratory of Aircraft Configuration Design, Xi’an 710072, PR China
*
Corresponding author: Ping-Fan Yang, yangpingfan@nwpu.edu.cn
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Abstract

We analyse the energy flux in compressible turbulence by generalizing the exact decomposition recently proposed by Johnson (2020 Phys. Rev. Lett. 124, 104501) to study incompressible turbulent flows. This allows us to characterize the effect of dilatational motion on the interscale 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 analysing numerical simulations of freely decaying and forced turbulence, we validate our theoretical derivations and provide a quantitative description of the role of solenoidal and dilatational motions in energy transfer. In particular, we determine the scaling dependence of the dilatational contributions on the turbulent Mach number. Moreover, our findings provide criteria for tuning the parameters in commonly used Smagorinsky and Yoshizawa models for large-eddy simulations of compressible turbulence.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Turbulence theory Turbulent Flows: Homogeneous turbulence

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JFM Papers
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Journal of Fluid Mechanics , Volume 1018 , 10 September 2025 , A7
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© The Author(s), 2025. Published by Cambridge University Press

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