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Non-universality and dissipative anomaly in compressible magnetohydrodynamic turbulence

Published online by Cambridge University Press:  27 August 2024

Cheng Li ,
Yan Yang ,
William H. Matthaeus Open the ORCID record for William H. Matthaeus [Opens in a new window] ,
Bin Jiang Open the ORCID record for Bin Jiang [Opens in a new window] ,
Minping Wan Open the ORCID record for Minping Wan [Opens in a new window]  and
Shiyi Chen
Cheng Li
Affiliation:
Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications, Southern University of Science and Technology, Shenzhen 518055, PR China
Yan Yang
Affiliation:
Department of Physics and Astronomy, University of Delaware, DE 19716, USA
William H. Matthaeus
Affiliation:
Department of Physics and Astronomy, University of Delaware, DE 19716, USA
Bin Jiang
Affiliation:
Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications, Southern University of Science and Technology, Shenzhen 518055, PR China
Minping Wan*
Affiliation:
Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications, Southern University of Science and Technology, Shenzhen 518055, PR China
Shiyi Chen
Affiliation:
Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen 518055, PR China Guangdong-Hong Kong-Macao Joint Laboratory for Data-Driven Fluid Mechanics and Engineering Applications, Southern University of Science and Technology, Shenzhen 518055, PR China Eastern Institute for Advanced Study, Eastern Institute of Technology, Ningbo 315200, PR China
*
†Email address for correspondence: wanmp@sustech.edu.cn
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Abstract

We systematically study the dissipative anomaly in compressible magnetohydrodynamic (MHD) turbulence using direct numerical simulations, and show that the total dissipation remains finite as viscosity diminishes. The dimensionless dissipation rate $\mathcal {C}_{\varepsilon }$ fits well with the model $\mathcal {C}_{\varepsilon } = \mathcal {C}_{\varepsilon,\infty } + \mathcal {D}/R_L^-$ for all levels of flow compressibility considered here, where $R_L^-$ is the generalized large-scale Reynolds number. The asymptotic value $\mathcal {C}_{\varepsilon,\infty }$ describes the total energy transfer flux, and decreases with increase of the flow compressibility, indicating non-universality of the dimensionless dissipation rate in compressible MHD turbulence. After introducing an empirically modified dissipation rate, the data from compressible cases collapse to a form similar to the incompressible MHD case depending only on the modified Reynolds number.

JFM classification

Turbulent Flows: Turbulence theory MHD and Electrohydrodynamics: MHD turbulence Turbulent Flows: Compressible turbulence
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 992 , 10 August 2024 , A9
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Copyright
© The Author(s), 2024. Published by Cambridge University Press

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