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Does dissipative anomaly hold for compressible turbulence?

Published online by Cambridge University Press:  10 June 2021

John Panickacheril John ,
Diego A. Donzis Open the ORCID record for Diego A. Donzis [Opens in a new window]  and
Katepalli R. Sreenivasan
John Panickacheril John
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX77843, USA
Diego A. Donzis*
Affiliation:
Department of Aerospace Engineering, Texas A&M University, College Station, TX77843, USA
Katepalli R. Sreenivasan
Affiliation:
Department of Mechanical and Aerospace Engineering, Department of Physics, and Courant Institute of Mathematical Sciences, New York University, New York, NY10012, USA
*
†Email address for correspondence: donzis@tamu.edu
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Abstract

We systematically study dissipative anomaly in compressible turbulence using a direct numerical simulations (DNS) database spanning a large parameter space, and show that the classical incompressible scaling does not hold for the total dissipation field. We assess the scaling for the solenoidal and dilatational parts separately. The solenoidal dissipation obeys the same scaling as incompressible turbulence when rescaled on solenoidal variables. We propose new scaling laws for total dissipation that predict the transition between regimes dominated by the solenoidal and dilatational components, and confirm them by the DNS data. An analysis of dilatational dissipation shows that dissipative anomaly may hold if properly scaled for certain regimes; on this empirical basis, we propose a new criterion for the energy cascade in the dilatational component.

JFM classification

Turbulent Flows: Compressible turbulence Turbulent Flows: Turbulence simulation Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 920 , 10 August 2021 , A20
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Copyright
© The Author(s), 2021. Published by Cambridge University Press

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