Hostname: page-component-586b7cd67f-r5fsc Total loading time: 0 Render date: 2024-11-24T08:17:06.106Z Has data issue: false hasContentIssue false
  • English
  • Français

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: [email protected]
Get access Rights & Permissions [Opens in a new window]

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
Check for updates
Copyright
© The Author(s), 2021. Published by Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

Aluie, H. 2011 Compressible turbulence: the cascade and its locality. Phys. Rev. Lett. 106 (17), 174502.CrossRefGoogle ScholarPubMed
Aluie, H., Li, S. & Li, H. 2012 Conservative cascade of kinetic energy in compressible turbulence. Astrophys. J. Lett. 751 (2), L29.CrossRefGoogle Scholar
Batchelor, G.K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Bos, W.J.T., Shao, L. & Bertoglio, J.P. 2007 Spectral imbalance and the normalized dissipation rate of turbulence. Phys. Fluids 19 (4), 045101.CrossRefGoogle Scholar
Chen, S., Wang, J., Li, H., Wan, M. & Chen, S. 2018 Spectra and Mach number scaling in compressible homogeneous shear turbulence. Phys. Fluids 30 (6), 065109.CrossRefGoogle Scholar
Doering, C.R. & Foias, C. 2002 Energy dissipation in body-forced turbulence. J. Fluid Mech. 467, 289–306.CrossRefGoogle Scholar
Donzis, D.A. & Jagannathan, S. 2013 a Fluctuations of thermodynamic variables in stationary compressible turbulence. J. Fluid Mech. 733, 221–244.CrossRefGoogle Scholar
Donzis, D.A. & Jagannathan, S. 2013 b On the relation between small-scale intermittency and shocks in turbulent flows. Procedia IUTAM 9, 3–15.CrossRefGoogle Scholar
Donzis, D.A. & John, J.P. 2020 Universality and scaling in homogeneous compressible turbulence. Phys. Rev. Fluids 5, 084609.CrossRefGoogle Scholar
Donzis, D.A., Sreenivasan, K.R. & Yeung, P.K. 2005 Scalar dissipation rate and dissipative anomaly in isotropic turbulence. J. Fluid Mech. 532, 199–216.CrossRefGoogle Scholar
Donzis, D.A., Sreenivasan, K.R. & Yeung, P.K. 2010 The Batchelor spectrum for mixing of passive scalars in isotropic turbulence. Flow Turbul. Combust. 85, 549–566.CrossRefGoogle Scholar
Eswaran, V. & Pope, S.B. 1988 An examination of forcing in direct numerical simulations of turbulence. Comput. Fluids 16, 257–278.CrossRefGoogle Scholar
Eyink, G.L. & Drivas, T.D. 2018 Cascades and dissipative anomalies in compressible fluid turbulence. Phys. Rev. X 8, 011022.Google Scholar
Federrath, C. & Klessen, R.S. 2012 The star formation rate of turbulent magnetized clouds: comparing theory, simulations, and observations. Astrophys. J. 761 (2), 156.CrossRefGoogle Scholar
Federrath, C., Rathborne, J.M., Longmore, S.N., Kruijssen, J.M.D., Bally, J., Contreras, Y., Crocker, R.M., Garay, G., Jackson, J.M., Testi, L., et al. 2016 The link between turbulence, magnetic fields, filaments, and star formation in the central molecular zone cloud $\textrm {G}0.253+0.016$. Astrophys. J. 832 (2), 143.CrossRefGoogle Scholar
Jagannathan, S. & Donzis, D.A. 2012 Massively parallel direct numerical simulations of forced compressible turbulence: a hybrid MPI/OpenMP approach. In Proceedings of the 1st Conference of the Extreme Science and Engineering Discovery Environment, p. 23.Google Scholar
Jagannathan, S. & Donzis, D.A. 2016 Reynolds and Mach number scaling in solenoidally-forced compressible turbulence using high-resolution direct numerical simulations. J. Fluid Mech. 789, 669–707.CrossRefGoogle Scholar
Jin, K., Salim, D.M., Federrath, C., Tasker, E.J., Habe, A. & Kainulainen, J.T. 2017 On the effective turbulence driving mode of molecular clouds formed in disc galaxies. Mon. Not. R. Astron. Soc. 469 (1), 383–393.CrossRefGoogle Scholar
John, J.P., Donzis, D.A & Sreenivasan, K.R. 2019 Solenoidal scaling laws for compressible mixing. Phys. Rev. Lett. 123 (22), 224501.CrossRefGoogle Scholar
John, J.P., Donzis, D.A. & Sreenivasan, K.R. 2020 Compressibility effects on the scalar dissipation rate. Combust. Sci. Technol. 192 (7), 1320–1333.CrossRefGoogle Scholar
Kaneda, Y., Ishihara, T., Yokokawa, M., Itakura, K. & Uno, A. 2003 Energy dissipation rate and energy spectrum in high resolution direct numerical simulations of turbulence in a periodic box. Phys. Fluids 15, L21–L24.CrossRefGoogle Scholar
Kolmogorov, A.N. 1941 a Local structure of turbulence in an incompressible fluid for very large Reynolds numbers. Dokl. Akad. Nauk. SSSR 30, 299–303.Google Scholar
Kolmogorov, A.N. 1941 b On degeneration (decay) of isotropic turbulence in an incompressible viscous liquid. In Doklady Akademii Nauk SSSR, vol. 31, pp. 538–540.Google Scholar
McComb, W.D., Berera, A., Salewski, M. & Yoffe, S. 2010 Taylor's (1935) dissipation surrogate reinterpreted. Phys. Fluids 22 (6), 061704.CrossRefGoogle Scholar
Monin, A.S. & Yaglom, A.M. 1975 Statistical Fluid Mechanics, II. MIT Press.Google Scholar
Onsager, L. 1949 Statistical hydrodynamics. Il Nuovo Cimento (1943-1954) 6 (2), 279–287.CrossRefGoogle Scholar
Orkisz, J.H., Pety, J., Gerin, M., Bron, E., Guzmán, V.V., Bardeau, S., Goicoechea, J.R., Gratier, P., Le Petit, F., Levrier, F., et al. 2017 Turbulence and star formation efficiency in molecular clouds: solenoidal versus compressive motions in Orion B. Astron. Astrophys. 599, A99.CrossRefGoogle Scholar
Pearson, B., Krogstad, P.Å. & Van De Water, W. 2002 Measurements of the turbulent energy dissipation rate. Phys. Fluids 14 (3), 1288–1290.CrossRefGoogle Scholar
Pearson, B.R., Yousef, T.A., Haugen, N.E.L., Brandenburg, A. & Krogstad, P.-Å. 2004 Delayed correlation between turbulent energy injection and dissipation. Phys. Rev. E 70 (5), 056301.CrossRefGoogle ScholarPubMed
Sarkar, S., Erlebacher, G., Hussaini, M.Y. & Kreiss, H.O. 1991 The analysis and modelling of dilatational terms in compressible turbulence. J. Fluid Mech. 227, 473–493.CrossRefGoogle Scholar
Sreenivasan, K.R. 1984 On the scaling of the turbulence energy-dissipation rate. Phys. Fluids 27, 1048–1051.CrossRefGoogle Scholar
Sreenivasan, K.R. 1998 An update on the energy dissipation rate in isotropic turbulence. Phys. Fluids 10, 528–529.CrossRefGoogle Scholar
Taylor, G.I. 1935 Statistical theory of turbulence. Proc. R. Soc. Lond. A 151, 421–444.Google Scholar
Valente, P.C. & Vassilicos, J.C. 2011 The decay of turbulence generated by a class of multiscale grids. J. Fluid Mech. 687, 300–340.CrossRefGoogle Scholar
Vassilicos, J.C. 2015 Dissipation in turbulent flows. Ann. Rev. Fluid Mech. 47, 95–114.CrossRefGoogle Scholar
Wang, J., Wan, M., Chen, S. & Chen, S. 2018 Kinetic energy transfer in compressible isotropic turbulence. J. Fluid Mech. 841, 581–613.CrossRefGoogle Scholar
Wang, J., Wang, L.-P., Xiao, Z., Shi, Y. & Chen, S. 2010 A hybrid numerical simulation of isotropic compressible turbulence. J. Comput. Phys. 229, 5257–5279.CrossRefGoogle Scholar
Wang, J., Yang, Y., Shi, Y., Xiao, Z., He, X.T. & Chen, S. 2013 Cascade of kinetic energy in three-dimensional compressible turbulence. Phy. Rev. Lett 110 (21), 214505.CrossRefGoogle ScholarPubMed
Wang, L.P., Chen, S., Brasseur, J.G. & Wyngaard, J.C. 1996 Examination of hypotheses in the Kolmogorov refined turbulence theory through high-resolution simulations. 1. Velocity field. J. Fluid Mech. 309, 113–156.CrossRefGoogle Scholar