Hostname: page-component-848d4c4894-m9kch Total loading time: 0 Render date: 2024-05-28T14:32:49.530Z Has data issue: false hasContentIssue false
  • English
  • Français

Local fluxes in magnetohydrodynamic turbulence

Published online by Cambridge University Press:  02 November 2022

Alexandros Alexakis Open the ORCID record for Alexandros Alexakis [Opens in a new window]  and
Sergio Chibbaro
Alexandros Alexakis*
Affiliation:
Laboratoire de Physique de l'Ecole Normale Supérieure, ENS, Université PSL, CNRS, Sorbonne Université, Université Paris-Diderot, Sorbonne Paris Cité, Paris, France
Sergio Chibbaro
Affiliation:
Université Paris-Saclay, CNRS, LISN, 91400 Orsay, France
*
†Email address for correspondence: alexakis@phys.ens.fr
Get access Rights & Permissions [Opens in a new window]

Abstract

Using highly resolved direct numerical simulations we examine the statistical properties of the local energy flux rate $\varPi _\ell (x)$ towards small scales for three isotropic turbulent magnetohydrodynamic flows, which differ in strength and structure of the magnetic field. We analyse the cascade process in both kinetic and magnetic energy, disentangling the different flux contributions to the overall energy dynamics. The results show that the probability distribution of the local energy flux develops long tails related to extreme events, similar to the hydrodynamic case. The different terms of the energy flux display different properties and show sensitivity to the type of the flow examined. We further examine the joint probability density function between the local energy flux and the gradients of the involved fields. The results point out a correlation with the magnetic field gradients, showing, however, a dispersion much stronger than what is observed in hydrodynamic flows. Finally, it is also shown that the local energy flux shows some dependence on the local amplitude of the magnetic field. The present results have implications for subgrid-scale models, which we discuss.

Keywords

plasma flowsplasma simulation
Type
Research Article
Information
Journal of Plasma Physics , Volume 88 , Issue 5 , October 2022 , 905880515
Check for updates
Copyright
Copyright © The Author(s), 2022. 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

Agullo, O., Müller, W.-C., Knaepen, B. & Carati, D. 2001 Large eddy simulation of decaying magnetohydrodynamic turbulence with dynamic subgrid-modeling. Phys. Plasmas 8 (7), 3502–3505.CrossRefGoogle Scholar
Alexakis, A. 2013 Large-scale magnetic fields in magnetohydrodynamic turbulence. Phys. Rev. Lett. 110 (8), 084502.CrossRefGoogle ScholarPubMed
Alexakis, A. & Biferale, L. 2018 Cascades and transitions in turbulent flows. Phys. Rep. 767, 1–101.CrossRefGoogle Scholar
Alexakis, A. & Chibbaro, S. 2020 Local energy flux of turbulent flows. Phys. Rev. Fluids 5 (9), 094604.CrossRefGoogle Scholar
Alexakis, A., Mininni, P.D. & Pouquet, A. 2005 Shell-to-shell energy transfer in magneto- hydrodynamics. I. Steady state turbulence. Phys. Rev. E 72 (4), 046301.CrossRefGoogle Scholar
Alexakis, A., Mininni, P.D. & Pouquet, A. 2007 Turbulent cascades, transfer, and scale interactions in magnetohydrodynamics. New J. Phys. 9 (8), 298.CrossRefGoogle Scholar
Aluie, H. 2017 Coarse-grained incompressible magnetohydrodynamics: analyzing the turbulent cascades. New J. Phys. 19 (2), 025008.CrossRefGoogle Scholar
Aluie, H. & Eyink, G.L. 2009 Localness of energy cascade in hydrodynamic turbulence. II. Sharp spectral filter. Phys. Fluids 21 (11), 115108.CrossRefGoogle Scholar
Aluie, H. & Eyink, G.L. 2010 Scale locality of magnetohydrodynamic turbulence. Phys. Rev. Lett. 104 (8), 081101.CrossRefGoogle ScholarPubMed
Battaner, E. 1996 Astrophysical Fluid Dynamics. Cambridge University Press.CrossRefGoogle Scholar
Beresnyak, A. 2011 Spectral slope and Kolmogorov constant of MHD turbulence. Phys. Rev. Lett. 106 (7), 075001.CrossRefGoogle ScholarPubMed
Bian, X. & Aluie, H. 2019 Decoupled cascades of kinetic and magnetic energy in magnetohydrodynamic turbulence. Phys. Rev. Lett. 122 (13), 135101.CrossRefGoogle ScholarPubMed
Bian, X., Shang, J.K., Blackman, E.G., Collins, G.W. & Aluie, H. 2021 Scaling of turbulent viscosity and resistivity: extracting a scale-dependent turbulent magnetic Prandtl number. Astrophys. J. Lett. 917 (1), L3.CrossRefGoogle Scholar
Biferale, L., Bonaccorso, F., Buzzicotti, M. & Iyer, K.P. 2019 Self-similar subgrid-scale models for inertial range turbulence and accurate measurements of intermittency. Phys. Rev. Lett. 123 (1), 014503.CrossRefGoogle ScholarPubMed
Biskamp, D. 2003 Magnetohydrodynamic Turbulence. Cambridge University Press.CrossRefGoogle Scholar
Boldyrev, S. 2006 Spectrum of magnetohydrodynamic turbulence. Phys. Rev. Lett. 96, 115002.CrossRefGoogle ScholarPubMed
Borue, V. & Orszag, S.A. 1998 Local energy flux and subgrid-scale statistics in three-dimensional turbulence. J. Fluid Mech. 366, 1–31.CrossRefGoogle Scholar
Brandenburg, A., Sokoloff, D. & Subramanian, K. 2012 Current status of turbulent dynamo theory. Space Sci. Rev. 169 (1), 123–157.CrossRefGoogle Scholar
Brandenburg, A. & Subramanian, K. 2005 Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417 (1–4), 1–209.CrossRefGoogle Scholar
Bruno, R. & Carbone, V. 2013 The solar wind as a turbulence laboratory. Living Rev. Sol. Phys. 10 (1), 1–208.CrossRefGoogle Scholar
Buzzicotti, M., Linkmann, M., Aluie, H., Biferale, L., Brasseur, J. & Meneveau, C. 2018 Effect of filter type on the statistics of energy transfer between resolved and subfilter scales from a-priori analysis of direct numerical simulations of isotropic turbulence. J. Turbul. 19 (2), 167–197.CrossRefGoogle Scholar
Camporeale, E., Sorriso-Valvo, L., Califano, F. & Retinò, A. 2018 Coherent structures and spectral energy transfer in turbulent plasma: a space-filter approach. Phys. Rev. Lett. 120 (12), 125101.CrossRefGoogle ScholarPubMed
Carrasco, F., Viganò, D. & Palenzuela, C. 2020 Gradient subgrid-scale model for relativistic MHD large-eddy simulations. Phys. Rev. D 101 (6), 063003.CrossRefGoogle Scholar
Casciola, C.M., Gualtieri, P., Benzi, R. & Piva, R. 2003 Scale-by-scale budget and similarity laws for shear turbulence. J. Fluid Mech. 476, 105–114.CrossRefGoogle Scholar
Cerri, S.S. & Camporeale, E. 2020 Space-filter techniques for quasi-neutral hybrid-kinetic models. Phys. Plasmas 27 (8), 082102.CrossRefGoogle Scholar
Chen, Q., Chen, S. & Eyink, G.L. 2003 The joint cascade of energy and helicity in three-dimensional turbulence. Phys. Fluids 15 (2), 361–374.CrossRefGoogle Scholar
Chen, S., Eyink, G.L., Wan, M. & Xiao, Z. 2006 Is the Kelvin theorem valid for high Reynolds number turbulence? Phys. Rev. Lett. 97 (14), 144505.CrossRefGoogle ScholarPubMed
Chernyshov, A.A., Karelsky, K.V. & Petrosyan, A.S. 2014 Subgrid-scale modeling for the study of compressible magnetohydrodynamic turbulence in space plasmas. Phys. Uspekhi 57 (5), 421.CrossRefGoogle Scholar
Cimarelli, A., De Angelis, E. & Casciola, C.M. 2013 Paths of energy in turbulent channel flows. J. Fluid Mech. 715, 436–451.CrossRefGoogle Scholar
Danaila, L., Anselmet, F., Zhou, T. & Antonia, R.A. 2001 Turbulent energy scale budget equations in a fully developed channel flow. J. Fluid Mech. 430, 87–109.CrossRefGoogle Scholar
Dar, G., Verma, M.K. & Eswaran, V. 2001 Energy transfer in two-dimensional magnetohydrodynamic turbulence: formalism and numerical results. Physica D 157 (3), 207–225.CrossRefGoogle Scholar
Davidson, P.A. 2002 An Introduction to Magnetohydrodynamics. Cambridge University Press.Google Scholar
Domaradzki, J.A., Teaca, B. & Carati, D. 2009 Locality properties of the energy flux in turbulence. Phys. Fluids 21 (2), 025106.CrossRefGoogle Scholar
Dubrulle, B. 2019 Beyond Kolmogorov cascades. J. Fluid Mech. 867, P1.CrossRefGoogle Scholar
Eyink, G. & Sreenivasan, K. 2006 Onsager and the theory of hydrodynamic turbulence. Rev. Mod. Phys 78, 87–135.CrossRefGoogle Scholar
Eyink, G., Vishniac, E., Lalescu, C., Aluie, H., Kanov, K., Bürger, K., Burns, R., Meneveau, C. & Szalay, A. 2013 Flux-freezing breakdown in high-conductivity magnetohydrodynamic turbulence. Nature 497 (7450), 466–469.CrossRefGoogle ScholarPubMed
Eyink, G.L. 2005 Locality of turbulent cascades. Physica D 207 (1–2), 91–116.CrossRefGoogle Scholar
Eyink, G.L. 2018 Cascades and dissipative anomalies in nearly collisionless plasma turbulence. Phys. Rev. X 8 (4), 041020.Google Scholar
Eyink, G.L. & Aluie, H. 2009 Localness of energy cascade in hydrodynamic turbulence. I. Smooth coarse graining. Phys. Fluids 21 (11), 115107.CrossRefGoogle Scholar
Frisch, U. 1995 Turbulence. The Legacy of A.N. Kolmogorov. Cambridge University Press.CrossRefGoogle Scholar
Galtier, S. 2009 Exact vectorial law for axisymmetric magnetohydrodynamics turbulence. Astrophys. J. 704 (2), 1371.CrossRefGoogle Scholar
Galtier, S. 2016 Introduction to Modern Magnetohydrodynamics. Cambridge University Press.CrossRefGoogle Scholar
Galtier, S. 2018 On the origin of the energy dissipation anomaly in (Hall) magnetohydrodynamics. J. Phys. A: Math. Theor. 51 (20), 205501.CrossRefGoogle Scholar
Germano, M. 1992 Turbulence: the filtering approach. J. Fluid Mech. 238, 325–336.CrossRefGoogle Scholar
Germano, M., Piomelli, U., Moin, P. & Cabot, W.H. 1991 A dynamic subgrid-scale eddy viscosity model. Phys. Fluids A 3 (7), 1760–1765.CrossRefGoogle Scholar
Goldreich, P. & Sridhar, S. 1995 Toward a theory of interstellar turbulence. 2: strong Alfvenic turbulence. Astrophys. J. 438, 763–775.CrossRefGoogle Scholar
Goldstein, M.L., Roberts, D.A. & Matthaeus, W.H. 1995 Magnetohydrodynamic turbulence in the solar wind. Annu. Rev. Astron. Astrophys. 33 (1), 283–325.CrossRefGoogle Scholar
Grete, P., Vlaykov, D.G., Schmidt, W. & Schleicher, D.R.G. 2017 Comparative statistics of selected subgrid-scale models in large-eddy simulations of decaying, supersonic magnetohydrodynamic turbulence. Phys. Rev. E 95 (3), 033206.CrossRefGoogle ScholarPubMed
Innocenti, A., Jaccod, A., Popinet, S. & Chibbaro, S. 2021 Direct numerical simulation of bubble-induced turbulence. J. Fluid Mech. 918, A23.CrossRefGoogle Scholar
Iroshnikov, P.S. 1964 Turbulence of a conducting fluid in a strong magnetic field. Sov. Astron. 7, 566.Google Scholar
Kessar, M., Balarac, G. & Plunian, F. 2016 The effect of subgrid-scale models on grid-scale/subgrid-scale energy transfers in large-eddy simulation of incompressible magneto- hydrodynamic turbulence. Phys. Plasmas 23 (10), 102305.CrossRefGoogle Scholar
Kolmogorov, A.N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. C. R. Acad. Sci. 30, 301–305.Google Scholar
Kraichnan, R.H. 1965 Inertial-range spectrum of hydromagnetic turbulence. Phys. Fluids 8 (7), 1385–1387.CrossRefGoogle Scholar
Kraichnan, R.H. 1971 Inertial-range transfer in two-and three-dimensional turbulence. J. Fluid Mech. 47 (3), 525–535.CrossRefGoogle Scholar
Landau, L.D., Bell, J.S., Kearsley, M.J., Pitaevskii, L.P., Lifshitz, E.M. & Sykes, J.B. 2013 Electrodynamics of Continuous Media, vol. 8. Elsevier.Google Scholar
Leonard, A. 1975 Energy cascade in large-eddy simulations of turbulent fluid flows. In Advances in Geophysics, vol. 18, pp. 237–248. Elsevier.CrossRefGoogle Scholar
Lesieur, M., Métais, O. 2005 Large-Eddy Simulations of Turbulence. Cambridge University Press.CrossRefGoogle Scholar
Linkmann, M., Buzzicotti, M. & Biferale, L. 2018 Multi-scale properties of large eddy simulations: correlations between resolved-scale velocity-field increments and subgrid-scale quantities. J. Turbul. 19 (6), 493–527.CrossRefGoogle Scholar
Liu, S., Meneveau, C. & Katz, J. 1994 On the properties of similarity subgrid-scale models as deduced from measurements in a turbulent jet. J. Fluid Mech. 275, 83–119.CrossRefGoogle Scholar
McKee, C.F. & Ostriker, E.C. 2007 Theory of star formation. Annu. Rev. Astron. Astrophys. 45, 565–687.CrossRefGoogle Scholar
Meneveau, C. 1994 Statistics of turbulence subgrid-scale stresses: necessary conditions and experimental tests. Phys. Fluids 6 (2), 815–833.CrossRefGoogle Scholar
Meneveau, C. & Katz, J. 2000 Scale-invariance and turbulence models for large-eddy simulation. Annu. Rev. Fluid Mech. 32 (1), 1–32.CrossRefGoogle Scholar
Miesch, M., Matthaeus, W., Brandenburg, A., Petrosyan, A., Pouquet, A., Cambon, C., Jenko, F., Uzdensky, D., Stone, J., Tobias, S., et al. 2015 Large-eddy simulations of magnetohydrodynamic turbulence in heliophysics and astrophysics. Space Sci. Rev. 194 (1), 97–137.CrossRefGoogle Scholar
Mininni, P., Alexakis, A. & Pouquet, A. 2005 Shell-to-shell energy transfer in magneto- hydrodynamics. II. Kinematic dynamo. Phys. Rev. E 72 (4), 046302.CrossRefGoogle Scholar
Mininni, P.D., Rosenberg, D., Reddy, R. & Pouquet, A. 2011 A hybrid MPI–OpenMP scheme for scalable parallel pseudospectral computations for fluid turbulence. Parallel Comput. 37 (6–7), 316–326.CrossRefGoogle Scholar
Misra, A. & Pullin, D.I. 1997 A vortex-based subgrid stress model for large-eddy simulation. Phys. Fluids 9 (8), 2443–2454.CrossRefGoogle Scholar
Moll, R., Graham, J.P., Pratt, J., Cameron, R.H., Müller, W.-C. & Schüssler, M. 2011 Universality of the small-scale dynamo mechanism. Astrophys. J. 736 (1), 36.CrossRefGoogle Scholar
Monin, A.S. & Yaglom, A.M. 1975 Statistical Fluid Mechanics. MIT.Google Scholar
Müller, W.-C. & Carati, D. 2002 Dynamic gradient-diffusion subgrid models for incompressible magnetohydrodynamic turbulence. Phys. Plasmas 9 (3), 824–834.CrossRefGoogle Scholar
Piomelli, U., Cabot, W.H., Moin, P. & Lee, S. 1991 Subgrid-scale backscatter in turbulent and transitional flows. Phys. Fluids A 3 (7), 1766–1771.CrossRefGoogle Scholar
Politano, H. & Pouquet, A. 1998 von Kármán–Howarth equation for magnetohydrodynamics and its consequences on third-order longitudinal structure and correlation functions. Phys. Rev. E 57 (1), R21.CrossRefGoogle Scholar
Ponty, Y., Mininni, P.D., Laval, J.-P., Alexakis, A., Baerenzung, J., Daviaud, F., Dubrulle, B., Pinton, J.-F., Politano, H. & Pouquet, A. 2008 Linear and non-linear features of the Taylor–Green dynamo. C. R. Phys. 9 (7), 749–756.CrossRefGoogle Scholar
Pope, S.B. 2000 Turbulent Flows. Cambridge University Press.CrossRefGoogle Scholar
Sagaut, P. 2001 Large Eddy Simulation for Incompressible Flows, vol. 20. Springer.CrossRefGoogle Scholar
Schekochihin, A.A., Cowley, S.C., Taylor, S.F., Maron, J.L. & McWilliams, J.C. 2004 Simulations of the small-scale turbulent dynamo. Astrophys. J. 612 (1), 276.CrossRefGoogle Scholar
Smagorinsky, J. 1963 General circulation experiments with the primitive equations: I. The basic experiment. Mon. Weath. Rev. 91 (3), 99–164.2.3.CO;2>CrossRefGoogle Scholar
Sorriso-Valvo, L., Marino, R., Carbone, V., Noullez, A., Lepreti, F., Veltri, P., Bruno, R., Bavassano, B. & Pietropaolo, E. 2007 Observation of inertial energy cascade in interplanetary space plasma. Phys. Rev. Lett. 99 (11), 115001.CrossRefGoogle ScholarPubMed
Speziale, C.G. 1985 Galilean invariance of subgrid-scale stress models in the large-eddy simulation of turbulence. J. Fluid Mech. 156, 55–62.CrossRefGoogle Scholar
Teaca, B., Carati, D. & Andrzej Domaradzki, J. 2011 On the locality of magnetohydrodynamic turbulence scale fluxes. Phys. Plasmas 18 (11), 112307.CrossRefGoogle Scholar
Teaca, B., Gorbunov, E.A., Told, D., Navarro, A.B. & Jenko, F. 2021 Sub-grid-scale effects in magnetised plasma turbulence. J. Plasma Phys. 87 (2), 905870209.CrossRefGoogle Scholar
Teaca, B., Verma, M.K., Knaepen, B. & Carati, D. 2009 Energy transfer in anisotropic magnetohydrodynamic turbulence. Phys. Rev. E 79 (4), 046312.CrossRefGoogle ScholarPubMed
Tennekes, H. & Lumley, J.L. 1990 A First Course in Turbulence. MIT.Google Scholar
Theobald, M.L., Fox, P.A. & Sofia, S. 1994 A subgrid-scale resistivity for magnetohydrodynamics. Phys. Plasmas 1 (9), 3016–3032.CrossRefGoogle Scholar
Valori, V., Innocenti, A., Dubrulle, B. & Chibbaro, S. 2020 Weak formulation and scaling properties of energy fluxes in three-dimensional numerical turbulent Rayleigh–Bénard convection. J. Fluid Mech. 885, A14.CrossRefGoogle Scholar
Verma, M.K. 2004 Statistical theory of magnetohydrodynamic turbulence: recent results. Phys. Rep. 401 (5–6), 229–380.CrossRefGoogle Scholar
Verma, M.K. 2019 Energy Transfers in Fluid Flows: Multiscale and Spectral Perspectives. Cambridge University Press.CrossRefGoogle Scholar
Verma, M.K. 2022 Variable energy flux in turbulence. J. Phys. A: Math. Theor 55, 013002.CrossRefGoogle Scholar
Verma, M.K. & Kumar, S. 2004 Large-eddy simulations of fluid and magnetohydrodynamic turbulence using renormalized parameters. Pramana 63 (3), 553–561.CrossRefGoogle Scholar
Viganò, D., Aguilera-Miret, R. & Palenzuela, C. 2019 Extension of the subgrid-scale gradient model for compressible magnetohydrodynamics turbulent instabilities. Phys. Fluids 31 (10), 105102.CrossRefGoogle Scholar
Vlaykov, D.G., Grete, P., Schmidt, W. & Schleicher, D.R.G. 2016 A nonlinear structural subgrid-scale closure for compressible MHD. I. Derivation and energy dissipation properties. Phys. Plasmas 23 (6), 062316.CrossRefGoogle Scholar
Vreman, B., Geurts, B. & Kuerten, H. 1994 Realizability conditions for the turbulent stress tensor in large-eddy simulation. J. Fluid Mech. 278, 351–362.CrossRefGoogle Scholar
Vreman, B., Geurts, B. & Kuerten, H. 1997 Large-eddy simulation of the turbulent mixing layer. J. Fluid Mech. 339, 357–390.CrossRefGoogle Scholar
Yang, Y., Matthaeus, W.H., Roy, S., Roytershteyn, V., Parashar, T.N., Bandyopadhyay, R. & Wan, M. 2022 Pressure–strain interaction as the energy dissipation estimate in collisionless plasma. Astrophys. J. 929 (2), 142.CrossRefGoogle Scholar