Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-23T08:42:20.425Z Has data issue: false hasContentIssue false
  • English
  • Français

Energy budget in decaying compressible MHD turbulence

Published online by Cambridge University Press:  06 April 2021

Yan Yang ,
Minping Wan Open the ORCID record for Minping Wan [Opens in a new window] ,
William H. Matthaeus Open the ORCID record for William H. Matthaeus [Opens in a new window]  and
Shiyi Chen
Yan Yang
Affiliation:
Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Southern University of Science and Technology, Shenzhen518055, PR China Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China University of Science and Technology of China, Hefei230026, PR China
Minping Wan*
Affiliation:
Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Southern University of Science and Technology, Shenzhen518055, PR China Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou), Guangzhou511458, PR China
William H. Matthaeus
Affiliation:
University of Delaware, Newark, DE19716, USA
Shiyi Chen
Affiliation:
Guangdong Provincial Key Laboratory of Turbulence Research and Applications, Southern University of Science and Technology, Shenzhen518055, PR China Department of Mechanics and Aerospace Engineering, Southern University of Science and Technology, Shenzhen518055, PR China Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou), Guangzhou511458, PR China
*
†Email address for correspondence: [email protected]
Get access Rights & Permissions [Opens in a new window]

Abstract

We study the decay of compressible magnetohydrodynamic (MHD) turbulence, emphasizing exchanges of energy between compressive and incompressive kinetic energies, magnetic energy, and thermal energy. A recently developed high order finite difference code is employed for compressible runs with a Mach number up to 2. Varying the nature of the initial conditions (magnitudes of velocity and magnetic fluctuations), and initial Mach numbers permits examination of various dynamical regimes characterized here by the changes between different energy reservoirs. Acoustic waves are responsible for the oscillatory exchange between compressive kinetic and thermal energy through the pressure dilatation term. The results indicate that exchange between kinetic and magnetic energy is dominated by interactions involving the solenoidal velocity. Several systematic rapid adjustments are found to be reproducible with simple scalings derived from the empirical data.

JFM classification

MHD and Electrohydrodynamics: MHD turbulence Turbulent Flows: Compressible turbulence Turbulent Flows: Turbulence theory
Type
JFM Papers
Information
Journal of Fluid Mechanics , Volume 916 , 10 June 2021 , A4
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

Adhikari, L., et al. 2020 Turbulence transport modeling and first orbit parker solar probe (PSP) observations. Astrophys. J. Suppl. 246 (2), 38.CrossRefGoogle Scholar
Aluie, H. & Eyink, G.L. 2010 Scale locality of magnetohydrodynamic turbulence. Phys. Rev. Lett. 104, 081101.CrossRefGoogle ScholarPubMed
Aluie, H., Li, S. & Li, H. 2012 Conservative cascade of kinetic energy in compressible turbulence. Astrophys. J. Lett. 751, L29.CrossRefGoogle Scholar
Andrés, N., Sahraoui, F., Galtier, S., Hadid, L.Z., Dmitruk, P. & Mininni, P.D. 2018 Energy cascade rate in isothermal compressible magnetohydrodynamic turbulence. J. Plasma Phys. 84 (4), 905840404.CrossRefGoogle Scholar
Andrés, N., Sahraoui, F., Galtier, S., Hadid, L.Z., Ferrand, R. & Huang, S.Y. 2019 Energy cascade rate measured in a collisionless space plasma with MMS data and compressible Hall magnetohydrodynamic turbulence theory. Phys. Rev. Lett. 123 (24), 245101.CrossRefGoogle Scholar
Armstrong, J.W., Cordes, J.M. & Rickett, B.J. 1981 Density power spectrum in the local interstellar medium. Nature 291 (5816), 561–564.CrossRefGoogle Scholar
Bandyopadhyay, R., Matthaeus, W.H., Oughton, S. & Wan, M. 2019 Evolution of similarity lengths in anisotropic magnetohydrodynamic turbulence. J. Fluid Mech. 876, 5–18.CrossRefGoogle Scholar
Banerjee, S. & Galtier, S. 2013 Exact relation with two-point correlation functions and phenomenological approach for compressible magnetohydrodynamic turbulence. Phys. Rev. E 87, 013019.CrossRefGoogle ScholarPubMed
Banerjee, S., Hadid, L.Z., Sahraoui, F. & Galtier, S. 2016 a Scaling of compressible magnetohydrodynamic turbulence in the fast solar wind. Astrophys. J. Lett. 829 (2), L27.CrossRefGoogle Scholar
Banerjee, S., Hadid, L.Z., Sahraoui, F. & Galtier, S. 2016 b Scaling of compressible magnetohydrodynamic turbulence in the fast solar wind. Astrophys. J. Lett. 829, L27.CrossRefGoogle Scholar
Barnes, A. 1979 Hydromagnetic waves and turbulence in the solar wind. In Solar System Plasma Physics, I (ed. E.N. Parker, C.F. Kennel & L.J. Lanzerotti), p. 251. North-Holland.Google Scholar
Bavassano, B., Bruno, R. & Klein, L.W. 1995 Density-temperature correlation in solar-wind magnetohydrodynamic fluctuations—a test for nearly incompressible models. J. Geophys. Res. 100, 5871–5875.CrossRefGoogle Scholar
Bavassano, B., Pietropaolo, E. & Bruno, R. 2004 Compressive fluctuations in high-latitude solar wind. In Annales Geophysicae, vol. 22, pp. 689–696. Copernicus GmbH.CrossRefGoogle Scholar
Bavassano, R. & Bruno, R. 1995 Density fluctuations and turbulent Mach numbers in the inner solar wind. J. Geophys. Res. 100, 9475–9480.CrossRefGoogle Scholar
Bec, J. & Khanin, K. 2007 Burgers turbulence. Phys. Rep. 447 (1–2), 1–66.CrossRefGoogle Scholar
Benzi, R., Biferale, L., Fisher, R.T., Kadanoff, L.P., Lamb, D.Q. & Toschi, F. 2008 Intermittency and universality in fully developed inviscid and weakly compressible turbulent flows. Phys. Rev. Lett. 100 (23), 234503.CrossRefGoogle ScholarPubMed
Beresnyak, A., Lazarian, A. & Cho, J. 2005 Density scaling and anisotropy in supersonic magnetohydrodynamic turbulence. Astrophys. J. Lett. 624 (2), L93.CrossRefGoogle Scholar
Bhattacharjee, A., Ng, C.S., Ghosh, S. & Goldstein, M.L. 1999 A comparative study of four-field and fully compressible magnetohydrodynamic turbulence in the solar wind. J. Geophys. Res. 104 (A11), 24835–24843.CrossRefGoogle Scholar
Bhattacharjee, A., Ng, C.S. & Spangler, S.R. 1998 Weakly compressible magnetohydrodynamic turbulence in the solar wind and the interstellar medium. Astrophys. J. 494 (1), 409–418.CrossRefGoogle Scholar
Bigot, B., Galtier, S. & Politano, H. 2008 Energy decay laws in strongly anisotropic magnetohydrodynamic turbulence. Phys. Rev. Lett. 100 (7), 074502.CrossRefGoogle ScholarPubMed
Biskamp, D. & Müller, W.-C. 1999 Decay laws for three-dimensional magnetohydrodynamic turbulence. Phys. Rev. Lett. 83 (11), 2195–2198.CrossRefGoogle Scholar
Borovsky, J.E. 2010 Contribution of strong discontinuities to the power spectrum of the solar wind. Phys. Rev. Lett. 105 (11), 111102.CrossRefGoogle ScholarPubMed
Borovsky, J.E., Denton, M.H. & Smith, C.W. 2019 Some properties of the solar wind turbulence at 1 AU statistically examined in the different types of solar wind plasma. J. Geophys. Res. 124 (4), 2406–2424.Google Scholar
Brandenburg, A. & Kahniashvili, T. 2017 Classes of hydrodynamic and magnetohydrodynamic turbulent decay. Phys. Rev. Lett. 118 (5), 055102.CrossRefGoogle ScholarPubMed
Brandenburg, A. & Lazarian, A. 2013 Astrophysical hydromagnetic turbulence. Space Sci. Rev. 178 (2–4), 163–200.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
Bruno, R., Telloni, D., Primavera, L., Pietropaolo, E., D'Amicis, R., Sorriso-Valvo, L., Carbone, V., Malara, F. & Veltri, P. 2014 Radial evolution of the intermittency of density fluctuations in the fast solar wind. Astrophys. J. 786 (1), 53.CrossRefGoogle Scholar
Burlaga, L.F., Mish, W.H. & Roberts, D.A. 1989 Large-scale fluctuations in the solar wind at 1 AU: 1978–1982. J. Geophys. Res. 94 (A1), 177–184.CrossRefGoogle Scholar
Carbone, F., Sorriso-Valvo, L., Alberti, T., Lepreti, F., Chen, C.H.K., Němeček, Z. & Šafránková, J. 2018 Arbitrary-order hilbert spectral analysis and intermittency in solar wind density fluctuations. Astrophys. J. 859 (1), 27.CrossRefGoogle Scholar
Carbone, V., Marino, R., Sorriso-Valvo, L., Noullez, A. & Bruno, R. 2009 Scaling laws of turbulence and heating of fast solar wind: the role of density fluctuations. Phys. Rev. Lett. 103 (6), 061102.CrossRefGoogle ScholarPubMed
Celani, A., Lanotte, A., Mazzino, A. & Vergassola, M. 2000 Universality and saturation of intermittency in passive scalar turbulence. Phys. Rev. Lett. 84 (11), 2385.CrossRefGoogle ScholarPubMed
Celani, A., Lanotte, A., Mazzino, A. & Vergassola, M. 2001 Fronts in passive scalar turbulence. Phys. Fluids 13 (6), 1768–1783.CrossRefGoogle Scholar
Cerretani, J. & Dmitruk, P. 2019 Coexistence of acoustic waves and turbulence in low mach number compressible flows. Phys. Fluids 31 (4), 045102.CrossRefGoogle Scholar
Chen, C.H.K. 2016 Recent progress in astrophysical plasma turbulence from solar wind observations. J. Plasma Phys. 82 (6), 535820602.CrossRefGoogle Scholar
Chen, C.H.K., Salem, C.S., Bonnell, J.W., Mozer, F.S. & Bale, S.D. 2012 Density fluctuation spectrum of solar wind turbulence between ion and electron scales. Phys. Rev. Lett. 109 (3), 035001.CrossRefGoogle ScholarPubMed
Cho, J. & Lazarian, A. 2002 Compressibe sub-Alfvén MHD turbulence in low-$\beta$ plasmas. Phys. Rev. Lett. 88, 245001.CrossRefGoogle ScholarPubMed
Cho, J. & Lazarian, A. 2003 Compressible magnetohydrodynamic turbulence: mode coupling, scaling relations, anisotropy, viscosity-damped regime and astrophysical implications. Mon. Not. R. Astron. Soc. 345, 325–339.CrossRefGoogle Scholar
Elmegreen, B.G. & Scalo, J. 2004 Interstellar turbulence I: observations and processes. Annu. Rev. Astron. Astrophys. 42, 211–273.CrossRefGoogle Scholar
Federrath, C., Chabrier, G., Schober, J., Banerjee, R., Klessen, R.S. & Schleicher, D.R.G. 2011 Mach number dependence of turbulent magnetic field amplification: solenoidal versus compressive flows. Phys. Rev. Lett. 107 (11), 114504.CrossRefGoogle ScholarPubMed
Federrath, C., Roman-Duval, J., Klessen, R.S., Schmidt, W. & Mac Low, M.-M. 2010 Comparing the statistics of interstellar turbulence in simulations and observations-solenoidal versus compressive turbulence forcing. Astron. Astrophys. 512, A81.CrossRefGoogle Scholar
Federrath, C., Schober, J., Bovino, S. & Schleicher, D.R.G. 2014 The turbulent dynamo in highly compressible supersonic plasmas. Astrophys. J. Lett. 797 (2), L19.CrossRefGoogle Scholar
Fu, X., Li, H., Guo, F., Li, X. & Roytershteyn, V. 2018 Parametric decay instability and dissipation of low-frequency Alfvén waves in low-beta turbulent plasmas. Astrophys. J. 855 (2), 139.CrossRefGoogle Scholar
Fyfe, D., Montgomery, D. & Joyce, G. 1977 Dissipative, forced turbulence in two-dimensional magnetohydrodynamics. J. Plasma Phys. 17, 369–398.CrossRefGoogle Scholar
Galtier, S., Politano, H. & Pouquet, A. 1997 Self-similar energy decay in magnetohydrodynamic turbulence. Phys. Rev. Lett. 79 (15), 2807–2810.CrossRefGoogle Scholar
Gary, S.P., Skoug, R.M., Steinberg, J.T. & Smith, C.W. 2001 Proton temperature anisotropy constraint in the solar wind: ace observations. Geophys. Res. Lett. 28 (14), 2759–2762.CrossRefGoogle Scholar
Ghosh, S. & Matthaeus, W.H. 1990 Relaxation processes in a turbulent compressible magnetofluid. Phys. Fluids B 2 (7), 1520–1534.CrossRefGoogle Scholar
Ghosh, S. & Matthaeus, W.H. 1992 Low Mach number two-dimensional hydrodynamic turbulence: energy budgets and density fluctuations in a polytropic fluid. Phys. Fluids A 4 (1), 148–164.CrossRefGoogle Scholar
Goldstein, B. & Siscoe, G.L. 1972 Spectra and cross spectra of solar wind parameters from mariner 5. NASA Special Publ. 308, 506–516.Google Scholar
Grappin, R., Velli, M. & Mangeney, A. 1991 ‘Alfvénic’ versus ‘standard’ turbulence in the solar wind. Ann. Geophys. 9, 416–426.Google Scholar
Grete, P., O'Shea, B.W., Beckwith, K., Schmidt, W. & Christlieb, A. 2017 Energy transfer in compressible magnetohydrodynamic turbulence. Phys. Plasmas 24 (9), 092311.CrossRefGoogle Scholar
Hadid, L.Z., Sahraoui, F. & Galtier, S. 2017 Energy cascade rate in compressible fast and slow solar wind turbulence. Astrophys. J. 838 (1), 9.CrossRefGoogle Scholar
Hadid, L.Z., Sahraoui, F., Galtier, S. & Huang, S.Y. 2018 Compressible magnetohydrodynamic turbulence in the earth's magnetosheath: estimation of the energy cascade rate using in situ spacecraft data. Phys. Rev. Lett. 120 (5), 055102.CrossRefGoogle ScholarPubMed
Hellinger, P., Verdini, A., Landi, S., Franci, L. & Matteini, L. 2018 von Kármán–Howarth equation for Hall magnetohydrodynamics: hybrid simulations. Astrophys. J. Lett. 857 (2), L19.CrossRefGoogle Scholar
Hnat, B., Chapman, S.C. & Rowlands, G. 2005 Compressibility in solar wind plasma turbulence. Phys. Rev. Lett. 94 (20), 204502.CrossRefGoogle ScholarPubMed
Hossain, M., Gray, P.C., Pontius, D.H. Jr., Matthaeus, W.H. & Oughton, S. 1995 Phenomenology for the decay of energy-containing eddies in homogeneous mhd turbulence. Phys. Fluids 7, 2886–2904.CrossRefGoogle Scholar
Howes, G.G., Bale, S.D., Klein, K.G., Chen, C.H.K., Salem, C.S. & TenBarge, J.M. 2012 The slow-mode nature of compressible wave power in solar wind turbulence. Astrophys. J. Lett. 753 (1), L19.CrossRefGoogle Scholar
Huang, Y.X., Schmitt, F.G., Lu, Z.M., Fougairolles, P., Gagne, Y. & Liu, Y.L. 2010 Second-order structure function in fully developed turbulence. Phys. Rev. E 82 (2), 026319.CrossRefGoogle ScholarPubMed
Hunana, P. & Zank, G.P. 2010 Inhomogeneous nearly incompressible description of magnetohydrodynamic turbulence. Astrophys. J. 718 (1), 148.CrossRefGoogle Scholar
Iroshnikov, P.S. 1964 Turbulence of a conducting fluid in a strong magnetic field. Sov. Astron. 7, 566–571.Google Scholar
Kida, S. & Orszag, S.A. 1990 Energy and spectral dynamics in forced compressible turbulence. J. Sci. Comput. 5, 85–125.CrossRefGoogle Scholar
Kida, S. & Orszag, S.A. 1992 Energy and spectral dynamics in decaying compressible turbulence. J. Sci. Comput. 7 (1), 1–34.CrossRefGoogle Scholar
Kinney, R., McWilliams, J.C. & Tajima, T. 1995 Coherent structures and turbulent cascades in two-dimensional incompressible magnetohydrodynamic turbulence. Phys. Plasmas 2 (10), 3623–3639.CrossRefGoogle Scholar
Klainerman, S. & Majda, A. 1981 Singular limits of quasilinear hyperbolic systems with large parameters and the incompressible limit of compressible fluids. Commun. Pure Appl. Maths 34 (4), 481–524.CrossRefGoogle Scholar
Klainerman, S. & Majda, A. 1982 Compressible and incompressible fluids. Commun. Pure Appl. Maths 35, 629–651.CrossRefGoogle Scholar
Klein, K.G., Howes, G.G., TenBarge, J.M., Bale, S.D., Chen, C.H.K. & Salem, C.S. 2012 Using synthetic spacecraft data to interpret compressible fluctuations in solar wind turbulence. Astrophys. J. 755 (2), 159.CrossRefGoogle Scholar
Klein, L., Bruno, R., Bavassano, B. & Rosenbauer, H. 1993 Scaling of density fluctuations with Mach number and density-temperature anticorrelations in the inner heliosphere. J. Geophys. Res. 98 (A5), 7837–7841.CrossRefGoogle Scholar
Kolmogorov, A.N. 1941 The local structure of turbulence in incompressible viscous fluid for very large Reynolds numbers. Dokl. Akad. Nauk SSSR 30, 301–305.Google Scholar
Kowal, G. & Lazarian, A. 2007 Scaling relations of compressible MHD turbulence. Astrophys. J. 666, L67–L72.CrossRefGoogle Scholar
Kowal, G. & Lazarian, A. 2010 Velocity field of compressible magnetohydrodynamic turbulence: wavelet decomposition and mode scalings. Astrophys. Galaxies 720, 742–756.CrossRefGoogle Scholar
Kraichnan, R.H. 1955 On the statistical mechanics of an adiabatically compressible fluid. J. Acoust. Soc. Am. 27 (3), 438–441.CrossRefGoogle Scholar
Kraichnan, R.H. 1965 Inertial-range spectrum of hydromagnetic turbulence. Phys. Fluids 8 (7), 1385–1387.CrossRefGoogle Scholar
Kritsuk, A.G., Wagner, R. & Norman, M.L. 2013 Energy cascade and scaling in supersonic isothermal turbulence. J. Fluid Mech. 729, R1.CrossRefGoogle Scholar
Lee, K., Yu, D. & Girimaji, S.S. 2006 Lattice Boltzmann DNS of decaying compressible isotropic turbulence with temperature fluctuations. Intl J. Comput. Fluid Dyn. 20 (6), 401–413.CrossRefGoogle Scholar
Lemaster, M.N. & Stone, J.M. 2009 Dissipation and heating in supersonic hydrodynamic and MHD turbulence. Astrophys. J. 691 (2), 1092.CrossRefGoogle Scholar
Lithwick, Y. & Goldreich, P. 2001 Compressible magnetohydrodynamic turbulence in interstellar plasmas. Astrophys. J. 562, 279–296.CrossRefGoogle Scholar
Mac Low, M.-M. 1999 The energy dissipation rate of supersonic, magnetohydrodynamic turbulence in molecular clouds. Astrophys. J. 524 (1), 169–178.CrossRefGoogle Scholar
Mac Low, M.-M. & Klessen, R.S. 2004 Control of star formation by supersonic turbulence. Astrophysics 76, 125–194.Google Scholar
Mac Low, M.-M., Klessen, R.S., Burkert, A. & Smith, M.D. 1998 Kinetic energy decay rates of supersonic and super-Alfvénic turbulence in star-forming clouds. Phys. Rev. Lett. 80 (13), 2754–2757.CrossRefGoogle Scholar
Majda, A.J. & Embid, P. 1998 Averaging over fast gravity waves for geophysical flows with unbalanced initial data. Theor. Comput. Fluid Dyn. 11, 155–169.CrossRefGoogle Scholar
Makwana, K.D. & Yan, H. 2020 Properties of magnetohydrodynamic modes in compressively driven plasma turbulence. Phys. Rev. X 10 (3), 031021.Google Scholar
Maruca, B.A., Bale, S.D., Sorriso-Valvo, L., Kasper, J.C. & Stevens, M.L. 2013 Collisional thermalization of hydrogen and helium in solar-wind plasma. Phys. Rev. Lett. 111, 241101.CrossRefGoogle ScholarPubMed
Matthaeus, W.H. & Brown, M.R. 1988 Nearly incompressible magnetohydrodynamics at low Mach number. Phys. Fluids 31 (12), 3634–3644.CrossRefGoogle Scholar
Matthaeus, W.H., Klein, L.W., Ghosh, S. & Brown, M.R. 1991 Nearly incompressible magnetohydrodynamics, pseudosound, and solar wind fluctuations. J. Geophys. Res. 96, 5421–5435.CrossRefGoogle Scholar
Mininni, P.D. 2011 Scale interactions in magnetohydrodynamic turbulence. Annu. Rev. Fluid Mech. 43, 377–397.CrossRefGoogle Scholar
Miura, H. & Kida, S. 1995 Acoustic energy exchange in compressible turbulence. Phys. Fluids 7, 1732–1742.CrossRefGoogle Scholar
Moffatt, H.K. 1978 Field Generation in Electrically Conducting Fluids. Cambridge University Press.Google Scholar
Montgomery, D., Brown, M.R. & Matthaeus, W.H. 1987 Density fluctuation spectra in magnetohydrodynamic turbulence. J. Geophys. Res. 92 (A1), 282–284.CrossRefGoogle Scholar
Montgomery, D., Turner, L. & Vahala, G. 1978 Three-dimensional magnetohydrodynamic turbulence in cylindrical geometry. Phys. Fluids 21 (5), 757–764.CrossRefGoogle Scholar
Oughton, S., Matthaeus, W.H., Wan, M. & Osman, K.T. 2015 Anisotropy in solar wind plasma turbulence. Phil. Trans. R. Soc. Lond. A 373, 20140152.Google ScholarPubMed
Padoan, P. & Nordlund, Å. 1999 A super-Alfvénic model of dark clouds. Astrophys. J. 526 (1), 279–294.CrossRefGoogle Scholar
Pan, S. & Johnsen, E. 2017 The role of bulk viscosity on the decay of compressible, homogeneous, isotropic turbulence. J. Fluid Mech. 833, 717–744.CrossRefGoogle Scholar
Parker, E.N. 1957 Sweet's mechanism for merging magnetic fields in conducting fluids. J. Geophys. Res. 62 (4), 509–520.CrossRefGoogle Scholar
Pine, Z.B., et al. 2020 Solar wind turbulence from 1 to 45 AU. III. Anisotropy of magnetic fluctuations in the inertial range using voyager and ace observations. Astrophys. J. 900 (2), 93.CrossRefGoogle Scholar
Podesta, J.J. 2008 Laws for third-order moments in homogeneous anisotropic incompressible magnetohydrodynamic turbulence. J. Fluid Mech. 609, 171–194.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, R21–R24.CrossRefGoogle Scholar
Pouquet, A., Brachet, M.-E., Lee, E., Mininni, P., Rosenberg, D. & Uritsky, V. 2010 Lack of universality in mhd turbulence, and the possible emergence of a new paradigm? Proc. Intl Astronom. Union 6 (S271), 304–316.CrossRefGoogle Scholar
Pouquet, A., Sulem, P.L. & Meneguzzi, M. 1988 Influence of velocity-magnetic field correlations on decaying magnetohydrodynamic turbulence with neutral X points. Phys. Fluids 31 (9), 2635–2643.CrossRefGoogle Scholar
Praturi, D.S. & Girimaji, S.S. 2019 Effect of pressure-dilatation on energy spectrum evolution in compressible turbulence. Phys. Fluids 31 (5), 055114.CrossRefGoogle Scholar
Praturi, D.S. & Girimaji, S.S. 2020 Magnetic–internal–kinetic energy interactions in high-speed turbulent magnetohydrodynamic jets. Trans. ASME J. Fluids Engng 142 (10), 101213.CrossRefGoogle Scholar
Reid, H.A.S. & Kontar, E.P. 2010 Solar wind density turbulence and solar flare electron transport from the sun to the earth. Astrophys. J. 721 (1), 864.CrossRefGoogle Scholar
Riazantseva, M.O., Budaev, V.P., Zelenyi, L.M., Zastenker, G.N., Pavlos, G.P., Safrankova, J., Nemecek, Z., Prech, L. & Nemec, F. 2015 Dynamic properties of small-scale solar wind plasma fluctuations. Phil. Trans. R. Soc. Lond. A 373 (2041), 20140146.Google ScholarPubMed
Ristorcelli, J.R. 1997 A pseudo-sound constitutive relationship for the dilatational covariances in compressible turbulence. J. Fluid Mech. 347, 37–70.CrossRefGoogle Scholar
Roberts, D.A. & Goldstein, M.L. 1987 Spectral signatures of jumps and turbulence in interplanetary speed and magnetic field data. J. Geophys. Res. 92 (A9), 10105–10110.CrossRefGoogle Scholar
Roberts, O.W., Narita, Y., Li, X., Escoubet, C.P. & Laakso, H. 2017 Multipoint analysis of compressive fluctuations in the fast and slow solar wind. J. Geophys. Res. 122 (7), 6940–6963.CrossRefGoogle Scholar
Salvesen, G., Beckwith, K., Simon, J.B., O'Neill, S.M. & Begelman, M.C. 2014 Quantifying energetics and dissipation in magnetohydrodynamic turbulence. Mon. Not. R. Astron. Soc. 438 (2), 1355–1376.CrossRefGoogle Scholar
Sarkar, S. 1992 The pressure-dilatation correlation in compressible flows. Phys. Fluids A 4, 2674–2682.CrossRefGoogle Scholar
Schmidt, W., Federrath, C. & Klessen, R. 2008 Is the scaling of supersonic turbulence universal? Phys. Rev. Lett. 101, 194505.CrossRefGoogle ScholarPubMed
Servidio, S., Matthaeus, W.H. & Dmitruk, P. 2008 Depression of nonlinearity in decaying isotropic MHD turbulence. Phys. Rev. Lett. 100, 095005.CrossRefGoogle ScholarPubMed
Shebalin, J.V., Matthaeus, W.H. & Montgomery, D. 1983 Anisotropy in MHD turbulence due to a mean magnetic field. J. Plasma Phys. 29, 525–547.CrossRefGoogle Scholar
Shebalin, J.V. & Montgomery, D. 1988 Turbulent magnetohydrodynamic density fluctuations. J. Plasma Phys. 39 (2), 339–367.CrossRefGoogle Scholar
Shoda, M., Suzuki, T.K., Asgari-Targhi, M. & Yokoyama, T. 2019 Three-dimensional simulation of the fast solar wind driven by compressible magnetohydrodynamic turbulence. Astrophys. J. Lett. 880 (1), L2.CrossRefGoogle Scholar
Siscoe, G.L., Davis, L. Jr., Coleman, P.J. Jr., Smith, E.J. & Jones, D.E. 1968 Power spectra and discontinuities of the interplanetary magnetic field: mariner 4. J. Geophys. Res. 73 (1), 61–82.CrossRefGoogle Scholar
Smith, C.W., Vasquez, B.J. & Hamilton, K. 2006 Interplanetary magnetic fluctuation anisotropy in the inertial range. J. Geophys. Res. 111, A09111.Google Scholar
Spangler, S.R. & Spitler, L.G. 2004 An empirical investigation of compressibility in magnetohydrodyna- mic turbulence. Phys. Plasmas 11 (5), 1969–1977.CrossRefGoogle Scholar
Sreenivasan, K.R. 1991 On local isotropy of passive scalars in turbulent shear flows. Proc. R. Soc. Lond. A 434 (1890), 165–182.Google Scholar
Stone, J.M., Ostriker, E.C. & Gammie, C.F. 1998 Dissipation in compressible magnetohydrodynamic turbulence. Astrophys. J. Lett. 508 (1), L99.CrossRefGoogle Scholar
Stribling, T. & Matthaeus, W.H. 1991 Relaxation processes in a low-order three-dimensional magnetohydrodynamics model. Phys. Fluids B 3 (8), 1848–1864.CrossRefGoogle Scholar
Taylor, J.B. 1974 Relaxation of toroidal plasma and generation of reverse magnetic fields. Phys. Rev. Lett. 33 (19), 1139–1141.CrossRefGoogle Scholar
Tu, C.-Y. & Marsch, E. 1994 On the nature of compressive fluctuations in the solar wind. J. Geophys. Res. 99 (A11), 21481–21509.CrossRefGoogle Scholar
Tu, C.-Y. & Marsch, E. 1995 MHD structures, waves and turbulence in the solar wind: observations and theories. Space Sci. Rev. 73, 1–210.CrossRefGoogle Scholar
Wan, M., Oughton, S., Servidio, S. & Matthaeus, W.H. 2012 von Kármán self-preservation hypothesis for magnetohydrodynamic turbulence and its consequences for universality. J. Fluid Mech. 697, 296–315.CrossRefGoogle Scholar
Wang, J., Gotoh, T. & Watanabe, T. 2017 Scaling and intermittency in compressible isotropic turbulence. Phys. Rev. Fluids 2 (5), 053401.CrossRefGoogle Scholar
Wang, J., Wan, M., Chen, S., Xie, C., Lian-Ping, W. & Chen, S. 2019 Cascades of temperature and entropy fluctuations in compressible turbulence. J. Fluid Mech. 867, 195–215.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. Phys. Rev. Lett. 110 (21), 214505.CrossRefGoogle ScholarPubMed
Wicks, R.T., Mallet, A., Horbury, T.S., Chen, C.H.K., Schekochihin, A.A. & Mitchell, J.J. 2013 Alignment and scaling of large-scale fluctuations in the solar wind. Phys. Rev. Lett. 110 (2), 025003.CrossRefGoogle ScholarPubMed
Yang, L., Zhang, L., He, J., Tu, C., Li, S., Wang, X. & Wang, L. 2018 Coexistence of slow-mode and Alfvén-mode waves and structures in 3D compressive MHD turbulence. Astrophys. J. 866 (1), 41.CrossRefGoogle Scholar
Yang, Y. 2019 Hybrid scheme for compressible MHD turbulence. In Energy Transfer and Dissipation in Plasma Turbulence, pp. 35–67. Springer.CrossRefGoogle Scholar
Yang, Y., Matthaeus, W.H., Shi, Y., Wan, M. & Chen, S. 2017 Compressibility effect on coherent structures, energy transfer and scaling in magnetohydrodynamic turbulence. Phys. Fluids 29, 035105.CrossRefGoogle Scholar
Yang, Y., Shi, Y., Wan, M., Matthaeus, W.H. & Chen, S. 2016 a Energy cascade and its locality in compressible magnetohydrodynamic turbulence. Phys. Rev. E 93, 061102.CrossRefGoogle ScholarPubMed
Yang, Y., Wan, M., Shi, Y., Yang, K. & Chen, S. 2016 b A hybrid scheme for compressible magnetohydrodynamic turbulence. J. Comput. Phys. 306, 73–91.CrossRefGoogle Scholar
Yao, S., He, J.-S., Marsch, E., Tu, C.-Y., Pedersen, A., Rème, H. & Trotignon, J.-G. 2011 Multi-scale anti-correlation between electron density and magnetic field strength in the solar wind. Astrophys. J. 728 (2), 146.CrossRefGoogle Scholar
Zank, G.P. & Matthaeus, W.H. 1990 Nearly incompressible hydrodynamics and heat conduction. Phys. Rev. Lett. 64 (11), 1243–1246.CrossRefGoogle ScholarPubMed
Zank, G.P. & Matthaeus, W.H. 1993 Nearly incompressible fluids. II: magnetohydrodynamics, turbulence, and waves. Phys. Fluids A 5 (1), 257–273.CrossRefGoogle Scholar
Zank, G.P., Nakanotani, M. & Webb, G.M. 2019 Compressible and incompressible magnetic turbulence observed in the very local interstellar medium by voyager 1. Astrophys. J. 887 (2), 116.CrossRefGoogle Scholar
Zank, G.P. & Matthaeus, W.H. 1992 Waves and turbulence in the solar wind. J. Geophys. Res. 97 (A11), 17189–17194.CrossRefGoogle Scholar
Zank, G.P., Matthaeus, W.H. & Klein, L.W. 1990 Temperature and density anti-correlations in the solar wind. Geophys. Res. Lett. 17, 1239–1242.CrossRefGoogle Scholar