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Inverse transfer of magnetic helicity in direct numerical simulations of compressible isothermal turbulence: scaling laws

Published online by Cambridge University Press:  11 March 2021

Jean-Mathieu Teissier Open the ORCID record for Jean-Mathieu Teissier [Opens in a new window]  and
Wolf-Christian Müller
Jean-Mathieu Teissier*
Affiliation:
Technische Universität Berlin, ER 3-2, Hardenbergstr. 36a, D-10623 Berlin, Germany
Wolf-Christian Müller
Affiliation:
Technische Universität Berlin, ER 3-2, Hardenbergstr. 36a, D-10623 Berlin, Germany Max-Planck/Princeton Center for Plasma Physics
*
†Email address for correspondence: jm.teissier@astro.physik.tu-berlin.de
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Abstract

The inverse transfer of magnetic helicity is investigated through direct numerical simulations of large-scale mechanically driven turbulent flows in the isothermal ideal magnetohydrodynamics framework. The mechanical forcing is either purely solenoidal or purely compressive and the turbulent statistically stationary states considered exhibit root mean square (RMS) Mach numbers $0.1 \lesssim {\mathcal {M}} \lesssim 11$. A continuous small-scale electromotive forcing injects magnetic helical fluctuations, which lead to the build-up of ever larger magnetic structures. Spectral scaling exponents are observed which, for low Mach numbers, are consistent with previous research done in the incompressible case. Higher compressibility leads to smaller absolute values of the magnetic helicity scaling exponents. The deviations from the incompressible case are comparatively small for solenoidally driven turbulence, even at high Mach numbers, as compared with those for compressively driven turbulence, where strong deviations are already visible at relatively mild RMS Mach numbers ${\mathcal {M}}\gtrsim 3$. Compressible effects can thus play an important role in the inverse transfer of magnetic helicity, especially when the turbulence drivers are rather compressive. Theoretical results observed in the incompressible case can, however, be transferred to supersonic turbulence by an appropriate change of variables, using the Alfvén velocity in place of the magnetic field.

JFM classification

Turbulent Flows: Turbulence simulation Turbulent Flows: Compressible turbulence MHD and Electrohydrodynamics: MHD turbulence

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Type
JFM Papers
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Journal of Fluid Mechanics , Volume 915 , 25 May 2021 , A23
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© The Author(s), 2021. Published by Cambridge University Press

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References

REFERENCES

Alexakis, A. & Biferale, L. 2018 Cascades and transitions in turbulent flows. Phys. Rep. 767–769, 1–101.CrossRefGoogle Scholar
Alexakis, A., Mininni, P.D. & Pouquet, A. 2006 On the inverse cascade of magnetic helicity. Astrophys. J. 640, 335–343.CrossRefGoogle Scholar
Alfvén, H. 1942 On the existence of electromagnetic-hydrodynamic waves. Ark. Mat. Astron. Fys. 29B (2), 1–7.Google Scholar
Aluie, H. 2013 Scale decomposition in compressible turbulence. Physica D 247, 54–65.CrossRefGoogle Scholar
Aluie, H. 2017 Coarse-grained incompressible magnetohydrodynamics: analyzing the turbulent cascades. New J. Phys. 19, 025008.CrossRefGoogle Scholar
Balsara, D. & Pouquet, A. 1999 The formation of large-scale structures in supersonic magnetohydrodynamic flows. Phys. Plasmas 6 (1), 89–99.CrossRefGoogle Scholar
Balsara, D.S. 2010 Multidimensional HLLE Riemann solver: application to Euler and magnetohydrodynamic flows. J. Comput. Phys. 229, 1970–1993.CrossRefGoogle Scholar
Balsara, D.S. 2012 Self-adjusting, positivity preserving high order schemes for hydrodynamics and magnetohydrodynamics. J. Comput. Phys. 231, 7504–7517.CrossRefGoogle Scholar
Berger, M.A. 1997 Magnetic helicity in a periodic domain. J. Geophys. Res. 102 (A2), 2637–2644.CrossRefGoogle Scholar
Berger, M.A. 1999 Introduction to magnetic helicity. Plasma Phys. Control. Fusion 41, B167–B175.CrossRefGoogle Scholar
Bieber, J.W., Evenson, P.A. & Matthaeus, W.H. 1987 Magnetic helicity of the Parker field. Astrophys. J. 315, 700–705.CrossRefGoogle Scholar
Biskamp, D. 1993 Nonlinear Magnetohydrodynamics. Cambridge University Press.CrossRefGoogle Scholar
Brandenburg, A. 2001 The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence. Astrophys. J. 550, 824–840.CrossRefGoogle Scholar
Brandenburg, A. & Lazarian, A. 2013 Astrophysical hydromagnetic turbulence. Space Sci. Rev. 178, 163–200.CrossRefGoogle Scholar
Brandenburg, A. & Subramanian, K. 2005 Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417, 1–209.CrossRefGoogle Scholar
Buchmüller, P. & Helzel, C. 2014 Improved accuracy of high-order WENO finite volume methods on cartesian grids. J. Sci. Comput. 61, 343–368.CrossRefGoogle Scholar
Chen, Q., Chen, S. & Eyink, G.L. 2003 The joint cascade of energy and helicity in three-dimensional turbulence. Phys. Fluids 15, 361–374.CrossRefGoogle Scholar
Christensson, M., Hindmarsh, M. & Brandenburg, A. 2001 Inverse cascade in decaying three-dimensional magnetohydrodynamic turbulence. Phys. Rev. E 64, 056405.CrossRefGoogle ScholarPubMed
Colella, P. & Woodward, P.R. 1984 The piecewise parabolic method (PPM) for gas-dynamical simulations. J. Comput. Phys. 54, 174–201.CrossRefGoogle Scholar
Dobler, W., Haugen, N.E.L., Yousef, T.A. & Brandenburg, A. 2003 Bottleneck effect in three-dimensional turbulence simulations. Phys. Rev. E 68, 026304.CrossRefGoogle ScholarPubMed
Elmegreen, B.G. & Scalo, J. 2004 Interstellar turbulence I: observations. Annu. Rev. Astron. Astrophys. 42, 211–273.CrossRefGoogle Scholar
Elsässer, W.M. 1956 Hydromagnetic dynamo theory. Rev. Mod. Phys. 28 (2), 135–163.CrossRefGoogle Scholar
Escande, D.F. et al. . 2000 Quasi-single-helicity reversed-field-pinch plasmas. Phys. Rev. Lett. 85 (8), 1662–1665.CrossRefGoogle ScholarPubMed
Evans, C.R. & Hawley, J.F. 1988 Simulation of magnetohydrodynamic flows: a constrained transport method. Astrophys. J. 332, 659–677.CrossRefGoogle Scholar
Falkovich, G. 1994 Bottleneck phenomenon in developed turbulence. Phys. Fluids 6, 1411–1414.CrossRefGoogle Scholar
Federrath, C. 2013 On the universality of supersonic turbulence. Mon. Not. R. Astron. Soc. 436, 1245–1257.CrossRefGoogle Scholar
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
Fleck, R.C. Jr. 1996 Scaling relations for the turbulent, non-self-gravitating, neutral component of the interstellar medium. Astrophys. J. 458, 739–741.CrossRefGoogle Scholar
Frisch, U., Pouquet, A., Léorat, J. & Mazure, A. 1975 Possibility of an inverse cascade of magnetic helicity in magnetohydrodynamic turbulence. J. Fluid Mech. 68 (Part 4), 769–778.CrossRefGoogle Scholar
Graham, J.P., Mininni, P.D. & Pouquet, A. 2011 High Reynolds number magnetohydrodynamic turbulence using a Lagrangian model. Phys. Rev. E 84, 016314.CrossRefGoogle ScholarPubMed
Ketcheson, D.I. 2008 Highly efficient strong stability-preserving Runge–Kutta methods with low-storage implementations. SIAM J. Sci. Comput. 30 (4), 2113–2136.CrossRefGoogle Scholar
Kraichnan, R.H. & Nagarajan, S. 1967 Growth of turbulent magnetic fields. Phys. Fluids 10, 859–870.CrossRefGoogle Scholar
Kritsuk, A.G., Norman, M.L., Padoan, P. & Wagner, R. 2007 The statistics of supersonic isothermal turbulence. Astrophys. J. 665, 416–431.CrossRefGoogle Scholar
Kumar, A. & Rust, D.M. 1996 Interplanetary magnetic clouds, helicity conservation, and current-core flux-ropes. J. Geophys. Res. 101, 667–684.Google Scholar
Levy, D., Puppo, G. & Russo, G. 1999 Central WENO schemes for hyperbolic systems of conservation laws. Math. Modelling Numer. Anal. 33 (3), 547–571.CrossRefGoogle Scholar
Linkmann, M. & Dallas, V. 2016 Large-scale dynamics of magnetic helicity. Phys. Rev. E 94, 053209.CrossRefGoogle ScholarPubMed
Linkmann, M., Sahoo, G., McKay, M., Berera, A. & Biferale, L. 2017 Effects of magnetic and kinetic helicities on the growth of magnetic fields in laminar and turbulent flows by helical Fourier decomposition. Astrophys. J. 836, 26.CrossRefGoogle Scholar
Low, B.C. 1994 Magnetohydrodynamic processes in the solar corona: flares, coronal mass ejections, and magnetic helicity. Phys. Plasmas 1, 1684–1690.CrossRefGoogle Scholar
Mac Low, M.-M. 1999 The energy dissipation rate of supersonic, MHD turbulence in molecular clouds. Astrophys. J. 524, 169–178.CrossRefGoogle Scholar
Malapaka, S.K. 2009 A study of magnetic helicity in decaying and forced 3D-MHD turbulence. PhD thesis, Universität Bayreuth.Google Scholar
McCorquodale, P. & Colella, P. 2011 A high-order finite-volume method for conservation laws on locally refined grids. Commun. Appl. Maths Comput. Sci. 6 (1), 1–25.CrossRefGoogle Scholar
Meneguzzi, M., Frisch, U. & Pouquet, A. 1981 Helical and nonhelical turbulent dynamos. Phys. Rev. Lett. 47 (15), 1060–1064.CrossRefGoogle Scholar
Miesch, M. et al. . 2015 Large-eddy simulations of magnetohydrodynamic turbulence in astrophysics and space physics. Space Sci. Rev. 194, 97–137.CrossRefGoogle Scholar
Mininni, P.D. & Pouquet, A. 2009 Finite dissipation and intermittency in magnetohydrodynamics. Phys. Rev. E 80, 025401(R).CrossRefGoogle ScholarPubMed
Moffatt, H.K. 1969 The degree of knottedness of tangled vortex lines. J. Fluid Mech. 35, 117–129.CrossRefGoogle Scholar
Müller, W.-C., Malapaka, S.K. & Busse, A. 2012 Inverse cascade of magnetic helicity in magnetohydrodynamic turbulence. Phys. Rev. E 85, 015302(R).CrossRefGoogle ScholarPubMed
Orszag, S.A. 1970 Analytical theories of turbulence. J. Fluid Mech. 41, 363–386.CrossRefGoogle Scholar
Pouquet, A., Frisch, U. & Léorat, J. 1976 Strong MHD helical turbulence and the nonlinear dynamo effect. J. Fluid Mech. 77 (Part 2), 321–354.CrossRefGoogle Scholar
Pouquet, A. & Patterson, G.S. 1978 Numerical simulation of helical magnetohydrodynamic turbulence. J. Fluid Mech. 85 (Part 2), 305–323.CrossRefGoogle Scholar
Núñez-de la Rosa, J. & Munz, C.-D. 2016 XTROEM-FV: a new code for computational astrophysics based on very high-order finite volume methods- I. Magnetohydrodynamics. Mon. Not. R. Astron. Soc. 455, 3458–3479.CrossRefGoogle Scholar
Rusanov, V.V. 1961 The calculation of the interaction of non-stationary shock waves with barriers. Zh. Vychislit. Mat. Mat. Fiz. 1 (2), 267–279 (translation in English USSR Comput. Math. Math. Phys. 1(2), 1962, pp. 304–320).Google Scholar
Schmidt, W., Hillebrandt, W. & Niemeyer, J.C. 2006 Numerical dissipation and the bottleneck effect in simulations of compressible isotropic turbulence. Comput. Fluids 35, 353–371.CrossRefGoogle Scholar
Teissier, J.-M. 2020 Magnetic helicity inverse transfer in isothermal supersonic magnetohydrodynamic turbulence. PhD thesis, Technische Universität Berlin.CrossRefGoogle Scholar
Verma, P.S., Teissier, J.-M., Henze, O. & Müller, W.-C. 2019 Fourth-order accurate finite-volume CWENO scheme for astrophysical MHD problems. Mon. Not. R. Astron. Soc. 482, 416–437.CrossRefGoogle Scholar
Vishniac, E.T. & Cho, J. 2001 Magnetic helicity conservation and astrophysical dynamos. Astrophys. J. 550, 752–760.CrossRefGoogle Scholar
Waleffe, F. 1992 The nature of triad interactions in homogeneous turbulence. Phys. Fluids A 4, 350–363.CrossRefGoogle Scholar
Woltjer, L. 1958 A theorem on force-free magnetic fields. Proc. Natl Acad. Sci. USA 44 (6), 489–491.CrossRefGoogle ScholarPubMed