Hostname: page-component-cc8bf7c57-5wl6q Total loading time: 0 Render date: 2024-12-12T02:12:21.206Z Has data issue: false hasContentIssue false

Mass and internal-energy transports in strongly compressible magnetohydrodynamic turbulence

Published online by Cambridge University Press:  11 December 2018

N. Yokoi*
Affiliation:
Institute of Industrial Science, University of Tokyo, 4-6-1, Komaba, Tokyo 153-8505, Japan Nordic Institute for Theoretical Physics (NORDITA), Roslagstullsbacken 23, 106 91 Stockholm, Sweden
*
Email address for correspondence: [email protected]

Abstract

Turbulent mass and internal-energy transports in strongly compressible magnetohydrodynamic (MHD) turbulence are investigated in the framework of the multiple-scale direct-interaction approximation, an analytical closure scheme for inhomogeneous turbulence at very high Reynolds numbers. Utilising the analytical representations for the turbulent mass and internal-energy fluxes and their transport coefficients, which are expressed in terms of the correlation and response functions, turbulence models for these fluxes are proposed. In addition to the usual gradient-diffusion transports, cross-diffusion transports mediated by the density variance and the transports along the mean magnetic field mediated by the compressional or dilatational turbulent cross-helicity (velocity–magnetic-field correlation coupled with compressive motions) are shown to arise. These compressibility effects are of fundamental importance since they provide deviations from the usual gradient-diffusion transports. Analogies of the dilatational cross-helicity effects to the magnetoacoustic waves are also argued.

Type
Research Article
Copyright
© Cambridge University Press 2018 

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

Aluie, H. 2011 Compressible turbulence: the cascade and its locality. Phys. Rev. Lett. 106, 174502.Google Scholar
Batchelor, G. K. 1953 The Theory of Homogeneous Turbulence. Cambridge University Press.Google Scholar
Braginsky, S. & Roberts, P. 1995 Equations governing convection in Earth’s core and the geodynamo. Geophys. Astrophys. Fluid Dyn. 79, 197.Google Scholar
Bruno, R. & Carbone, V. 2016 Turbulence in the Solar Wind. Springer.Google Scholar
Chassaing, P., Antonia, R. A., Anselmet, F., Joly, L. & Sarkar, S. 2002 Variable Density Fluid Turbulence. Kluwer.Google Scholar
Cramer, N. F. 2001 The Physics of Alfvén Waves. Wiley-VCH.Google Scholar
Cross, R. 1988 An Introduction to Alfven Waves. Adam Hilger.Google Scholar
Federrath, C. & Klessen, R. S. 2012 The star formation rate of turbulent magnetized clouds: comparing theory, simulations, and observations. Astrophys. J. 761, 156.Google Scholar
Gurnett, D. & Bhattacharjee, A. 2017 Introduction to Plasma Physics: With Space, Laboratory and Astrophysical Applications, 2nd edn. Cambridge University Press.Google Scholar
Hamba, F. 1987 Statistical analysis of chemically reacting passive scalars in turbulent shear flow. J. Phys. Soc. Japan 56, 7996.Google Scholar
Higashimori, K., Yokoi, N. & Hoshino, M. 2013 Explosive turbulent magnetic reconnection. Phys. Rev. Lett. 110, 255001.Google Scholar
Hinze, J. O. 1975 Turbulence, 2nd edn. Springer.Google Scholar
Kaviany, M. 2001 Principles of Convective Heat Transfer, 2nd edn. Springer.Google Scholar
Kraichnan, R. 1959 The structure of isotropic turbulence at very high Reynolds number. J. Fluid Mech. 5, 497543.Google Scholar
Krause, F. & Rädler, K.-H. 1980 Mean-Field Magnetohydrodynamics and Dynamo Theory. Pergamon.Google Scholar
Kritsuk, A., Ustyugov, S. D. & Norman, M. L. 2017 The structure and statistics of interstellar turbulence. New J. Phys. 19, 065003.Google Scholar
Kupka, F. 2009 Turbulent convection and numerical simulations in solar and stellar astrophysics. In Interdisciplinary Aspects of Turbulence (ed. Hillebrandt, W. & Kupka, F.), Lecture Notes in Physics, vol. 756, pp. 49105. Springer.Google Scholar
Lesieure, M. 2008 Turbulence in Fluids: Fourth Revised and Enlarged Edition. Springer.Google Scholar
Linden, P. F. 2000 Convection in the environment. In Perspectives in Fluid Dynamics: A Collective Introduction to Current Research (ed. Batchelor, G. K., Moffatt, H. K. & Worster, M. G.), pp. 289345. Cambridge University Press.Google Scholar
Mabanta, Q. A. & Murphy, J. W. 2018 How turbulence enables core-collapse supernova explosion. Astrophys. J. 856, 22-1-14.Google Scholar
Mac Low, M.-M. & Klessen, R. S. 2004 Control of star formation by supersonic turbulence. Rev. Mod. Phys. 76, 125194.Google Scholar
McKee, C. F. & Ostriker, E. C. 2007 Theory of star formation. Annu. Rev. Astron. Astrophys. 45, 565687.Google Scholar
Meakin, C. & Arnett, W. D. 2010 Some properties of the kinetic energy flux and dissipation in turbulent stellar convection zones. Astrophys. Space Sci. 328, 221225.Google Scholar
Mihalas, D. & Weibel-Mihalas, B. 1984 Foundations of Radiation Hydrodynamics. Oxford University Press.Google Scholar
Moffatt, H. K. 1978 Magnetic Field Generation in Electrically Conducting Fluids. Cambridge University Press.Google Scholar
Murphy, J. W. & Meakin, C. 2011 A global turbulence model for neutrino-driven convection in core-collapse supernovae. Astrophys. J. 742, 74-1-21.Google Scholar
Parker, E. N. 1955 Hydromagnetic dynamo models. Astrophys. J. 122, 293314.Google Scholar
Rogachevskii, I. & Kleeorin, N. 2015 Turbulent fluxes of entropy and internal energy in temperature stratified flows. J. Plasma Phys. 81, 395810504.Google Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence in Turbulence. MIT Press.Google Scholar
Tu, C.-Y. & Marsch, E. 1995 MHD Structures, Waves and Turbulence in the Solar Wind: Observations and Theories. Kluwer.Google Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.Google Scholar
Widmer, F., Büchner, J. & Yokoi, N. 2016 Sub-grid-scale description of turbulent magnetic reconnection in magnetohydrodynamics. Phys. Plasmas 23, 042311.Google Scholar
Widmer, F., Büchner, J. & Yokoi, N. 2016 Characterizing plasmoid reconnection by turbulence dynamics. Phys. Plasmas 23, 092304.Google Scholar
Woltjer, L. 1958 A theorem on force-free magnetic fields. Proc. Natl Acad. Sci. USA 44, 489491.Google Scholar
Yokoi, N. 2011 Modeling the turbulent cross-helicity evolution: production, dissipation, and transport rates. J. Turbul. 12, N27-1-33.Google Scholar
Yokoi, N. 2013 Cross helicity and related dynamo. Geophys. Astrophys. Fluid Dyn. 107, 114184.Google Scholar
Yokoi, N. 2018 Electromotive force in strongly compressible magnetohydrodynamic turbulence. J. Plasma Phys. 84, 735840501.Google Scholar
Yokoi, N. & Balarac, G. 2011 Cross-helicity effects and turbulent transport in magnetohydrodynamic flow. J. Phys. Conf. Ser. 318, 072039.Google Scholar
Yokoi, N. & Brandenburg, A. 2016 Large-scale flow generation by inhomogeneous helicity. Phys. Rev. E 93, 033125.Google Scholar
Yokoi, N. & Hoshino, M. 2011 Flow–turbulence interaction in magnetic reconnection. Phys. Plasmas 18, 111208.Google Scholar
Yokoi, N. & Yoshizawa, A. 1993 Statistical analysis of the effects of helicity in inhomogeneous turbulence. Phys. Fluids A 5, 464477.Google Scholar
Yokoi, N., Higashimori, K. & Hoshino, M. 2013 Transport enhancement and suppression in turbulent magnetic reconnection: a self-consistent turbulence model. Phys. Plasmas 20, 122310.Google Scholar
Yoshizawa, A. 1984 Statistical analysis of the deviation of the Reynolds stress from its eddy-viscosity representation. Phys. Fluids 27, 13771387.Google Scholar
Yoshizawa, A. 1990 Self-consistent turbulent dynamo modeling of reversed field pinches and planetary magnetic fields. Phys. Fluids B 2, 15891600.Google Scholar
Yoshizawa, A. 1996 Compressibility and rotation effects on transport suppression in magnetohydrodynamic turbulence. Phys. Plasmas 3, 889900.Google Scholar
Yoshizawa, A. & Yokoi, N. 1993 Turbulent magnetohydrodynamic dynamo for accretion disks using the cross-helicity effect. Astrophys. J. 407, 540548.Google Scholar