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Electromotive force in strongly compressible magnetohydrodynamic turbulence

Published online by Cambridge University Press:  06 September 2018

Nobumitsu Yokoi*
Affiliation:
Institute of Industrial Science, University of Tokyo, Komaba, Meguro, Tokyo 153-8505, Japan
*
Email address for correspondence: [email protected]

Abstract

Fully compressible magnetohydrodynamic (MHD) turbulence is investigated in the framework of the multiple-scale direct-interaction approximation. With the aid of the propagators (correlation and Green’s functions), fluctuating fields are solved, and turbulent correlations are estimated in highly compressible turbulence. We focus on the expression of the turbulent electromotive force (EMF). Obliqueness between the mean magnetic field and the mean-density gradient, the mean internal density gradient and the non-equilibrium mean velocity contributes to the EMF in the presence of the density variance, which is ubiquitous in turbulence in strongly variable density flows such as the shock-front region. This density-variance effect is expected to locally enhance the turbulence intensity across the shock front, leading to a fast reconnection.

Type
Research Article
Copyright
© Cambridge University Press 2018 

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References

Aluie, H. 2011 Compressible turbulence: the cascade and its locality. Phys. Rev. Lett. 106, 174502.Google 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.Google Scholar
Bender, C. M. & Orszag, S. A. 1978 Advanced Mathematical Methods for Scientists and Engineers. McGraw-Hill.Google Scholar
Brandenburg, A. & Subramanian, K. Astrophysical magnetic fields and nonlinear dynamo theory. Phys. Rep. 417, 1209.Google Scholar
Chassaing, P., Antonia, R. A., Anselmet, F., Joly, L. & Sarker, S. 2002 Variable Density Fluid Turbulence. Kluwer.Google Scholar
Federrath, C. 2016 Magnetic field amplification in turbulent astrophysical plasmas. J. Phlasma Phys. 82, 535820601.Google Scholar
Federrath, C. & Klessen, R. S. 2012 The star formation rate of turbulent magnetized clouds: comparing theory, simulation, and observations. Astrophys. J. 761, 156.Google 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. Astron. Astrophys. 512, A81.Google Scholar
Galtier, S. & Banerjee, S. 2011 Exact relation for correlation functions in compressible isothermal turbulence. Phys. Rev. Lett. 107, 134501.Google Scholar
Garnier, E., Adams, N. & Sagaut, P. 2009 Large Eddy Simulation for Compressible Flows. Springer.Google Scholar
Hamba, F. 1987 Statistical analysis of chemically reacting passive scalars in turbulent shear flows. J. Phys. Soc. Japan 56, 7996.Google Scholar
Hamba, F. & Sato, H. 2008 Turbulent transport coefficients and residual energy in mean-field dynamo theory. Phys. Plasmas 15, 022302.Google Scholar
Higashimori, K., Yokoi, N. & Hoshino, M. 2013 Explosive turbulent magnetic reconnection. Phys. Rev. Lett. 110, 255001.Google Scholar
Karimabadi, H. & Lazarian, A. 2013 Magnetic reconnection in the presence of externally driven and self-generated turbulence. Phys. Plasmas 20, 112102.Google Scholar
Kraichnan, R. 1959 The structure of isotropic turbulence at very high Reynolds number. J. Fluid Mech. 5, 497543.Google Scholar
Kovasznay, L. S. G. 1953 Turbulence in supersonic flow. J. Aerosp. Sci. 20, 657682.Google Scholar
Lee, S., Lele, S. K. & Moin, P. 1993 Direct numerical simulation of isotropic turbulence interacting with a weak shock wave. J. Fluid Mech. 251, 533562.Google Scholar
Lee, S., Lele, S. K. & Moin, P. 1997 Direct numerical simulation of isotropic turbulence interacting with a weak shock wave. J. Fluid Mech. 340, 225247.Google Scholar
Petschek, H. E. 1964 Magnetic field annihilation. The Physics of Solar Flares: Proceedings of the AAS-NASA Symposium, Greenbelt, p. 425. NASA Science and Technical Information Division.Google Scholar
Rädler, K.-H., Kleeorin, N. & Rogachevskii, I. 2003 The mean electromotive force for MHD turbulence: the case of a weak mean magnetic field and slow rotation. Geophys. Astrophys. Fluid Dyn. 97, 249274.Google Scholar
Rädler, K.-H., Brandenburg, A., Del Sordo, F. & Rheinhardt, M. 2011 Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows. Phys. Rev. E 84, 046321.Google Scholar
Rogachevskii, I. & Kleeorin, N. 2001 Nonlinear turbulent magnetic diffusion and mean-field dynamo. Phys. Rev. E 64, 056307.Google Scholar
Rogachevskii, I. & Kleeorin, N. 2004 Nonlinear theory of a shear-current effect and mean-field magnetic dynamos. Phys. Rev. E 70, 046310.Google Scholar
Rogachevskii, I., Kleeorin, N. & Brandenburg, A.2018 Compressibility effects in turbulent MHD and passive scalar transport: mean-field theory. arXiv:1801-01804 submitted to J. Plasma Physics.Google Scholar
Sagaut, P. & Cambon, C. 2008 Homogeneous Turbulence Dynamics. Cambridge University Press.Google Scholar
Schmidt, W., Federrath, C. & Klessen, R. 2008 Is the scaling of supersonic turbulence universal? Phys. Rev. Lett. 101, 194505.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
Yokoi, N. 2013 Cross helicity and related dynamo. Geophys. Astrophys. Fluid Dyn. 107, 114184.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