Dynamo-generated Turbulence and Large-Scale Magnetic Fields in a Keplerian Shear Flow

The nonlinear evolution of magnetized Keplerian shear ows is simulated in a local, three-dimensional model, including the eeects of compressibility and stratiication. Supersonic ows are initially generated by the Balbus-Hawley magnetic shear instability. The resulting ows regenerate a turbulent magnetic eld which, in turn, reinforces the turbulence. Thus, the system acts like a dynamo that generates its own turbulence. However, unlike usual dynamos, the magnetic energy exceeds the kinetic energy of the turbulence by a factor of 3{10. By assuming the eld to be vertical on the outer (upper and lower) surfaces we do not constrain the horizontal magnetic ux. Indeed, a large scale toroidal magnetic eld is generated, mostly in the form of toroidal ux tubes with lengths comparable to the toroidal extent of the box. This large scale eld is mainly of 1 even (i.e. quadrupolar) parity with respect to the midplane and changes direction on a timescale of about 30 orbits, in a possibly cyclic manner. The eeective Shakura-Sunyaev alpha viscosity parameter is between 0.001 and 0.005, and the contribution from the Maxwell stress is about 3-7 times larger than the contribution from the Reynolds stress.

[1]  H. Spruit,et al.  Numerical Simulations of Shock-driven Accretion , 1993 .

[2]  Kerr.  Histograms of helicity and strain in numerical turbulence. , 1987, Physical review letters.

[3]  B. Dubrulle,et al.  Nonlinear instability of viscous plane Couette flow Part 1. Analytical approach to a necessary condition , 1991, Journal of Fluid Mechanics.

[4]  Evgenii Pavlovich Velikhov,et al.  Stability of an ideally conducting liquid flowing between cylinders rotating in a magnetic field , 1959 .

[5]  E. Zweibel.  The Theory of the Galactic Magnetic Field , 1987 .

[6]  S. Chandrasekhar,et al.  THE STABILITY OF NON-DISSIPATIVE COUETTE FLOW IN HYDROMAGNETICS. , 1960, Proceedings of the National Academy of Sciences of the United States of America.

[7]  Steven A. Orszag,et al.  Transition to turbulence in plane Poiseuille and plane Couette flow , 1980, Journal of Fluid Mechanics.

[8]  C. Tout,et al.  Accretion disc viscosity: a simple model for a magnetic dynamo. , 1992 .

[9]  Å. Nordlund,et al.  3-D simulation of turbulent cyclonic magneto-convection , 1990 .

[10]  D. Raine,et al.  Accretion power in astrophysics , 1985 .

[11]  S. Lele.  Compact finite difference schemes with spectral-like resolution , 1992 .

[12]  Guohong Xu,et al.  Parasitic instabilities in magnetized, differentially rotating disks , 1994 .

[13]  E. Zweibel,et al.  The Formation of Sharp Structures by Ambipolar Diffusion , 1994 .

[14]  E. Knobloch.  On the stability of magnetized accretion discs , 1992 .

[15]  J. Papaloizou,et al.  The dynamical stability of differentially rotating discs with constant specific angular momentum , 1984 .

[16]  Michael L. Norman,et al.  Incorporation of Ambipolar Diffusion into the ZEUS Magnetohydrodynamics Code , 1995 .

[17]  T. Tajima,et al.  Magnetic interchange instability of accretion disks , 1992 .

[18]  J. Pollack,et al.  Direct numerical simulations of turbulent convection: II. variable gravity and differential rotation , 1992 .

[19]  M. Walker.  Radiation dynamics in X-ray binaries. I - Type 1 bursts. II - Type 2 bursts. III - Extremely compact objects , 1992 .

[20]  B. Dubrulle.  Differential Rotation as a Source of Angular Momentum Transfer in the Solar Nebula , 1993 .

[21]  P. Moin,et al.  The structure of the vorticity field in homogeneous turbulent flows , 1987, Journal of Fluid Mechanics.

[22]  E. Velikhov.  STABILITY OF AN IDEALLY CONDUCTING LIQUID FLOWING BETWEEN ROTATING CYLINDERS IN A MAGNETIC FIELD , 1959 .

[23]  M. Steenbeck,et al.  Berechnung der mittleren Lorentz-Feldstärke für ein elektrisch leitendes Medium in turbulenter, durch Coriolis-Kräfte beeinflußter Bewegung , 1966 .

[24]  C. Campbell.  Magnetically-controlled disc accretion , 1992 .

[25]  J. M. Hyman,et al.  Method of lines approach to the numerical solution of conservation laws , 1979 .

[26]  R. Pudritz.  Dynamo action in turbulent accretion discs around black holes – II. The mean magnetic field , 1981 .

[27]  Eugene N. Parker,et al.  Cosmical Magnetic Fields: Their Origin and their Activity , 2019 .

[28]  O. Blaes,et al.  LOCAL SHEAR INSTABILITIES IN WEAKLY IONIZED, WEAKLY MAGNETIZED DISKS , 1994 .

[29]  M. Miller,et al.  Effect of radiation forces on disk accretion by weakly magnetic neutron stars , 1993 .

[30]  R. A. Wentzell,et al.  Hydrodynamic and Hydromagnetic Stability. By S. CHANDRASEKHAR. Clarendon Press: Oxford University Press, 1961. 652 pp. £5. 5s. , 1962, Journal of Fluid Mechanics.

[31]  A. Kerstein,et al.  Alignment of vorticity and scalar gradient with strain rate in simulated Navier-Stokes turbulence , 1987 .

[32]  M. M. Rogers.  THE STRUCTURE OF A PASSIVE SCALAR FIELD WITH A UNIFORM MEAN GRADIENT IN RAPIDLY SHEARED HOMOGENEOUS TURBULENT FLOW , 1991 .

[33]  John F. Hawley,et al.  A Powerful Local Shear Instability in Weakly Magnetized Disks. II. Nonlinear Evolution , 1991 .

[34]  D. O. Gough,et al.  Nonlinear cellular motions in Poiseuille channel flow , 1974, Journal of Fluid Mechanics.

[35]  T. Stepinski,et al.  Generation of dynamo magnetic fields in protoplanetary and other astrophysical accretion disks , 1988 .

[36]  R. Kulsrud,et al.  The stabilizing effects of cloud reacceleration - Microturbulence, and rotation of Parker's instability , 1975 .

[37]  H. K. Moffatt.  Magnetic Field Generation in Electrically Conducting Fluids , 1978 .

[38]  E. Szuszkiewicz,et al.  Vortices on accretion disks , 1992, Nature.

[39]  Н.И. Шакура,et al.  Black Holes in Binary Systems. Observational Appearance , 1973 .

[40]  Juri Toomre,et al.  Magnetic fields interacting with nonlinear compressible convection , 1988 .

[41]  D. Ryu,et al.  Convective instability in differentially rotating disks , 1992 .

[42]  John F. Hawley,et al.  A powerful local shear instability in weakly magnetized disks. III - Long-term evolution in a shearing sheet. IV - Nonaxisymmetric perturbations , 1992 .

[43]  Robert E. Wilson,et al.  BLACK HOLES IN BINARY SYSTEMS , 1973 .

[44]  J. Cannizzo,et al.  On the outburst recurrence time for the accretion disk limit cycle mechanism in dwarf novae , 1988 .

[45]  Å. Nordlund,et al.  3-D simulations of solar and stellar convection and magnetoconvection , 1990 .

[46]  H. Yoshimura.  Solar-cycle dynamo wave propagation , 1975 .

[47]  B. Elmegreen.  Gravitational collapse in dust lanes and the appearance of spiral structure in galaxies , 1979 .

[48]  E. Vishniac.  The Internal Wave Driven Dynamo in Accretion Disks , 1993 .

[49]  M. Rieutord,et al.  Magnetic structures in a dynamo simulation , 1996, Journal of Fluid Mechanics.

[50]  G. Batchelor,et al.  An Introduction to Fluid Dynamics , 1968 .

[51]  Jack Wisdom,et al.  Local simulations of planetary rings , 1986 .

[52]  P. Diamond,et al.  Dynamo Action by Internal Waves in Accretion Disks , 1990 .

[53]  D. Hughes,et al.  The nonlinear breakup of a magnetic layer: instability to interchange modes , 1988, Journal of Fluid Mechanics.