scholarly journals Global bifurcations to subcritical magnetorotational dynamo action in Keplerian shear flow

2013 ◽  
Vol 731 ◽  
pp. 1-45 ◽  
Author(s):  
A. Riols ◽  
F. Rincon ◽  
C. Cossu ◽  
G. Lesur ◽  
P.-Y. Longaretti ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Shear Flows ◽  
Three Dimensional ◽  
Transition To Turbulence ◽  
Global Bifurcations ◽  
Magnetic Field Generation ◽  
Dynamo Action ◽  
Systems Research ◽  
Hydrodynamic Shear

AbstractMagnetorotational dynamo action in Keplerian shear flow is a three-dimensional nonlinear magnetohydrodynamic process, the study of which is relevant to the understanding of accretion processes and magnetic field generation in astrophysics. Transition to this form of dynamo action is subcritical and shares many characteristics with transition to turbulence in non-rotating hydrodynamic shear flows. This suggests that these different fluid systems become active through similar generic bifurcation mechanisms, which in both cases have eluded detailed understanding so far. In this paper, we build on recent work on the two problems to investigate numerically the bifurcation mechanisms at work in the incompressible Keplerian magnetorotational dynamo problem in the shearing box framework. Using numerical techniques imported from dynamical systems research, we show that the onset of chaotic dynamo action at magnetic Prandtl numbers larger than unity is primarily associated with global homoclinic and heteroclinic bifurcations of nonlinear magnetorotational dynamo cycles born out of saddle-node bifurcations. These global bifurcations are found to be supplemented by local bifurcations of cycles marking the beginning of period-doubling cascades. The results suggest that nonlinear magnetorotational dynamo cycles provide the pathway to injection of both kinetic and magnetic energy for the problem of transition to turbulence and dynamo action in incompressible magnetohydrodynamic Keplerian shear flow in the absence of an externally imposed magnetic field. Studying the nonlinear physics and bifurcations of these cycles in different regimes and configurations may subsequently help to understand better the physical conditions of excitation of magnetohydrodynamic turbulence and instability-driven dynamos in a variety of astrophysical systems and laboratory experiments. The detailed characterization of global bifurcations provided for this three-dimensional subcritical fluid dynamics problem may also prove useful for the problem of transition to turbulence in hydrodynamic shear flows.

scholarly journals Periodic magnetorotational dynamo action as a prototype of nonlinear magnetic-field generation in shear flows

2011 ◽  
Vol 84 (3) ◽  
Author(s):  
J. Herault ◽  
F. Rincon ◽  
C. Cossu ◽  
G. Lesur ◽  
G. I. Ogilvie ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Shear Flows ◽  
Magnetic Field Generation ◽  
Dynamo Action ◽  
Field Generation

scholarly journals Simulations of Core Convection Dynamos in Rotating A-type Stars

2004 ◽  
Vol 215 ◽  
pp. 376-377
Author(s):  
Matthew Browning ◽  
Allan Sacha Brun ◽  
Juri Toomre
Keyword(s):  
Magnetic Field ◽  
Numerical Simulations ◽  
Differential Rotation ◽  
Three Dimensional ◽  
Dynamo Action ◽  
The Core ◽  
Core Convection ◽  
Seed Field ◽  
Initial Seed ◽  
Three Dimensional Simulations

We have conducted preliminary numerical simulations of a core convection dynamo operating within an A-type star of two solar masses. Convection within the core clearly can admit magnetic dynamo action. Magnetic field strengths in our three-dimensional simulations grow by many orders of magnitude, from an initial seed field to kilo-Gauss levels. We discuss the differential rotation and magnetic field sustained in our simulations.

Compressible magnetoconvection in three dimensions: planforms and nonlinear behaviour

1995 ◽  
Vol 305 ◽  
pp. 281-305 ◽  
Author(s):  
P. C. Matthews ◽  
M. R. E. Proctor ◽  
N. O. Weiss
Keyword(s):  
Magnetic Field ◽  
Shear Flow ◽  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Nonlinear Behaviour ◽  
Two Dimensional ◽  
Horizontal Shear ◽  
Mean Flow ◽  
The Magnetic Field

Convection in a compressible fiuid with an imposed vertical magnetic field is studied numerically in a three-dimensional Cartesian geometry with periodic lateral boundary conditions. Attention is restricted to the mildly nonlinear regime, with parameters chosen first so that convection at onset is steady, and then so that it is oscillatory.Steady convection occurs in the form of two-dimensional rolls when the magnetic field is weak. These rolls can become unstable to a mean horizontal shear flow, which in two dimensions leads to a pulsating wave in which the direction of the mean flow reverses. In three dimensions a new pattern is found in which the alignment of the rolls and the shear flow alternates.If the magnetic field is sufficiently strong, squares or hexagons are stable at the onset of convection. Both the squares and the hexagons have an asymmetrical topology, with upflow in plumes and downflow in sheets. For the squares this involves a resonance between rolls aligned with the box and rolls aligned digonally to the box. The preference for three-dimensional flow when the field is strong is a consequence of the compressibility of the layer- for Boussinesq magnetoconvection rolls are always preferred over squares at onset.In the regime where convection is oscillatory, the preferred planform for moderate fields is found to be alternating rolls - standing waves in both horizontal directions which are out of phase. For stronger fields, both alternating rolls and two-dimensional travelling rolls are stable. As the amplitude of convection is increased, either by dcereasing the magnetic field strength or by increasing the temperature contrast, the regular planform structure seen at onset is soon destroyed by secondary instabilities.

Magnetic field generation by baroclinic waves

1975 ◽  
Vol 347 (1648) ◽  
pp. 125-140 ◽  
Keyword(s):  
Magnetic Field ◽  
Plane Layer ◽  
Rotating Magnetic Field ◽  
Magnetic Field Generation ◽  
Dynamo Action ◽  
Wind Speeds ◽  
Baroclinic Waves ◽  
The Face ◽  
Layer I ◽  
Horizontal Density Gradient

The general theory of the linear instabilities created by density differences in a rotating magnetic system is considered, and is applied to a plane layer stably stratified but with a slight superimposed horizontal density gradient that can give rise to baroclinic waves, modified by the presence of a horizontal co-rotating magnetic field parallel to the thermal wind. It is shown that, unlike the conceptually similar models of Gilman, regeneration of this magnetic field by the waves in the face of a slight resistivity of the medium can only occur within the critical layer, i. e. the diffusive layer surrounding the level at which wave and wind speeds are equal. Conditions for such self-sustaining dynamo action are given.

scholarly journals Magnetic field amplification in electron phase-space holes and related effects

2012 ◽  
Vol 30 (4) ◽  
pp. 711-724 ◽  
Author(s):  
R. A. Treumann ◽  
W. Baumjohann
Keyword(s):  
Magnetic Field ◽  
Phase Space ◽  
Flux Tube ◽  
Magnetic Moments ◽  
Three Dimensional ◽  
Cosmic Ray ◽  
Magnetic Fabric ◽  
Magnetic Field Generation ◽  
Electron Holes ◽  
The Magnetic Field

Abstract. Three-dimensional electron phase-space holes are shown to have positive charges on the plasma background, which produce a radial electric field and force the trapped electron component into an azimuthal drift. In this way electron holes generate magnetic fields in the hole. We solve the cylindrical hole model exactly for the hole charge, electric potential and magnetic field. In electron holes, the magnetic field is amplified on the flux tube of the hole; equivalently, in ion holes the field would be decreased. The flux tube adjacent to the electron hole is magnetically depleted by the external hole dipole field. This causes magnetic filamentation. It is also shown that holes are massive objects, each carrying a finite magnetic moment. Binary magnetic dipole interaction of these moments will cause alignment of the holes into chains along the magnetic field or, in the three-dimensional case, produce a magnetic fabric in the volume of hole formation. Since holes, in addition to being carriers of charges and magnetic moments, also have finite masses, they behave like quasi-particles, performing E × B, magnetic field, and diamagnetic drifts. In an inhomogeneous magnetic field, their magnetic moments experience torque, which causes nutation of the hole around the direction of the magnetic field, presumably giving rise to low frequency magnetic modulations like pulsations. A gas of many such holes may allow for a kinetic description, in which holes undergo binary dipole interactions. This resembles the polymeric behaviour. Both magnetic field generation and magnetic structure formation are of interest in auroral, solar coronal and shock physics, in particular in the problem of magnetic field filamentation in relativistic foreshocks and cosmic ray acceleration.

scholarly journals The effect of velocity shear on dynamo action due to rotating convection

2013 ◽  
Vol 717 ◽  
pp. 395-416 ◽  
Author(s):  
D. W. Hughes ◽  
M. R. E. Proctor
Keyword(s):  
Magnetic Field ◽  
Velocity Field ◽  
Large Scale ◽  
Mean Field ◽  
Magnetic Reynolds Number ◽  
Velocity Shear ◽  
Magnetic Field Generation ◽  
Dynamo Action ◽  
Rotating Convection ◽  
The Magnetic Field

AbstractRecent numerical simulations of dynamo action resulting from rotating convection have revealed some serious problems in applying the standard picture of mean field electrodynamics at high values of the magnetic Reynolds number, and have thereby underlined the difficulties in large-scale magnetic field generation in this regime. Here we consider kinematic dynamo processes in a rotating convective layer of Boussinesq fluid with the additional influence of a large-scale horizontal velocity shear. Incorporating the shear flow enhances the dynamo growth rate and also leads to the generation of significant magnetic fields on large scales. By the technique of spectral filtering, we analyse the modes in the velocity that are principally responsible for dynamo action, and show that the magnetic field resulting from the full flow relies crucially on a range of scales in the velocity field. Filtering the flow to provide a true separation of scales between the shear and the convective flow also leads to dynamo action; however, the magnetic field in this case has a very different structure from that generated by the full velocity field. We also show that the nature of the dynamo action is broadly similar irrespective of whether the flow in the absence of shear can support dynamo action.

scholarly journals Dynamo action in the presence of an imposed magnetic field

2009 ◽  
Vol 465 (2105) ◽  
pp. 1599-1616 ◽  
Author(s):  
D.W. Hughes ◽  
M.R.E. Proctor
Keyword(s):  
Magnetic Field ◽  
Linear Stability ◽  
Uniform Magnetic Field ◽  
Three Dimensional ◽  
Background Field ◽  
Magnetic Reynolds Number ◽  
Dynamo Action ◽  
Circularly Polarized ◽  
Forcing Function ◽  
Basic States

We consider the linear stability to three-dimensional perturbations of two-dimensional nonlinear magnetohydrodynamic basic states obtained from a specified forcing function in the presence of an imposed initially uniform magnetic field of strength B 0 . The forcing is chosen such that it drives the ‘circularly polarized’ (CP) flow of Galloway & Proctor ( Galloway & Proctor 1992 Nature 356 , 691–693) when B 0 =0. We first examine the properties of these basic states and their dependence on B 0 and the magnetic Reynolds number Rm . The linear stability of these states is then investigated. It is found that, at a given Rm , the presence of a background field is stabilizing. The results also allow us to speculate that, at a fixed value of B 0 , the growth of the unstable perturbations is ‘fast’, in the sense that the growth rate becomes independent of Rm as Rm →∞.

scholarly journals dc-Magnetic-Field Generation in Unmagnetized Shear Flows

2013 ◽  
Vol 111 (1) ◽  
Author(s):  
T. Grismayer ◽  
E. P. Alves ◽  
R. A. Fonseca ◽  
L. O. Silva
Keyword(s):  
Magnetic Field ◽  
Shear Flows ◽  
Magnetic Field Generation ◽  
Dc Magnetic Field ◽  
Field Generation

On the measurement of turbulent magnetic diffusivities: the three-dimensional case

2013 ◽  
Vol 735 ◽  
pp. 457-472
Author(s):  
F. Cattaneo ◽  
S. M. Tobias
Keyword(s):  
Magnetic Field ◽  
Three Dimensional ◽  
Passive Scalar ◽  
Three Dimensions ◽  
Two Dimensional ◽  
Large Aspect Ratio ◽  
Turbulent Diffusivity ◽  
Dynamo Action ◽  
Thermally Driven ◽  
Special Case

AbstractIt has been shown that it is possible to measure the turbulent diffusivity of a magnetic field by a method involving oscillatory sources. So far the method has only been tried in the special case of two-dimensional fields and flows. Here we extend the method to three dimensions and consider the case where the flow is thermally driven convection in a large-aspect-ratio domain. We demonstrate that if the diffusing field is horizontal the method is successful even if the underlying flow can sustain dynamo action. We show that the resulting turbulent diffusivity is comparable with, although not exactly the same as, that of a passive scalar. We were not able to measure unambiguously the diffusivity if the diffusing field is vertical, but argue that such a measurement is possible if enough resources are utilized on the problem.

Sign in / Sign up

Export Citation Format

Share Document