2,201 research outputs found
Numerical Simulations of Dynamos Generated in Spherical Couette Flows
We numerically investigate the efficiency of a spherical Couette flow at
generating a self-sustained magnetic field. No dynamo action occurs for
axisymmetric flow while we always found a dynamo when non-axisymmetric
hydrodynamical instabilities are excited. Without rotation of the outer sphere,
typical critical magnetic Reynolds numbers are of the order of a few
thousands. They increase as the mechanical forcing imposed by the inner core on
the flow increases (Reynolds number ). Namely, no dynamo is found if the
magnetic Prandtl number is less than a critical value .
Oscillating quadrupolar dynamos are present in the vicinity of the dynamo
onset. Saturated magnetic fields obtained in supercritical regimes (either
or ) correspond to the equipartition between magnetic and
kinetic energies. A global rotation of the system (Ekman numbers ) yields to a slight decrease (factor 2) of the critical magnetic
Prandtl number, but we find a peculiar regime where dynamo action may be
obtained for relatively low magnetic Reynolds numbers (). In this
dynamical regime (Rossby number , spheres in opposite direction) at
a moderate Ekman number (), a enhanced shear layer around the inner
core might explain the decrease of the dynamo threshold. For lower
() this internal shear layer becomes unstable, leading to small
scales fluctuations, and the favorable dynamo regime is lost. We also model the
effect of ferromagnetic boundary conditions. Their presence have only a small
impact on the dynamo onset but clearly enhance the saturated magnetic field in
the ferromagnetic parts. Implications for experimental studies are discussed
Modeling the Parker instability in a rotating plasma screw pinch
We analytically and numerically study the analogue of the Parker (magnetic
buoyancy) instability in a uniformly rotating plasma screw pinch confined in a
cylinder. Uniform plasma rotation is imposed to create a centrifugal
acceleration, which mimics the gravity required for the classical Parker
instability. The goal of this study is to determine how the Parker instability
could be unambiguously identified in a weakly magnetized, rapidly rotating
screw pinch, in which the rotation provides an effective gravity and a radially
varying azimuthal field is controlled to give conditions for which the plasma
is magnetically buoyant to inward motion. We show that an axial magnetic field
is also required to circumvent conventional current driven magnetohydrodynamic
(MHD) instabilities such as the sausage and kink modes that would obscure the
Parker instability. These conditions can be realized in the Madison Plasma
Couette Experiment (MPCX). Simulations are performed using the extended MHD
code NIMROD for an isothermal compressible plasma model. Both linear and
nonlinear regimes of the instability are studied, and the results obtained for
the linear regime are compared with analytical results from a slab geometry.
Based on this comparison, it is found that in a cylindrical pinch the magnetic
buoyancy mechanism dominates at relatively large Mach numbers (M>5), while at
low Mach numbers (M<1) the instability is due to the curvature of magnetic
field lines. At intermediate values of Mach number (1<M<5) the Coriolis force
has a strong stabilizing effect on the plasma. A possible scenario for
experimental demonstration of the Parker instability in MPCX is discussed
Observation of a Turbulence-Induced Large Scale Magnetic Field
An axisymmetric magnetic field is applied to a spherical, turbulent flow of
liquid sodium. An induced magnetic dipole moment is measured which cannot be
generated by the interaction of the axisymmetric mean flow with the applied
field, indicating the presence of a turbulent electromotive force. It is shown
that the induced dipole moment should vanish for any axisymmetric laminar flow.
Also observed is the production of toroidal magnetic field from applied
poloidal magnetic field (the omega-effect). Its potential role in the
production of the induced dipole is discussed.Comment: 5 pages, 4 figures Revisions to accomodate peer-reviewer concerns;
changes to main text including simplification of a proof, Fig. 2 updated, and
minor typos and clarifications; Added refrences. Resubmitted to Phys. Rev.
Let
Influence of turbulence on the dynamo threshold
We use direct and stochastic numerical simulations of the magnetohydrodynamic
equations to explore the influence of turbulence on the dynamo threshold. In
the spirit of the Kraichnan-Kazantsev model, we model the turbulence by a
noise, with given amplitude, injection scale and correlation time. The addition
of a stochastic noise to the mean velocity significantly alters the dynamo
threshold. When the noise is at small (resp. large) scale, the dynamo threshold
is decreased (resp. increased). For a large scale noise, a finite correlation
time reinforces this effect
The onset of a small-scale turbulent dynamo at low magnetic Prandtl numbers
We study numerically the dependence of the critical magnetic Reynolds number
Rmc for the turbulent small-scale dynamo on the hydrodynamic Reynolds number
Re. The turbulence is statistically homogeneous, isotropic, and
mirror--symmetric. We are interested in the regime of low magnetic Prandtl
number Pm=Rm/Re<1, which is relevant for stellar convective zones, protostellar
disks, and laboratory liquid-metal experiments. The two asymptotic
possibilities are Rmc->const as Re->infinity (a small-scale dynamo exists at
low Pm) or Rmc/Re=Pmc->const as Re->infinity (no small-scale dynamo exists at
low Pm). Results obtained in two independent sets of simulations of MHD
turbulence using grid and spectral codes are brought together and found to be
in quantitative agreement. We find that at currently accessible resolutions,
Rmc grows with Re with no sign of approaching a constant limit. We reach the
maximum values of Rmc~500 for Re~3000. By comparing simulations with Laplacian
viscosity, fourth-, sixth-, and eighth-order hyperviscosity and Smagorinsky
large-eddy viscosity, we find that Rmc is not sensitive to the particular form
of the viscous cutoff. This work represents a significant extension of the
studies previously published by Schekochihin et al. 2004, PRL 92, 054502 and
Haugen et al. 2004, PRE, 70, 016308 and the first detailed scan of the
numerically accessible part of the stability curve Rmc(Re).Comment: 4 pages, emulateapj aastex, 2 figures; final version as published in
ApJL (but with colour figures
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