446 research outputs found
Hall cascades versus instabilities in neutron star magnetic fields
Context. The Hall effect is an important nonlinear mechanism affecting the evolution of magnetic fields in neutron stars. Studies of the governing equation, both theoretical and numerical, have shown that the Hall effect proceeds in a turbulent cascade of energy from large to small scales. Aims. We investigate the small-scale Hall instability conjectured to exist from the linear stability analysis of Rheinhardt and Geppert. Methods. Identical linear stability analyses are performed to find a suitable background field to model Rheinhardt and Geppert’s ideas. The nonlinear evolution of this field is then modelled using a three-dimensional pseudospectral numerical MHD code. Combined with the background field, energy was injected at the ten specific eigenmodes with the greatest positive eigenvalues as inferred by the linear stability analysis. Results. Energy is transferred to different scales in the system, but not into small scales to any extent that could be interpreted as a Hall instability. Any instabilities are overwhelmed by a late-onset turbulent Hall cascade, initially avoided by the choice of background field, but soon generated by nonlinear interactions between the growing eigenmodes. The Hall cascade is shown here, and by several authors elsewhere, to be the dominant mechanism in this system
Instabilities of Shercliffe and Stewartson layers in spherical Couette flow
We explore numerically the flow induced in a spherical shell by differentially rotating the inner and outer spheres. The fluid is also taken to be electrically conducting (in the low magnetic Reynolds number limit), and a magnetic field is imposed parallel to the axis of rotation. If the outer sphere is stationary, the magnetic field induces a Shercliffe layer on the tangent cylinder, the cylinder just touching the inner sphere and parallel to the field. If the magnetic field is absent, but a strong overall rotation is present, Coriolis effects induce a Stewartson layer on the tangent cylinder. The nonaxisymmetric instabilities of both types of layer separately have been studied before; here, we consider the two cases side by side, as well as the mixed case, and investigate how magnetic and rotational effects interact. We find that if the differential rotation and the overall rotation are in the same direction, the overall rotation may have a destabilizing influence, whereas if the differential rotation and the overall rotation are in the opposite direction, the overall rotation always has a stabilizing influence
Forward and inverse cascades in decaying two-dimensional electron magnetohydrodynamic turbulence
Electron magnetohydrodynamic (EMHD) turbulence in two dimensions is studied
via high-resolution numerical simulations with a normal diffusivity. The
resulting energy spectra asymptotically approach a law with
increasing , the ratio of the nonlinear to linear timescales in the
governing equation. No evidence is found of a dissipative cutoff, consistent
with non-local spectral energy transfer. Dissipative cutoffs found in previous
studies are explained as artificial effects of hyperdiffusivity. Relatively
stationary structures are found to develop in time, rather than the variability
found in ordinary or MHD turbulence. Further, EMHD turbulence displays
scale-dependent anisotropy with reduced energy transfer in the direction
parallel to the uniform background field, consistent with previous studies.
Finally, the governing equation is found to yield an inverse cascade, at least
partially transferring magnetic energy from small to large scales.Comment: 16 pages, 6 figures, accepted by Physics of Plasmas. For high
resolution figures, please visit the PoP website or contact C.Warein
Differential rotation decay in the radiative envelopes of CP stars
Stars of spectral classes A and late B are almost entirely radiative. CP
stars are a slowly rotating subgroup of these stars. It is possible that they
possessed long-lived accretion disks in their T Tauri phase. Magnetic coupling
of disk and star leads to rotational braking at the surface of the star.
Microscopic viscosities are extremely small and will not be able to reduce the
rotation rate of the core of the star. We investigate the question whether
magneto-rotational instability can provide turbulent angular momentum
transport. We illuminate the question whether or not differential rotation is
present in CP stars. Numerical MHD simulations of thick stellar shells are
performed. An initial differential rotation law is subject to the influence of
a magnetic field. The configuration gives indeed rise to magneto-rotational
instability. The emerging flows and magnetic fields transport efficiently
angular momentum outwards. Weak dependence on the magnetic Prandtl number
(~0.01 in stars) is found from the simulations. Since the estimated time-scale
of decay of differential rotation is 10^7-10^8 yr and comparable to the
life-time of A stars, we find the braking of the core to be an ongoing process
in many CP stars. The evolution of the surface rotation of CP stars with age
will be an observational challenge and of much value for verifying the
simulations.Comment: 8 pages, 11 figures; submitted to Astron. & Astrophy
Helicity and alpha-effect by current-driven instabilities of helical magnetic fields
Helical magnetic background fields with adjustable pitch angle are imposed on
a conducting fluid in a differentially rotating cylindrical container. The
small-scale kinetic and current helicities are calculated for various field
geometries, and shown to have the opposite sign as the helicity of the
large-scale field. These helicities and also the corresponding -effect
scale with the current helicity of the background field. The -tensor is
highly anisotropic as the components and have
opposite signs. The amplitudes of the azimuthal -effect computed with
the cylindrical 3D MHD code are so small that the operation of an
dynamo on the basis of the current-driven, kink-type
instabilities of toroidal fields is highly questionable. In any case the low
value of the -effect would lead to very long growth times of a dynamo
in the radiation zone of the Sun and early-type stars of the order of
mega-years.Comment: 6 pages, 7 figures, submitted to MNRA
Experimental study of super-rotation in a magnetostrophic spherical Couette flow
We report measurements of electric potentials at the surface of a spherical
container of liquid sodium in which a magnetized inner core is differentially
rotating. The azimuthal angular velocities inferred from these potentials
reveal a strong super-rotation of the liquid sodium in the equatorial region,
for small differential rotation. Super-rotation was observed in numerical
simulations by Dormy et al. [1]. We find that the latitudinal variation of the
electric potentials in our experiments differs markedly from the predictions of
a similar numerical model, suggesting that some of the assumptions used in the
model - steadiness, equatorial symmetry, and linear treatment for the evolution
of both the magnetic and velocity fields - are violated in the experiments. In
addition, radial velocity measurements, using ultrasonic Doppler velocimetry,
provide evidence of oscillatory motion near the outer sphere at low latitude:
it is viewed as the signature of an instability of the super-rotating region
Magnetized Ekman Layer and Stewartson Layer in a Magnetized Taylor-Couette Flow
In this paper we present axisymmetric nonlinear simulations of magnetized
Ekman and Stewartson layers in a magnetized Taylor-Couette flow with a
centrifugally stable angular-momemtum profile and with a magnetic Reynolds
number below the threshold of magnetorotational instability. The magnetic field
is found to inhibit the Ekman suction. The width of the Ekman layer is reduced
with increased magnetic field normal to the end plate. A uniformly-rotating
region forms near the outer cylinder. A strong magnetic field leads to a steady
Stewartson layer emanating from the junction between differentially rotating
rings at the endcaps. The Stewartson layer becomes thinner with larger Reynolds
number and penetrates deeper into the bulk flow with stronger magnetic field
and larger Reynolds number. However, at Reynolds number larger than a critical
value , axisymmetric, and perhaps also nonaxisymmetric, instabilities
occur and result in a less prominent Stewartson layer that extends less far
from the boundary.Comment: 24 pages, 12 figures, accepted by PRE, revision according to referee
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