414 research outputs found
An unstable superfluid Stewartson layer in a differentially rotating neutron star
Experimental and numerical evidence is reviewed for the existence of a
Stewartson layer in spherical Couette flow at small Ekman and Rossby numbers
(\Ek \lsim 10^{-3}, \Ro \lsim 10^{-2}), the relevant hydrodynamic regime in
the superfluid outer core of a neutron star. Numerical simulations of a
superfluid Stewartson layer are presented for the first time, showing how the
layer is disrupted by nonaxisymmetric instabilities. The unstable ranges of
\Ek and \Ro are compared with estimates of these quantities in radio
pulsars that exhibit glitches. It is found that glitching pulsars lie on the
stable side of the instability boundary, allowing differential rotation to
build up before a glitch.Comment: 4 pages, 3 figures. Accepted for publication in ApJ Letter
On the necessary conditions for bursts of convection within the rapidly rotating cylindrical annulus
Zonal flows are often found in rotating convective systems. Not only are
these jet-flows driven by the convection, they can also have a profound effect
on the nature of the convection. In this work the cylindrical annulus geometry
is exploited in order to perform nonlinear simulations seeking to produce
strong zonal flows and multiple jets. The parameter regime is extended to
Prandtl numbers that are not unity. Multiple jets are found to be spaced
according to a Rhines scaling based on the zonal flow speed, not the convective
velocity speed. Under certain conditions the nonlinear convection appears in
quasi-periodic bursts. A mean field stability analysis is performed around a
basic state containing both the zonal flow and the mean temperature gradient
found from the nonlinear simulations. The convective growth rates are found to
fluctuate with both of these mean quantities suggesting that both are necessary
in order for the bursting phenomenon to occur
Nonaxisymmetric MHD instabilities of Chandrasekhar states in Taylor-Couette geometry
We consider axially periodic Taylor-Couette geometry with insulating boundary
conditions. The imposed basic states are so-called Chandrasekhar states, where
the azimuthal flow and magnetic field have the same radial
profiles. Mainly three particular profiles are considered: the Rayleigh limit,
quasi-Keplerian, and solid-body rotation. In each case we begin by computing
linear instability curves and their dependence on the magnetic Prandtl number
Pm. For the azimuthal wavenumber m=1 modes, the instability curves always scale
with the Reynolds number and the Hartmann number. For sufficiently small Pm
these modes therefore only become unstable for magnetic Mach numbers less than
unity, and are thus not relevant for most astrophysical applications. However,
modes with m>10 can behave very differently. For sufficiently flat profiles,
they scale with the magnetic Reynolds number and the Lundquist number, thereby
allowing instability also for the large magnetic Mach numbers of astrophysical
objects. We further compute fully nonlinear, three-dimensional equilibration of
these instabilities, and investigate how the energy is distributed among the
azimuthal (m) and axial (k) wavenumbers. In comparison spectra become steeper
for large m, reflecting the smoothing action of shear. On the other hand
kinetic and magnetic energy spectra exhibit similar behavior: if several
azimuthal modes are already linearly unstable they are relatively flat, but for
the rigidly rotating case where m=1 is the only unstable mode they are so steep
that neither Kolmogorov nor Iroshnikov-Kraichnan spectra fit the results. The
total magnetic energy exceeds the kinetic energy only for large magnetic
Reynolds numbers Rm>100.Comment: 12 pages, 14 figures, submitted to Ap
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
Hall drift of axisymmetric magnetic fields in solid neutron-star matter
Hall drift, i. e., transport of magnetic flux by the moving electrons giving
rise to the electrical current, may be the dominant effect causing the
evolution of the magnetic field in the solid crust of neutron stars. It is a
nonlinear process that, despite a number of efforts, is still not fully
understood. We use the Hall induction equation in axial symmetry to obtain some
general properties of nonevolving fields, as well as analyzing the evolution of
purely toroidal fields, their poloidal perturbations, and current-free, purely
poloidal fields. We also analyze energy conservation in Hall instabilities and
write down a variational principle for Hall equilibria. We show that the
evolution of any toroidal magnetic field can be described by Burgers' equation,
as previously found in plane-parallel geometry. It leads to sharp current
sheets that dissipate on the Hall time scale, yielding a stationary field
configuration that depends on a single, suitably defined coordinate. This
field, however, is unstable to poloidal perturbations, which grow as their
field lines are stretched by the background electron flow, as in instabilities
earlier found numerically. On the other hand, current-free poloidal
configurations are stable and could represent a long-lived crustal field
supported by currents in the fluid stellar core.Comment: 8 pages, 5 figure panels; new version with very small correction;
accepted by Astronomy & Astrophysic
Geodynamo alpha-effect derived from box simulations of rotating magnetoconvection
The equations for fully compressible rotating magnetoconvection are
numerically solved in a Cartesian box assuming conditions roughly suitable for
the geodynamo. The mean electromotive force describing the generation of mean
magnetic flux by convective turbulence in the rotating fluid is directly
calculated from the simulations, and the corresponding alpha-coefficients are
derived. Due to the very weak density stratification the alpha-effect changes
its sign in the middle of the box. It is positive at the top and negative at
the bottom of the convection zone. For strong magnetic fields we also find a
clear downward advection of the mean magnetic field. Both of the simulated
effects have been predicted by quasi-linear computations (Soward, 1979;
Kitchatinov and Ruediger, 1992). Finally, the possible connection of the
obtained profiles of the EMF with mean-field models of oscillating
alpha^2-dynamos is discussed.Comment: 17 pages, 9 figures, submitted to Phys. Earth Planet. Inte
Suppression of a laminar kinematic dynamo by a prescribed large-scale shear
We numerically solve the magnetic induction equation in a spherical
shell geometry, with a kinematically prescribed axisymmetric flow that consists of a
superposition of a small-scale helical flow and a large-scale shear flow. The small-scale
flow is chosen to be a local analog of the classical Roberts cells, consisting of strongly
helical vortex rolls. The large-scale flow is a shearing motion in either the radial or the
latitudinal directions. In the absence of large-scale shear, the small-scale flow operates
very effectively as a dynamo, in agreement with previous results. Adding increasingly
large shear flows strongly suppresses the dynamo efficiency, indicating that shear is
not always a favourable ingredient in dynamo action
Three-dimensional stability of the solar tachocline
The three-dimensional, hydrodynamic stability of the solar tachocline is
investigated based on a rotation profile as a function of both latitude and
radius. By varying the amplitude of the latitudinal differential rotation, we
find linear stability limits at various Reynolds numbers by numerical
computations. We repeated the computations with different latitudinal and
radial dependences of the angular velocity. The stability limits are all higher
than those previously found from two-dimensional approximations and higher than
the shear expected in the Sun. It is concluded that any part of the tachocline
which is radiative is hydrodynamically stable against small perturbations.Comment: 6 pages, 8 figures, accepted by Astron. & Astrophy
Compensation of compliance errors in parallel manipulators composed of non-perfect kinematic chains
The paper is devoted to the compliance errors compensation for parallel
manipulators under external loading. Proposed approach is based on the
non-linear stiffness modeling and reduces to a proper adjusting of a target
trajectory. In contrast to previous works, in addition to compliance errors
caused by machining forces, the problem of assembling errors caused by
inaccuracy in the kinematic chains is considered. The advantages and practical
significance of the proposed approach are illustrated by examples that deal
with groove milling with Orthoglide manipulator.Comment: Advances in Robot Kinematics, France (2012
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