127 research outputs found
Test-field method for mean-field coefficients with MHD background
Aims: The test-field method for computing turbulent transport coefficients
from simulations of hydromagnetic flows is extended to the regime with a
magnetohydrodynamic (MHD) background. Methods: A generalized set of test
equations is derived using both the induction equation and a modified momentum
equation. By employing an additional set of auxiliary equations, we derive
linear equations describing the response of the system to a set of prescribed
test fields. Purely magnetic and MHD backgrounds are emulated by applying an
electromotive force in the induction equation analogously to the ponderomotive
force in the momentum equation. Both forces are chosen to have Roberts
flow-like geometry. Results: Examples with an MHD background are studied where
the previously used quasi-kinematic test-field method breaks down. In cases
with homogeneous mean fields it is shown that the generalized test-field method
produces the same results as the imposed-field method, where the field-aligned
component of the actual electromotive force from the simulation is used.
Furthermore, results for the turbulent diffusivity tensor are given, which are
inaccessible to the imposed-field method. For MHD backgrounds, new mean-field
effects are found that depend on the occurrence of cross-correlations between
magnetic and velocity fluctuations. For strong imposed fields, is
found to be quenched proportional to the fourth power of the field strength,
regardless of the type of background studied.Comment: 17 pages, 10 figures, submitted to Astronomy & Astrophysic
Properties of - and -modes in hydromagnetic turbulence
With the ultimate aim of using the fundamental or -mode to study
helioseismic aspects of turbulence-generated magnetic flux concentrations, we
use randomly forced hydromagnetic simulations of a piecewise isothermal layer
in two dimensions with reflecting boundaries at top and bottom. We compute
numerically diagnostic wavenumber-frequency diagrams of the vertical velocity
at the interface between the denser gas below and the less dense gas above. For
an Alfv\'en-to-sound speed ratio of about 0.1, a 5% frequency increase of the
-mode can be measured when -, where is the
horizontal wavenumber and is the pressure scale height at the
surface. Since the solar radius is about 2000 times larger than ,
the corresponding spherical harmonic degree would be 6000-8000. For weaker
fields, a -dependent frequency decrease by the turbulent motions becomes
dominant. For vertical magnetic fields, the frequency is enhanced for
, but decreased relative to its nonmagnetic value for
.Comment: 17 pages, 22 figures, Version accepted in MNRA
Comment on ``The linear instability of magnetic Taylor-Couette flow with Hall effect''
In the paper we comment on (R\"udiger & Shalybkov, Phys. Rev. E. 69, 016303
(2004) (RS)), the instability of the Taylor--Couette flow interacting with a
homogeneous background field subject to Hall effect is studied. We correct a
falsely generalizing interpretation of results presented there which could be
taken to disprove the existence of the Hall--drift induced magnetic instability
described in Rheinhardt and Geppert, Phys. Rev. Lett. 88, 101103. It is shown
that in contrast to what is suggested by RS, no additional shear flow is
necessary to enable such an instability with a non--potential magnetic
background field, whereas for a curl--free one it is. In the latter case, the
instabilities found in RS in situations where neither a hydrodynamic nor a
magneto--rotational instability exists are demonstrated to be most likely
magnetic instead of magnetohydrodynamic. Further, some minor inaccuracies are
clarified.Comment: 3 pages, 1 figure; accepted by Physical Review
Testing turbulent closure models with convection simulations
We compare simple analytical closure models of homogeneous turbulent
Boussinesq convection for stellar applications with three-dimensional
simulations. We use simple analytical closure models to compute the fluxes of
angular momentum and heat as a function of rotation rate measured by the Taylor
number. We also investigate cases with varying angles between the angular
velocity and gravity vectors, corresponding to locating the computational
domain at different latitudes ranging from the pole to the equator of the star.
We perform three-dimensional numerical simulations in the same parameter
regimes for comparison. The free parameters appearing in the closure models are
calibrated by two fitting methods using simulation data. Unique determination
of the closure parameters is possible only in the non-rotating case or when the
system is placed at the pole. In the other cases the fit procedures yield
somewhat differing results. The quality of the closure is tested by
substituting the resulting coefficients back into the closure model and
comparing with the simulation results. To eliminate the possibilities that the
results obtained depend on the aspect ratio of the simulation domain or suffer
from too small Rayleigh numbers we performed runs varying these parameters. The
simulation data for the Reynolds stress and heat fluxes broadly agree with
previous compressible simulations. The closure works fairly well with slow and
fast rotation but its quality degrades for intermediate rotation rates. We find
that the closure parameters depend not only on rotation rate but also on
latitude. The weak dependence on Rayleigh number and the aspect ratio of the
domain indicates that our results are generally validComment: 21 pages, 9 figures, submitted to Astron. Nach
The Developmental Sentence Scoring Procedure
This paper investigates the usefulness of the Developmental Sentence Scoring Procedure (DSS) as a clinical tool in rating the syntactic performance of young children
The proto--neutron--star dynamo -- viability and impediments
We study convective motions taken from hydrodynamic simulations of rotating
proto--neutron stars (PNSs) with respect to their ability to excite a dynamo
instability which may be responsible for the giant neutron star magnetic
fields. Since it is impossible to simulate the magnetic field evolution
employing the actual magnetic Reynolds numbers (\Rm) resulting from the
hydrodynamic simulations, (smallest) critical \Rms and the corresponding
field geometries are derived on the kinematic level by rescaling the velocity
amplitudes. It turns out that the actual values of \Rm are by many orders of
magnitude larger than the critical values found. A dynamo might therefore start
to act vigorously very soon after the onset of convection. But as in general
dynamo growth rates are non--monotonous functions of \Rm the later fate of
the magnetic field is uncertain. Hence, no reliable statements on the existence
and efficiency of PNS dynamos can be drawn without considering the interplay of
magnetic field and convection from the beginning. Likewise, in so far as
convection inside the PNS is regarded to be essential in re--launching the
supernova explosion, a revision of its role in this respect could turn out to
be necessary.Comment: 7 pages, 4 figures, accepted by Astronomy & Astrophysic
Alpha effect due to buoyancy instability of a magnetic layer
A strong toroidal field can exist in form of a magnetic layer in the
overshoot region below the solar convection zone. This motivates a more
detailed study of the magnetic buoyancy instability with rotation. We calculate
the alpha effect due to helical motions caused by a disintegrating magnetic
layer in a rotating density-stratified system with angular velocity Omega
making an angle theta with the vertical. We also study the dependence of the
alpha effect on theta and the strength of the initial magnetic field. We carry
out three-dimensional hydromagnetic simulations in Cartesian geometry. A
turbulent EMF due to the correlations of the small scale velocity and magnetic
field is generated. We use the test-field method to calculate the transport
coefficients of the inhomogeneous turbulence produced by the layer. We show
that the growth rate of the instability and the twist of the magnetic field
vary monotonically with the ratio of thermal conductivity to magnetic
diffusivity. The resulting alpha effect is inhomogeneous and increases with the
strength of the initial magnetic field. It is thus an example of an
"anti-quenched" alpha effect. The alpha effect is nonlocal, requiring around
8--16 Fourier modes to reconstruct the actual EMF based on the actual mean
field.Comment: 14 pages, 19 figures 3 tables (submitted to A & A
Magnetars versus Radio Pulsars: MHD Stability in Newborn Highly Magnetized Neutron Stars
We study the stability/establishment of dipolar magnetostatic equilibrium
configurations in new--born neutron stars (NSs) in dependence on the rotational
velocity and on the initial angle between rotation and
magnetic axis. The NS is modeled as a sphere of a highly magnetized (G) incompressible fluid of uniform density which rotates rigidly. For
the initial dipolar background magnetic field, which defines the magnetic axis,
two different configurations are assumed. We solve the 3D non--linear MHD
equations by use of a spectral code. The problem in dimensionless form is
completely defined by the initial field strength (for a fixed field geometry),
the magnetic Prandtl number \Pm, and the normalized rotation rate. The
evolution of the magnetic and velocity fields is considered for initial
magnetic field strengths characterized by the ratio of ohmic diffusion and
initial \Alf{} travel times \ttOhm/\ttAO \approx 1000, for \Pm = 0.1, 1,
10, and the ratio of rotation period and initial \Alf{} travel time, P/\ttAO
= 0.012, 0.12, 1.2, 12. We find hints for the existence of a unique stable
dipolar magnetostatic configuration for any specific , independent of
the initial field geometry. Comparing NSs possessing the same field structure
at the end of their proto--NS phase, it turns out that sufficiently fast
rotating NSs (P\la6 ms) with \alpha \la 45^0 retain their magnetar field,
while the others lose almost all of their initial magnetic energy by
transferring it into magnetic and kinetic energy of relatively small--scaled
fields and continue their life as radio pulsars with a dipolar surface field of
G.Comment: 14 pages, 5 figures; accepted by Astronomy & Astrophysic
- …