398 research outputs found
Magnetic Helicity Conservation and Astrophysical Dynamos
We construct a magnetic helicity conserving dynamo theory which incorporates
a calculated magnetic helicity current. In this model the fluid helicity plays
a small role in large scale magnetic field generation. Instead, the dynamo
process is dominated by a new quantity, derived from asymmetries in the second
derivative of the velocity correlation function, closely related to the `twist
and fold' dynamo model. The turbulent damping term is, as expected, almost
unchanged. Numerical simulations with a spatially constant fluid helicity and
vanishing resistivity are not expected to generate large scale fields in
equipartition with the turbulent energy density. The prospects for driving a
fast dynamo under these circumstances are uncertain, but if it is possible,
then the field must be largely force-free. On the other hand, there is an
efficient analog to the dynamo. Systems whose turbulence is
driven by some anisotropic local instability in a shearing flow, like real
stars and accretion disks, and some computer simulations, may successfully
drive the generation of strong large scale magnetic fields, provided that
. We show that this
criterion is usually satisfied. Such dynamos will include a persistent,
spatially coherent vertical magnetic helicity current with the same sign as
, that is, positive for an accretion disk and negative for
the Sun. We comment on the role of random magnetic helicity currents in storing
turbulent energy in a disordered magnetic field, which will generate an
equipartition, disordered field in a turbulent medium, and also a declining
long wavelength tail to the power spectrum. As a result, calculations of the
galactic `seed' field are largely irrelevant.Comment: 28 pages, accepted by The Astrophysical Journa
An efficient shock-capturing central-type scheme for multidimensional relativistic flows. II. Magnetohydrodynamics
A third order shock-capturing numerical scheme for three-dimensional special
relativistic magnetohydrodynamics (3-D RMHD) is presented and validated against
several numerical tests. The simple and efficient central scheme described in
Paper I (Del Zanna and Bucciantini, Astron. Astrophys., 390, 1177--1186, 2002)
for relativistic hydrodynamics is here extended to the magnetic case by
following the strategies prescribed for classical MHD by Londrillo and Del
Zanna (Astrophys. J., 530, 508--524, 2000). The scheme avoids completely
spectral decomposition into characteristic waves, computationally expensive and
subject to many degenerate cases in the magnetic case, while it makes use of a
two-speed Riemann solver that just require the knowledge of the two local fast
magnetosonic velocities. Moreover, the onset of spurious magnetic monopoles,
which is a typical problem for multi-dimensional MHD upwind codes, is prevented
by properly taking into account the solenoidal constraint and the specific
antisymmetric nature of the induction equation. Finally, the extension to
generalized orthogonal curvilinear coordinate systems is included, thus the
scheme is ready to incorporate general relativistic (GRMHD) effects.Comment: 18 pages, Latex, 8 Encapsulated PostScript figures, accepted for
publication in A&
A high-order Godunov scheme for global 3D MHD accretion disks simulations. I. The linear growth regime of the magneto-rotational instability
We employ the PLUTO code for computational astrophysics to assess and compare
the validity of different numerical algorithms on simulations of the
magneto-rotational instability in 3D accretion disks. In particular we stress
on the importance of using a consistent upwind reconstruction of the
electro-motive force (EMF) when using the constrained transport (CT) method to
avoid the onset of numerical instabilities. We show that the electro-motive
force (EMF) reconstruction in the classical constrained transport (CT) method
for Godunov schemes drives a numerical instability. The well-studied linear
growth of magneto-rotational instability (MRI) is used as a benchmark for an
inter-code comparison of PLUTO and ZeusMP. We reproduce the analytical results
for linear MRI growth in 3D global MHD simulations and present a robust and
accurate Godunov code which can be used for 3D accretion disk simulations in
curvilinear coordinate systems
An efficient shock-capturing central-type scheme for multidimensional relativistic flows. I. Hydrodynamics
Multidimensional shock-capturing numerical schemes for special relativistic
hydrodynamics (RHD) are computationally more expensive than their correspondent
Euler versions, due to the nonlinear relations between conservative and
primitive variables and to the consequent complexity of the Jacobian matrices
(needed for the spectral decomposition in most of the approximate Riemann
solvers of common use). Here an efficient and easy-to-implement
three-dimensional (3-D) shock-capturing scheme for ideal RHD is presented.
Based on the algorithms developed by P. Londrillo and L. Del Zanna ({\em
Astrophys. J.} 530, 508-524, 2000) for the non-relativistic magnetohydrodynamic
(MHD) case, and having in mind its relativistic MHD extension (to appear in a
forthcoming paper), the scheme uses high order (third) Convex Essentially
Non-Oscillatory (CENO) finite difference interpolation routines and
central-type averaged Riemann solvers, which do not make use of time-consuming
characteristic decomposition. The scheme is very efficient and robust, and it
gives results comparable to those obtained with more sophisticated algorithms,
even in ultrarelativistic multidimensional test problems.Comment: 11 pages, Latex, 9 Encapsulated PostScript figures, accepted for
publication in A&
Higher order finite difference schemes for the magnetic induction equations
We describe high order accurate and stable finite difference schemes for the
initial-boundary value problem associated with the magnetic induction
equations. These equations model the evolution of a magnetic field due to a
given velocity field. The finite difference schemes are based on Summation by
Parts (SBP) operators for spatial derivatives and a Simultaneous Approximation
Term (SAT) technique for imposing boundary conditions. We present various
numerical experiments that demonstrate both the stability as well as high order
of accuracy of the schemes.Comment: 20 page
Orientations of the lamellar phase of block copolymer melts under oscillatory shear flow
We develop a theory to describe the reorientation phenomena in the lamellar
phase of block copolymer melt under reciprocating shear flow. We show that
similar to the steady-shear, the oscillating flow anisotropically suppresses
fluctuations and gives rise to the parallel-perpendicular orientation
transition. The experimentally observed high-frequency reverse transition is
explained in terms of interaction between the melt and the shear-cell walls.Comment: RevTex, 3 pages, 1 figure, submitted to PR
Diffusion in supersonic, turbulent, compressible flows
We investigate diffusion in supersonic, turbulent, compressible flows.
Supersonic turbulence can be characterized as network of interacting shocks. We
consider flows with different rms Mach numbers and where energy necessary to
maintain dynamical equilibrium is inserted at different spatial scales. We find
that turbulent transport exhibits super-diffusive behavior due to induced bulk
motions. In a comoving reference frame, however, diffusion behaves normal and
can be described by mixing length theory extended into the supersonic regime.Comment: 11 pages, incl. 5 figures, accepted for publication in Physical
Review E (a high-resolution version is available at
http://www.aip.de./~ralf/Publications/p21.abstract.html
- âŠ