661 research outputs found
Breaking Kelvin: Circulation conservation and vortex breakup in MHD at low Magnetic Prandtl Number
In this paper we examine the role of weak magnetic fields in breaking
Kelvin's circulation theorem and in vortex breakup in two-dimensional
magnetohydrodynamics for the physically important case of a low magnetic
Prandtl number (low ) fluid. We consider three canonical inviscid solutions
for the purely hydrodynamical problem, namely a Gaussian vortex, a circular
vortex patch and an elliptical vortex patch. We examine how magnetic fields
lead to an initial loss of circulation and attempt to derive scaling
laws for the loss of circulation as a function of field strength and diffusion
as measured by two non-dimensional parameters. We show that for all cases the
loss of circulation depends on the integrated effects of the Lorentz force,
with the patch cases leading to significantly greater circulation loss. For the
case of the elliptical vortex the loss of circulation depends on the total area
swept out by the rotating vortex and so this leads to more efficient
circulation loss than for a circular vortex.Comment: 21 pages, 12 figure
Adaptive mesh refinement with spectral accuracy for magnetohydrodynamics in two space dimensions
We examine the effect of accuracy of high-order spectral element methods,
with or without adaptive mesh refinement (AMR), in the context of a classical
configuration of magnetic reconnection in two space dimensions, the so-called
Orszag-Tang vortex made up of a magnetic X-point centered on a stagnation point
of the velocity. A recently developed spectral-element adaptive refinement
incompressible magnetohydrodynamic (MHD) code is applied to simulate this
problem. The MHD solver is explicit, and uses the Elsasser formulation on
high-order elements. It automatically takes advantage of the adaptive grid
mechanics that have been described elsewhere in the fluid context [Rosenberg,
Fournier, Fischer, Pouquet, J. Comp. Phys. 215, 59-80 (2006)]; the code allows
both statically refined and dynamically refined grids. Tests of the algorithm
using analytic solutions are described, and comparisons of the Orszag-Tang
solutions with pseudo-spectral computations are performed. We demonstrate for
moderate Reynolds numbers that the algorithms using both static and refined
grids reproduce the pseudo--spectral solutions quite well. We show that
low-order truncation--even with a comparable number of global degrees of
freedom--fails to correctly model some strong (sup--norm) quantities in this
problem, even though it satisfies adequately the weak (integrated) balance
diagnostics.Comment: 19 pages, 10 figures, 1 table. Submitted to New Journal of Physic
Wavelet transforms and their applications to MHD and plasma turbulence: a review
Wavelet analysis and compression tools are reviewed and different
applications to study MHD and plasma turbulence are presented. We introduce the
continuous and the orthogonal wavelet transform and detail several statistical
diagnostics based on the wavelet coefficients. We then show how to extract
coherent structures out of fully developed turbulent flows using wavelet-based
denoising. Finally some multiscale numerical simulation schemes using wavelets
are described. Several examples for analyzing, compressing and computing one,
two and three dimensional turbulent MHD or plasma flows are presented.Comment: Journal of Plasma Physics, 201
On the effect of rotation on magnetohydrodynamic turbulence at high magnetic Reynolds number
This article is focused on the dynamics of a rotating electrically conducting
fluid in a turbulent state. As inside the Earth's core or in various industrial
processes, a flow is altered by the presence of both background rotation and a
large scale magnetic field. In this context, we present a set of 3D direct
numerical simulations of incompressible decaying turbulence. We focus on
parameters similar to the ones encountered in geophysical and astrophysical
flows, so that the Rossby number is small, the interaction parameter is large,
but the Elsasser number, defining the ratio between Coriolis and Lorentz
forces, is about unity. These simulations allow to quantify the effect of
rotation and thus inertial waves on the growth of magnetic fluctuations due to
Alfv\'en waves. Rotation prevents the occurrence of equipartition between
kinetic and magnetic energies, with a reduction of magnetic energy at
decreasing Elsasser number {\Lambda}. It also causes a decrease of energy
transfer mediated by cubic correlations. In terms of flow structure, a decrease
of {\Lambda} corresponds to an increase in the misalignment of velocity and
magnetic field.Comment: 18 pages, 12 figure
The Magnetohydrodynamic Kelvin-Helmholtz Instability: A Three-Dimensional Study of Nonlinear Evolution
We investigate through high resolution 3D simulations the nonlinear evolution
of compressible magnetohydrodynamic flows subject to the Kelvin-Helmholtz
instability. We confirm in 3D flows the conclusion from our 2D work that even
apparently weak magnetic fields embedded in Kelvin-Helmholtz unstable plasma
flows can be fundamentally important to nonlinear evolution of the instability.
In fact, that statement is strengthened in 3D by this work, because it shows
how field line bundles can be stretched and twisted in 3D as the quasi-2D Cat's
Eye vortex forms out of the hydrodynamical motions. In our simulations twisting
of the field may increase the maximum field strength by more than a factor of
two over the 2D effect. If, by these developments, the Alfv\'en Mach number of
flows around the Cat's Eye drops to unity or less, our simulations suggest
magnetic stresses will eventually destroy the Cat's Eye and cause the plasma
flow to self-organize into a relatively smooth and apparently stable flow that
retains memory of the original shear. For our flow configurations the regime in
3D for such reorganization is , expressed in
terms of the Alfv\'en Mach number of the original velocity transition and the
initial Alfv\'en speed projected to the flow plan. For weaker fields the
instability remains essentially hydrodynamic in early stages, and the Cat's Eye
is destroyed by the hydrodynamic secondary instabilities of a 3D nature. Then,
the flows evolve into chaotic structures that approach decaying isotropic
turbulence. In this stage, there is considerable enhancement to the magnetic
energy due to stretching, twisting, and turbulent amplification, which is
retained long afterwards. The magnetic energy eventually catches up to the
kinetic energy, and the nature of flows become magnetohydrodynamic.Comment: 11 pages, 12 figures in degraded jpg format (2 in color), paper with
original quality figures available via ftp at
ftp://ftp.msi.umn.edu/pub/users/twj/mhdkh3dd.ps.gz or
ftp://canopus.chungnam.ac.kr/ryu/mhdkh3dd.ps.gz, to appear in The
Astrophysical Journa
The Lagrangian-averaged model for magnetohydrodynamics turbulence and the absence of bottleneck
We demonstrate that, for the case of quasi-equipartition between the velocity
and the magnetic field, the Lagrangian-averaged magnetohydrodynamics
alpha-model (LAMHD) reproduces well both the large-scale and small-scale
properties of turbulent flows; in particular, it displays no increased
(super-filter) bottleneck effect with its ensuing enhanced energy spectrum at
the onset of the sub-filter-scales. This is in contrast to the case of the
neutral fluid in which the Lagrangian-averaged Navier-Stokes alpha-model is
somewhat limited in its applications because of the formation of spatial
regions with no internal degrees of freedom and subsequent contamination of
super-filter-scale spectral properties. No such regions are found in LAMHD,
making this method capable of large reductions in required numerical degrees of
freedom; specifically, we find a reduction factor of 200 when compared to a
direct numerical simulation on a large grid of 1536^3 points at the same
Reynolds number.Comment: 22 pages, 9 figures; accepted Phys.Rev.
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