132 research outputs found
Spherical single-roll dynamos at large magnetic Reynolds numbers
This paper concerns kinematic helical dynamos in a spherical fluid body
surrounded by an insulator. In particular, we examine their behaviour in the
regime of large magnetic Reynolds number \Rm, for which dynamo action is
usually concentrated upon a simple resonant stream-surface. The dynamo
eigensolutions are computed numerically for two representative single-roll
flows using a compact spherical harmonic decomposition and fourth-order
finite-differences in radius. These solutions are then compared with the growth
rates and eigenfunctions of the Gilbert and Ponty (2000) large \Rm asymptotic
theory. We find good agreement between the growth rates when \Rm>10^4, and
between the eigenfunctions when \Rm>10^5.Comment: 36 pages, 8 figures. V2: incorrect labels in Fig3 corrected. The
article appears in Physics of Fluids, 22, 066601, and may be found at
http://pof.aip.org/phfle6/v22/i6/p066601_s1 . (Copyright 2010 American
Institute of Physics. This article may be downloaded for personal use only.
Any other use requires prior permission of the author and the American
Institute of Physics
The integral equation approach to kinematic dynamo theory and its application to dynamo experiments in cylindrical geometry
The conventional magnetic induction equation that governs hydromagnetic
dynamo action is transformed into an equivalent integral equation system. An
advantage of this approach is that the computational domain is restricted to
the region occupied by the electrically conducting fluid and to its boundary.
This integral equation approach is first employed to simulate kinematic dynamos
excited by Beltrami-like flows in a finite cylinder. The impact of externally
added layers around the cylinder on the onset of dynamo actions is
investigated. Then it is applied to simulate dynamo experiments within
cylindrical geometry including the von Karman sodium (VKS) experiment and the
Riga dynamo experiment. A modified version of this approach is utilized to
investigate magnetic induction effects under the influence of externally
applied magnetic fields which is also important to measure the proximity of a
given dynamo facility to the self-excitation threshold.Comment: 22 pages, 14 figure
Detection of a flow induced magnetic field eigenmode in the Riga dynamo facility
In an experiment at the Riga sodium dynamo facility, a slowly growing
magnetic field eigenmode has been detected over a period of about 15 seconds.
For a slightly decreased propeller rotation rate, additional measurements
showed a slow decay of this mode. The measured results correspond satisfactory
with numerical predictions for the growth rates and frequencies
Integral equations in MHD: theory and application
The induction equation of kinematic magnetohydrodynamics is mathematically
equivalent to a system of integral equations for the magnetic field in the bulk
of the fluid and for the electric potential at its boundary. We summarize the
recent developments concerning the numerical implementation of this scheme and
its applications to various forward and inverse problems in dynamo theory and
applied MHD.Comment: 17 pages, 4 figure
Why dynamos are prone to reversals
In a recent paper (Phys. Rev. Lett. 94 (2005), 184506; physics/0411050) it
was shown that a simple mean-field dynamo model with a spherically symmetric
helical turbulence parameter alpha can exhibit a number of features which are
typical for Earth's magnetic field reversals. In particular, the model produces
asymmetric reversals, a positive correlation of field strength and interval
length, and a bimodal field distribution. All these features are attributable
to the magnetic field dynamics in the vicinity of an exceptional point of the
spectrum of the non-selfadjoint dynamo operator. The negative slope of the
growth rate curve between the nearby local maximum and the exceptional point
makes the system unstable and drives it to the exceptional point and beyond
into the oscillatory branch where the sign change happens. A weakness of this
reversal model is the apparent necessity to fine-tune the magnetic Reynolds
number and/or the radial profile of alpha. In the present paper, it is shown
that this fine-tuning is not necessary in the case of higher supercriticality
of the dynamo. Numerical examples and physical arguments are compiled to show
that, with increasing magnetic Reynolds number, there is strong tendency for
the exceptional point and the associated local maximum to move close to the
zero growth rate line. Although exemplified again by the spherically symmetric
alpha^2 dynamo model, the main idea of this ''self-tuning'' mechanism of
saturated dynamos into a reversal-prone state seems well transferable to other
dynamos. As a consequence, reversing dynamos might be much more typical and may
occur much more frequently in nature than what could be expected from a purely
kinematic perspective.Comment: 11 pages, 10 figure
Two-dimensional solitons on the surface of magnetic fluids
We report an observation of a stable soliton-like structure on the surface of
a ferrofluid, generated by a local perturbation in the hysteretic regime of the
Rosensweig instability. Unlike other pattern-forming systems with localized 2D
structures, magnetic fluids are characterized by energy conservation; hence
their mechanism of soliton stabilization is different from the previously
discussed gain/loss balance mechanism. The radioscopic measurements of the
soliton's surface profile suggest that locking on the underlying periodic
structure is instrumental in its stabilization.Comment: accepted for publication by Physical Review Letter
Alpha-effect dynamos with zero kinetic helicity
A simple explicit example of a Roberts-type dynamo is given in which the
alpha-effect of mean-field electrodynamics exists in spite of point-wise
vanishing kinetic helicity of the fluid flow. In this way it is shown that
alpha-effect dynamos do not necessarily require non-zero kinetic helicity. A
mean-field theory of Roberts-type dynamos is established within the framework
of the second-order correlation approximation. In addition numerical solutions
of the original dynamo equations are given, that are independent of any
approximation of that kind. Both theory and numerical results demonstrate the
possibility of dynamo action in the absence of kinetic helicity.Comment: 6 pages, 3 figures, accepted for PR
Differential rotation and meridional flow in the solar supergranulation layer: Measuring the eddy viscosity
We measure the eddy viscosity in the outermost layers of the solar convection
zone by comparing the rotation law computed with the Reynolds stress resulting
from f-plane simulations of the angular momentum transport in rotating
convection with the observed differential rotation pattern. The simulations
lead to a negative vertical and a positive horizontal angular momentum
transport. The consequence is a subrotation of the outermost layers, as it is
indeed indicated both by helioseismology and the observed rotation rates of
sunspots. In order to reproduce the observed gradient of the rotation rate a
value of about 1.5 x 10^{13} cm/s for the eddy viscosity is necessary.
Comparison with the magnetic eddy diffusivity derived from the sunspot decay
yields a surprisingly large magnetic Prandtl number of 150 for the
supergranulation layer. The negative gradient of the rotation rate also drives
a surface meridional flow towards the poles, in agreement with the results from
Doppler measurements. The successful reproduction of the abnormally positive
horizontal cross correlation (on the northern hemisphere) observed for bipolar
groups then provides an independent test for the resulting eddy viscosity.Comment: 6 pages, 8 figures, Astronomy and Astrophysics (subm.
Diffusive Radiation in One-dimensional Langmuir Turbulence
We calculate spectra of radiation produced by a relativistic particle in the
presence of one-dimensional Langmuir turbulence which might be generated by a
streaming instability in the plasma, in particular, in the shock front or at
the shock-shock interactions. The shape of the radiation spectra is shown to
depend sensitively on the angle between the particle velocity and electric
field direction. The radiation spectrum in the case of exactly transverse
particle motion is degenerate and similar to that of spatially uniform Langmuir
oscillations. In case of oblique propagation, the spectrum is more complex, it
consists of a number of power-law regions and may contain a distinct
high-frequency spectral peak. %at \omega=2\omega\pe \gamma^2. The emission
process considered is relevant to various laboratory plasma settings and for
astrophysical objects as gamma-ray bursts and collimated jets.Comment: 4 pages, 1 figure, accepted for Phys. Rev.
Double Rosensweig instability in a ferrofluid sandwich structure
We consider a horizontal ferrofluid layer sandwiched between two layers of
immiscible non-magnetic fluids. In a sufficiently strong vertical magnetic
field the flat interfaces between magnetic and non-magnetic fluids become
unstable to the formation of peaks. We theoretically investigate the interplay
between these two instabilities for different combinations of the parameters of
the fluids and analyze the evolving interfacial patterns. We also estimate the
critical magnetic field strength at which thin layers disintegrate into an
ordered array of individual drops
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