197 research outputs found
Nonlinear dynamos at infinite magnetic Prandtl number
The dynamo instability is investigated in the limit of infinite magnetic
Prandtl number. In this limit the fluid is assumed to be very viscous so that
the inertial terms can be neglected and the flow is slaved to the forcing. The
forcing consist of an external forcing function that drives the dynamo flow and
the resulting Lorentz force caused by the back reaction of the magnetic field.
The flows under investigation are the Archontis flow, and the ABC flow forced
at two different scales. The investigation covers roughly three orders of
magnitude of the magnetic Reynolds number above onset. All flows show a weak
increase of the averaged magnetic energy as the magnetic Reynolds number is
increased. Most of the magnetic energy is concentrated in flat elongated
structures that produce a Lorentz force with small solenoidal projection so
that the resulting magnetic field configuration was almost force-free. Although
the examined system has zero kinetic Reynolds number at sufficiently large
magnetic Reynolds number the structures are unstable to small scale
fluctuations that result in a chaotic temporal behavior
On the Saturation of Astrophysical Dynamos: Numerical Experiments with the No-cosines flow
In the context of astrophysical dynamos we illustrate that the no-cosines
flow, with zero mean helicity, can drive fast dynamo action and study the
dynamo's mode of operation during both the linear and non-linear saturation
regime: It turns out that in addition to a high growth rate in the linear
regime, the dynamo saturates at a level significantly higher than normal
turbulent dynamos, namely at exact equipartition when the magnetic Prandtl
number is on the order of unity. Visualization of the magnetic and velocity
fields at saturation will help us to understand some of the aspects of the
non-linear dynamo problem.Comment: 8 pages, 5 figures, submitted to the proceedings of "Space Climate 1"
to be peer-reviewed to Solar Physic
Revisiting the ABC flow dynamo
The ABC flow is a prototype for fast dynamo action, essential to the origin
of magnetic field in large astrophysical objects. Probably the most studied
configuration is the classical 1:1:1 flow. We investigate its dynamo properties
varying the magnetic Reynolds number Rm. We identify two kinks in the growth
rate, which correspond respectively to an eigenvalue crossing and to an
eigenvalue coalescence. The dominant eigenvalue becomes purely real for a
finite value of the control parameter. Finally we show that even for Rm =
25000, the dominant eigenvalue has not yet reached an asymptotic behaviour. Its
still varies very significantly with the controlling parameter. Even at these
very large values of Rm the fast dynamo property of this flow cannot yet be
established
Buoyant magnetic flux ropes in a magnetized stellar envelope: Idealized numerical 2.5-D MHD simulations
Context: The context of this paper is buoyant toroidal magnetic flux ropes,
which is a part of flux tube dynamo theory and the framework of solar-like
magnetic activity. Aims: The aim is to investigate how twisted magnetic flux
ropes interact with a simple magnetized stellar model envelope--a magnetic
"convection zone"--especially to examine how the twisted magnetic field
component of a flux rope interacts with a poloidal magnetic field in the
convection zone. Method: Both the flux ropes and the atmosphere are modelled as
idealized 2.5-dimensional concepts using high resolution numerical
magneto-hydrodynamic (MHD) simulations. Results: It is illustrated that twisted
toroidal magnetic flux ropes can interact with a poloidal magnetic field in the
atmosphere to cause a change in both the buoyant rise dynamics and the flux
rope's geometrical shape. The details of these changes depend primarily on the
polarity and strength of the atmospheric field relative to the field strength
of the flux rope. It is suggested that the effects could be verified
observationally.Comment: 8 pages, 5 figures (9 files), accepted by A&
On the origin of the magnetic energy in the quiet solar chromosphere
The presence of magnetic field is crucial in the transport of energy through
the solar atmosphere. Recent ground-based and space-borne observations of the
quiet Sun have revealed that magnetic field accumulates at photospheric
heights, via a local dynamo or from small-scale flux emergence events. However,
most of this small-scale magnetic field may not expand into the chromosphere
due to the entropy drop with height at the photosphere. Here we present a study
that uses a high resolution 3D radiative MHD simulation of the solar atmosphere
with non-grey and non-LTE radiative transfer and thermal conduction along the
magnetic field to reveal that: 1) the net magnetic flux from the simulated
quiet photosphere is not sufficient to maintain a chromospheric magnetic field
(on average), 2) processes in the lower chromosphere, in the region dominated
by magneto-acoustic shocks, are able to convert kinetic energy into magnetic
energy, 3) the magnetic energy in the chromosphere increases linearly in time
until the r.m.s. of the magnetic field strength saturates at roughly 4 to 30 G
(horizontal average) due to conversion from kinetic energy, 4) and that the
magnetic features formed in the chromosphere are localized to this region.Comment: 12 pages, 14 figures, accepted to be published in Ap
Mean electromotive force proportional to mean flow in mhd turbulence
In mean-field magnetohydrodynamics the mean electromotive force due to
velocity and magnetic field fluctuations plays a crucial role. In general it
consists of two parts, one independent of and another one proportional to the
mean magnetic field. The first part may be nonzero only in the presence of mhd
turbulence, maintained, e.g., by small-scale dynamo action. It corresponds to a
battery, which lets a mean magnetic field grow from zero to a finite value. The
second part, which covers, e.g., the alpha effect, is important for large-scale
dynamos. Only a few examples of the aforementioned first part of mean
electromotive force have been discussed so far. It is shown that a mean
electromotive force proportional to the mean fluid velocity, but independent of
the mean magnetic field, may occur in an originally homogeneous isotropic mhd
turbulence if there are nonzero correlations of velocity and electric current
fluctuations or, what is equivalent, of vorticity and magnetic field
fluctuations. This goes beyond the Yoshizawa effect, which consists in the
occurrence of mean electromotive forces proportional to the mean vorticity or
to the angular velocity defining the Coriolis force in a rotating frame and
depends on the cross-helicity defined by the velocity and magnetic field
fluctuations. Contributions to the mean electromotive force due to
inhomogeneity of the turbulence are also considered. Possible consequences of
the above and related findings for the generation of magnetic fields in cosmic
bodies are discussed.Comment: 7 pages, 1 figure, Astron. Nachr. (submitted
Large-to small-scale dynamo in domains of large aspect ratio: kinematic regime
The Sunâs magnetic field exhibits coherence in space and time on much larger scales than
the turbulent convection that ultimately powers the dynamo. In this work, we look for numerical
evidence of a large-scale magnetic field as the magnetic Reynolds number, Rm, is
increased. The investigation is based on the simulations of the induction equation in elongated
periodic boxes. The imposed flows considered are the standard ABC flow (named after
Arnold, Beltrami & Childress) with wavenumber ku = 1 (small-scale) and a modulated ABC
flow with wavenumbers ku = m, 1, 1 ± m, where m is the wavenumber corresponding to
the long-wavelength perturbation on the scale of the box. The critical magnetic Reynolds
number Rcrit
m decreases as the permitted scale separation in the system increases, such that
Rcrit
m â [Lx /Lz]
â1/2. The results show that the α-effect derived from the mean-field theory
ansatz is valid for a small range of Rm after which small scale dynamo instability occurs and the
mean-field approximation is no longer valid. The transition from large- to small-scale dynamo
is smooth and takes place in two stages: a fast transition into a predominantly small-scale
magnetic energy state and a slower transition into even smaller scales. In the range of Rm
considered, the most energetic Fourier component corresponding to the structure in the long
x-direction has twice the length-scale of the forcing scale. The long-wavelength perturbation
imposed on the ABC flow in the modulated case is not preserved in the eigenmodes of the
magnetic field
Dynamo effect in parity-invariant flow with large and moderate separation of scales
It is shown that non-helical (more precisely, parity-invariant) flows capable
of sustaining a large-scale dynamo by the negative magnetic eddy diffusivity
effect are quite common. This conclusion is based on numerical examination of a
large number of randomly selected flows. Few outliers with strongly negative
eddy diffusivities are also found, and they are interpreted in terms of the
closeness of the control parameter to a critical value for generation of a
small-scale magnetic field. Furthermore, it is shown that, for parity-invariant
flows, a moderate separation of scales between the basic flow and the magnetic
field often significantly reduces the critical magnetic Reynolds number for the
onset of dynamo action.Comment: 44 pages,11 figures, significantly revised versio
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