3,141 research outputs found
The inverse cascade and nonlinear alpha-effect in simulations of isotropic helical hydromagnetic turbulence
A numerical model of isotropic homogeneous turbulence with helical forcing is
investigated. The resulting flow, which is essentially the prototype of the
alpha^2 dynamo of mean-field dynamo theory, produces strong dynamo action with
an additional large scale field on the scale of the box (at wavenumber k=1;
forcing is at k=5). This large scale field is nearly force-free and exceeds the
equipartition value. As the magnetic Reynolds number R_m increases, the
saturation field strength and the growth rate of the dynamo increase. However,
the time it takes to built up the large scale field from equipartition to its
final super-equipartition value increases with magnetic Reynolds number. The
large scale field generation can be identified as being due to nonlocal
interactions originating from the forcing scale, which is characteristic of the
alpha-effect. Both alpha and turbulent magnetic diffusivity eta_t are
determined simultaneously using numerical experiments where the mean-field is
modified artificially. Both quantities are quenched in a R_m-dependent fashion.
The evolution of the energy of the mean field matches that predicted by an
alpha^2 dynamo model with similar alpha and eta_t quenchings. For this model an
analytic solution is given which matches the results of the simulations. The
simulations are numerically robust in that the shape of the spectrum at large
scales is unchanged when changing the resolution from 30^3 to 120^3 meshpoints,
or when increasing the magnetic Prandtl number (viscosity/magnetic diffusivity)
from 1 to 100. Increasing the forcing wavenumber to 30 (i.e. increasing the
scale separation) makes the inverse cascade effect more pronounced, although it
remains otherwise qualitatively unchanged.Comment: 21 pages, 26 figures, ApJ (accepted
Turbulent transport in hydromagnetic flows
The predictive power of mean-field theory is emphasized by comparing theory
with simulations under controlled conditions. The recently developed test-field
method is used to extract turbulent transport coefficients both in kinematic as
well as nonlinear and quasi-kinematic cases. A striking example of the
quasi-kinematic method is provided by magnetic buoyancy-driven flows that
produce an alpha effect and turbulent diffusion.Comment: 17 pages, 6 figures, topical issue of Physica Scripta on turbulent
mixing and beyon
Cross helicity and turbulent magnetic diffusivity in the solar convection zone
In a density-stratified turbulent medium the cross helicity is
considered as a result of the interaction of the velocity fluctuations and a
large-scale magnetic field. By means of a quasilinear theory and by numerical
simulations we find the cross helicity and the mean vertical magnetic field
anti-correlated. In the high-conductivity limit the ratio of the helicity and
the mean magnetic field equals the ratio of the magnetic eddy diffusivity and
the (known) density scale height. The result can be used to predict that the
cross helicity at the solar surface exceeds the value of 1 Gauss km/s. Its sign
is anti-correlated with that of the radial mean magnetic field. Alternatively,
we can use our result to determine the value of the turbulent magnetic
diffusivity from observations of the cross helicity.Comment: 9 pages, 2 figures, submitted to Solar Physic
Solar dynamo model with nonlocal alpha-effect
The first results of the solar dynamo model that allows for the diamagnetic
effect of inhomogeneous turbulence and the nonlocal alpha-effect due to the
rise of magnetic loops are discussed. The nonlocal alpha-effect is not subject
to the catastrophic quenching related to the conservation of magnetic helicity.
Given the diamagnetic pumping, the magnetic fields are concentrated near the
base of the convection zone, although the distributed-type model covers the
entire thickness of the convection zone. The magnetic cycle period, the
equatorial symmetry of the field, its meridional drift, and the
polar-to-toroidal field ratio obtained in the model are in agreement with
observations. There is also some disagreement with observations pointing the
ways of improving the model.Comment: To appear in Astronomy Letters, 10 pages, 5 figure
New scaling for the alpha effect in slowly rotating turbulence
Using simulations of slowly rotating stratified turbulence, we show that the
alpha effect responsible for the generation of astrophysical magnetic fields is
proportional to the logarithmic gradient of kinetic energy density rather than
that of momentum, as was previously thought. This result is in agreement with a
new analytic theory developed in this paper for large Reynolds numbers. Thus,
the contribution of density stratification is less important than that of
turbulent velocity. The alpha effect and other turbulent transport coefficients
are determined by means of the test-field method. In addition to forced
turbulence, we also investigate supernova-driven turbulence and stellar
convection. In some cases (intermediate rotation rate for forced turbulence,
convection with intermediate temperature stratification, and supernova-driven
turbulence) we find that the contribution of density stratification might be
even less important than suggested by the analytic theory.Comment: 10 pages, 9 figures, revised version, Astrophys. J., in pres
Magnetic diffusivity tensor and dynamo effects in rotating and shearing turbulence
The turbulent magnetic diffusivity tensor is determined in the presence of
rotation or shear. The question is addressed whether dynamo action from the
shear-current effect can explain large-scale magnetic field generation found in
simulations with shear. For this purpose a set of evolution equations for the
response to imposed test fields is solved with turbulent and mean motions
calculated from the momentum and continuity equations. The corresponding
results for the electromotive force are used to calculate turbulent transport
coefficients. The diagonal components of the turbulent magnetic diffusivity
tensor are found to be very close together, but their values increase slightly
with increasing shear and decrease with increasing rotation rate. In the
presence of shear, the sign of the two off-diagonal components of the turbulent
magnetic diffusion tensor is the same and opposite to the sign of the shear.
This implies that dynamo action from the shear--current effect is impossible,
except perhaps for high magnetic Reynolds numbers. However, even though there
is no alpha effect on the average, the components of the alpha tensor display
Gaussian fluctuations around zero. These fluctuations are strong enough to
drive an incoherent alpha--shear dynamo. The incoherent shear--current effect,
on the other hand, is found to be subdominant.Comment: 12 pages, 13 figures, improved version, accepted by Ap
Current status of turbulent dynamo theory: From large-scale to small-scale dynamos
Several recent advances in turbulent dynamo theory are reviewed. High
resolution simulations of small-scale and large-scale dynamo action in periodic
domains are compared with each other and contrasted with similar results at low
magnetic Prandtl numbers. It is argued that all the different cases show
similarities at intermediate length scales. On the other hand, in the presence
of helicity of the turbulence, power develops on large scales, which is not
present in non-helical small-scale turbulent dynamos. At small length scales,
differences occur in connection with the dissipation cutoff scales associated
with the respective value of the magnetic Prandtl number. These differences are
found to be independent of whether or not there is large-scale dynamo action.
However, large-scale dynamos in homogeneous systems are shown to suffer from
resistive slow-down even at intermediate length scales. The results from
simulations are connected to mean field theory and its applications. Recent
work on helicity fluxes to alleviate large-scale dynamo quenching, shear
dynamos, nonlocal effects and magnetic structures from strong density
stratification are highlighted. Several insights which arise from analytic
considerations of small-scale dynamos are discussed.Comment: 36 pages, 11 figures, Spa. Sci. Rev., submitted to the special issue
"Magnetism in the Universe" (ed. A. Balogh
The kinetic helicity needed to drive large-scale dynamos
Magnetic field generation on scales large compared with the scale of the
turbulent eddies is known to be possible via the so-called effect when
the turbulence is helical and if the domain is large enough for the
effect to dominate over turbulent diffusion. Using three-dimensional turbulence
simulations, we show that the energy of the resulting mean magnetic field of
the saturated state increases linearly with the product of normalized helicity
and the ratio of domain scale to eddy scale, provided this product exceeds a
critical value of around unity. This implies that large-scale dynamo action
commences when the normalized helicity is larger than the inverse scale ratio.
Our results show that the emergence of small-scale dynamo action does not have
any noticeable effect on the large-scale dynamo. Recent findings by Pietarila
Graham et al. (2012, Phys. Rev. E85, 066406) of a smaller minimal helicity may
be an artifact due to the onset of small-scale dynamo action at large magnetic
Reynolds numbers. However, the onset of large-scale dynamo action is difficult
to establish when the kinetic helicity is small. Instead of random forcing,
they used an ABC-flow with time-dependent phases. We show that such dynamos
saturate prematurely in a way that is reminiscent of inhomogeneous dynamos with
internal magnetic helicity fluxes. Furthermore, even for very low fractional
helicities, such dynamos display large-scale fields that change direction,
which is uncharacteristic of turbulent dynamos.Comment: 10 pages, 13 figure
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