4,532 research outputs found
Mean-field transport in stratified and/or rotating turbulence
We investigate the mean electromotive force in the kinematic framework, that
is, ignoring the back-reaction of the magnetic field on the fluid velocity,
under the assumption of axisymmetric turbulence determined by the presence of
either rotation, density stratification, or both. We use an analogous approach
for the mean passive scalar flux. As an alternative to convection, we consider
forced turbulence in an isothermal layer. When using standard ansatzes, the
mean magnetic transport is then determined by nine, and the mean passive scalar
transport by four coefficients. We give results for all these transport
coefficients. We use the test-field method and the test-scalar method, where
transport coefficients are determined by solving sets of equations with
properly chosen mean magnetic fields or mean scalars. These methods are adapted
to mean fields which may depend on all three space coordinates. We find the
anisotropy of turbulent diffusion to be moderate in spite of rapid rotation or
strong density stratification. Contributions to the mean electromotive force
determined by the symmetric part of the gradient tensor of the mean magnetic
field, which were ignored in several earlier investigations, turn out to be
important. In stratified rotating turbulence, the effect is strongly
anisotropic, suppressed along the rotation axis on large length scales, but
strongly enhanced at intermediate length scales. Also the \OO\times\meanJJ
effect is enhanced at intermediate length scales. The turbulent passive scalar
diffusivity is typically almost twice as large as the turbulent magnetic
diffusivity. Both magnetic and passive scalar diffusion are slightly enhanced
along the rotation axis, but decreased if there is gravity.Comment: 12 pages, 8 figures, A&A, publishe
Magnetic helicity in stellar dynamos: new numerical experiments
The theory of large scale dynamos is reviewed with particular emphasis on the
magnetic helicity constraint in the presence of closed and open boundaries. In
the presence of closed or periodic boundaries, helical dynamos respond to the
helicity constraint by developing small scale separation in the kinematic
regime, and by showing long time scales in the nonlinear regime where the scale
separation has grown to the maximum possible value. A resistively limited
evolution towards saturation is also found at intermediate scales before the
largest scale of the system is reached. Larger aspect ratios can give rise to
different structures of the mean field which are obtained at early times, but
the final saturation field strength is still decreasing with decreasing
resistivity. In the presence of shear, cyclic magnetic fields are found whose
period is increasing with decreasing resistivity, but the saturation energy of
the mean field is in strong super-equipartition with the turbulent energy. It
is shown that artificially induced losses of small scale field of opposite sign
of magnetic helicity as the large scale field can, at least in principle,
accelerate the production of large scale (poloidal) field. Based on mean field
models with an outer potential field boundary condition in spherical geometry,
we verify that the sign of the magnetic helicity flux from the large scale
field agrees with the sign of alpha. For solar parameters, typical magnetic
helicity fluxes lie around 10^{47} Mx^2 per cycle.Comment: 23 pages, 27 figures, Astron. Nach
Kinematic alpha effect in isotropic turbulence simulations
Using numerical simulations at moderate magnetic Reynolds numbers up to 220
it is shown that in the kinematic regime, isotropic helical turbulence leads to
an alpha effect and a turbulent diffusivity whose values are independent of the
magnetic Reynolds number, \Rm, provided \Rm exceeds unity. These turbulent
coefficients are also consistent with expectations from the first order
smoothing approximation. For small values of \Rm, alpha and turbulent
diffusivity are proportional to \Rm. Over finite time intervals meaningful
values of alpha and turbulent diffusivity can be obtained even when there is
small-scale dynamo action that produces strong magnetic fluctuations. This
suggests that small-scale dynamo-generated fields do not make a correlated
contribution to the mean electromotive force.Comment: Accepted for publication in MNRAS Letter
Minimal tau approximation and simulations of the alpha effect
The validity of a closure called the minimal tau approximation (MTA), is
tested in the context of dynamo theory, wherein triple correlations are assumed
to provide relaxation of the turbulent electromotive force. Under MTA, the
alpha effect in mean field dynamo theory becomes proportional to a relaxation
time scale multiplied by the difference between kinetic and current helicities.
It is shown that the value of the relaxation time is positive and, in units of
the turnover time at the forcing wavenumber, it is of the order of unity. It is
quenched by the magnetic field -- roughly independently of the magnetic
Reynolds number. However, this independence becomes uncertain at large magnetic
Reynolds number. Kinetic and current helicities are shown to be dominated by
large scale properties of the flow.Comment: 11 pages, 12 figures, accepted by A&
Enhancement of small-scale turbulent dynamo by large-scale shear
Small-scale dynamos are ubiquitous in a broad range of turbulent flows with
large-scale shear, ranging from solar and galactic magnetism to accretion
disks, cosmology and structure formation. Using high-resolution direct
numerical simulations we show that in non-helically forced turbulence with zero
mean magnetic field, large-scale shear supports small-scale dynamo action,
i.e., the dynamo growth rate increases with shear and shear enhances or even
produces turbulence, which, in turn, further increases the dynamo growth rate.
When the production rates of turbulent kinetic energy due to shear and forcing
are comparable, we find scalings for the growth rate of the
small-scale dynamo and the turbulent velocity with shear rate
that are independent of the magnetic Prandtl number: and
. For large fluid and magnetic Reynolds numbers,
, normalized by its shear-free value, depends only on shear. Having
compensated for shear-induced effects on turbulent velocity, we find that the
normalized growth rate of the small-scale dynamo exhibits the scaling,
, arising solely from the induction
equation for a given velocity field.Comment: Improved version submitted to the Astrophysical Journal Letters, 6
pages, 5 figure
Decay of helical and non-helical magnetic knots
We present calculations of the relaxation of magnetic field structures that
have the shape of particular knots and links. A set of helical magnetic flux
configurations is considered, which we call -foil knots of which the trefoil
knot is the most primitive member. We also consider two nonhelical knots;
namely, the Borromean rings as well as a single interlocked flux rope that also
serves as the logo of the Inter-University Centre for Astronomy and
Astrophysics in Pune, India. The field decay characteristics of both
configurations is investigated and compared with previous calculations of
helical and nonhelical triple-ring configurations. Unlike earlier nonhelical
configurations, the present ones cannot trivially be reduced via flux
annihilation to a single ring. For the -foil knots the decay is described by
power laws that range form to , which can be as slow as
the behavior for helical triple-ring structures that were seen in
earlier work. The two nonhelical configurations decay like , which is
somewhat slower than the previously obtained behavior in the decay
of interlocked rings with zero magnetic helicity. We attribute the difference
to the creation of local structures that contain magnetic helicity which
inhibits the field decay due to the existence of a lower bound imposed by the
realizability condition. We show that net magnetic helicity can be produced
resistively as a result of a slight imbalance between mutually canceling
helical pieces as they are being driven apart. We speculate that higher order
topological invariants beyond magnetic helicity may also be responsible for
slowing down the decay of the two more complicated nonhelical structures
mentioned above.Comment: 11 pages, 27 figures, submitted to Phys. Rev.
Fanning out of the -mode in presence of nonuniform magnetic fields
We show that in the presence of a harmonically varying magnetic field the
fundamental or -mode in a stratified layer is altered in such a way that it
fans out in the diagnostic diagram, but with mode power also within
the fan. In our simulations, the surface is defined by a temperature and
density jump in a piecewise isothermal layer. Unlike our previous work (Singh
et al. 2014) where a uniform magnetic field was considered, we employ here a
nonuniform magnetic field together with hydromagnetic turbulence at length
scales much smaller than those of the magnetic fields. The expansion of the
-mode is stronger for fields confined to the layer below the surface. In
some of those cases, the diagram also reveals a new class of low
frequency vertical stripes at multiples of twice the horizontal wavenumber of
the background magnetic field. We argue that the study of the -mode
expansion might be a new and sensitive tool to determining subsurface magnetic
fields with longitudinal periodicity.Comment: 6 pages, 4 figures, submitted to Astrophysical Journal Letter
The negative magnetic pressure effect in stratified turbulence
While the rising flux tube paradigm is an elegant theory, its basic
assumptions, thin flux tubes at the bottom of the convection zone with field
strengths two orders of magnitude above equipartition, remain numerically
unverified at best. As such, in recent years the idea of a formation of
sunspots near the top of the convection zone has generated some interest. The
presence of turbulence can strongly enhance diffusive transport mechanisms,
leading to an effective transport coefficient formalism in the mean-field
formulation. The question is what happens to these coefficients when the
turbulence becomes anisotropic due to a strong large-scale mean magnetic field.
It has been noted in the past that this anisotropy can also lead to highly
non-diffusive behaviour. In the present work we investigate the formation of
large-scale magnetic structures as a result of a negative contribution of
turbulence to the large-scale effective magnetic pressure in the presence of
stratification. In direct numerical simulations of forced turbulence in a
stratified box, we verify the existence of this effect. This phenomenon can
cause formation of large-scale magnetic structures even from initially uniform
large-scale magnetic field.Comment: 5 pages, 2 figures, submitted conference proceedings IAU symposium
273 "Physics of Sun and Star Spots
Turbulent magnetic pressure instability in stratified turbulence
A reduction of total mean turbulent pressure due to the presence of magnetic
fields was previously shown to be a measurable effect in direct numerical
simulations. However, in the studied parameter regime the formation of
large-scale structures, as anticipated from earlier mean-field simulations, was
not found. An analysis of the relevant mean-field parameter dependency and the
parameter domain of interest is conducted in order to clarify this apparent
discrepancy.Comment: 3 pages, 2 figures, proceedings of IAU Symp. 274, Advances in Plasma
Astrophysics, ed. A. Bonanno, E. de Gouveia dal Pino and A. Kosoviche
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