The program marked a highlight in the ERC-supported
Astrophysical
Dynamo Project at Nordita,
with two of the post-docs
(Piyali Chatterjee
and
Gustavo Guerrero,
right)
just departing.
The overall duration was 4 weeks. The program activity covered the following topics: Numerical simulations and mean-field theory, Recent results of numerical dynamo simulations, Effects of magnetic helicity and cross-helicity, Models of turbulent diffusivity and magnetic pumping, Progress in mean-field dynamo models.
As a rule, the morning hours were devoted to presentations and discussions, while the afternoons were left free for work, although most of us gathered for coffee each afternoon, during which some of the latest developments from participants were discussed.
The total number of program participants was 45
including 4 women, and 20 Nordic participant
(Denmark 1, Finland 3, Sweden 16, of which 12 from Stockholm).
A significant portion of the participants came from the US (5),
Russia (4), Brazil (2), as well as Germany (6), Israel (2),
and the UK (2).
Of the 33 people from outside Stockholm,
24 stayed for 3 weeks or longer.
The program marked a highlight in the ERC-supported
Astrophysical
Dynamo Project at Nordita,
with two of the post-docs
(Piyali Chatterjee
and
Gustavo Guerrero,
right)
just departing.
Solar dynamo
models and effects of magnetic helicity and cross-helicity (A. Brandenburg, A. Bonanno, V.
Pipin, D. Sokoloff, K. Kuzanyan, N. Yokoi, S. Candelaresi, D.
Mitra, M. Reshetnyak, G. Guerrero)
An important quadratic invariant of MHD is cross helicity.
Theory now predicts that at the solar surface is should be a
negative multiple of the mean radial field. Results from new
near-surface shear layer dynamos were presented, showing the
importance of magnetic helicity. In this connection, new aspects
of the Yoshizawa effect were also considered.
Flow-turbulence interaction in magnetic reconnection was
investigated. Breakage of symmetry associated with mean-field
configurations will lead to pseudoscalar generation in turbulence.
Cross helicity (velocity--magnetic-field correlation) is a
topological invariant of the magnetohydrodynamic equations.
Cross-helicity effects in the momentum and magnetic-induction
equations were analyzed. On the basis of this analysis, modulation
of magnetic-reconnection rate due to the turbulent cross-helicity
was estimated for the first time. Such work is expected to pave
the way for understanding the turbulence effects in magnetic
reconnection. Possibility and validity of the cross-helicity
effect in magnetic reconnection were discussed with several
researchers participating in this program. In relation to the
cross-helicity dynamo, spatiotemporal distributions of the
turbulent cross helicity were numerically investigated in the
local and global convection domains in collaboration with some
participants. In the context of solar activity cycle,
incorporation of the cross-helicity effects into dynamical-system
equations were examined.
Kinetic helicity is a topological invariant of the hydrodynamic
equations. According to the turbulence theory of inhomogeneous
hydrodynamic turbulence, inhomogeneity of turbulent helicity
coupled with the rotational motion has been expected to play an
important role in the large-scale vorticity generation. Such
effects should be examined in numerical simulations. Validation of
such effect using the pencil-code calculation has been preparing
in collaboration with NORDITA researchers.
Due to the limited statistics some of the mean-field quantities
considered in dynamo theory can fluctuate. These fluctuations can
produce new features in the dynamo systems. On an example of the
Parker's dynamo in the spherical shell we demonstrate how the
small fluctuations (about 5 percents) of the mean level of the
alpha-effect can cause significant equatorial asymmetry of the
oscillatory magnetic field, as well as propagation of the dynamo
wave through the equatorial plane.
Spherical convective rotating shells demonstrate existence of
kinematic helicity even in the incompressible case. However, due
to some theoretical background as well as to 3D simulations,
spatial distribution of the kinetic helicity for incompressible
and compressible systems can be quite different.
Solar dynamo with a positive alpha effect in the overshoot layer
and a deep meridional flow was investigated. In this model the
alpha effect is produced by a magnetic instability at the
tachocline. The parity selection mechanism was investigated.
Turbulence
models in dynamo theory (I. Rogachevskii, N. Kleeorin, K.-H. Raedler, N.
Mansour, M. Rheinhardt, A. Brandenburg, Y. Snellman)
The tau approach and other closure hypotheses were discussed at
length in a discussion session dedicated to this topic. Numerical
evidence for its validity is was presented, but a lack of overlap
with the second order correlation approximation was noted.
New work in connection with Reynolds stress modeling has been
discussed and simulations have been presented to quantify the
effect of the return to isotropy as a function of Reynolds number.
New work on two-dimensional turbulence has been performed using
graphics card computations and the saturation behavior of the
inversely cascading energy has been modeled with a 3-scale model.
Turbulent transport in stratified and/or rotating turbulence has
been investigated. The test-field method is used where transport
coefficients are determined by solving a set of equations with
properly chosen mean magnetic fields or mean scalars. The method
is adapted to mean fields which may depend on all thee space
coordinates. Anisotropy of turbulent diffusion is found 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
magnetic field turn out to be important. In stratified rotating
turbulence, the alpha effect is strongly anisotropic, suppressed
along the rotation axis on large length scales, but strongly
enhanced at intermediate length scales.
New ideas about the bottleneck effect in turbulence were
developed. This work emerged from one of the extended coffee
sessions. The closure in the one dimensional incompressible
Boussinesq case was investigated, and tried to modify it to better
match the numerical results from pencil-code. It would seem that
the results from the Pencil-code are much more affected by the
presence of vertical boundaries than the closure results. To shed
light on this problem a variety of different closure approaches
was investigated, none of which produced results similar to those
from pencil-code without some serious side effects. A lot of new
ideas and different approaches were discussed, and will most
probably lead to important breakthroughs in this field in the near
future.
Spontaneous Symmetry Breaking of the chiral symmetry in Tayler
Instability was investigated. The basic idea is to test the
recently proposed scenario for the SSB in MHD in the case of an
instability produced in stably stratified medium. In addition, to
study the Tayler Instability the pencil-code set-up was
implemented for the study of the possible helical modes that can
arise due to the instability. The aim is to see whether or not the
instability can give birth to a breaking of a non-helical state,
so causing the appearance of helicity. Several questions regarding
this phenomena are still unanswered, like the difference between
the linear and non-linear stages of the growth phase as well as
the role that such a breaking can have in generating a dynamo.
Magnetic
self-organization in turbulent plasma (I. Kitiashvili, N. Mansour, I.
Rogachevskii, N. Kleeorin, K. Kemel, A. Brandenburg)
The origin of magnetic flux concentrations in active regions and
sunspots was discussed. New work in connection with the negative
effective magnetic pressure instability has been initiated. A
related issue concerns the location of the solar dynamo, and more
work has been done to examine the idea that the solar dynamo is a
distributed one, shaped by near-surface shear.
Large-scale vortex instability and its applications to the
starspots in rapidly rotating stars were discussed. The mechanisms
of production of vorticity in the solar conditions were
investigated.
The first numerical demonstration of the negative effective
magnetic pressure instability was obtained in direct numerical
simulations of stably-stratified, externally-forced, isothermal
hydromagnetic turbulence. By the action of this instability,
initially uniform horizontal magnetic field forms flux
concentrations whose scale is large compared to the turbulent
scale. It is shown that the magnetic energy of these large-scale
structures is only weakly dependent on the magnetic Reynolds
number. The results supports earlier mean-field calculations and
analytic work which identified this instability. Applications to
the formation of active regions in the Sun are discussed.
The magnetic self-organization effects were also investigated in
realistic simulations of solar magnetoconvections, including
spontaneous formation of magnetic structures and the filamentary
structure of sunspots. The sunspot penumbra is a transition zone
between the strong vertical magnetic field area (sunspot umbra)
and the quiet Sun. The penumbra has a fine filamentary structure
that is characterized by magnetic field lines inclined toward the
surface. Numerical simulations of solar convection in inclined
magnetic field regions have provided an explanation of the
filamentary structure and the Evershed outflow in the penumbra.
The radiative MHD simulations were used to investigate the
influence of the magnetic field inclination on the power spectrum
of vertical velocity oscillations. The results revealed a strong
shift of the resonance mode peaks to higher frequencies in the
case of a highly inclined magnetic field. The frequency shift for
the inclined field is significantly greater than that in
vertical-field regions of similar strength. This is consistent
with the behavior of fast MHD waves.
Observational
input and constraints for the dynamo problem and solar MHD (J. Stenflo, P. Goode, D. Sokoloff,
V. Pipin, K. Kuzanyan, A. Kosovichev, G. Scharmer)
Simulations of plasmoid ejections from convection in a spherical shell have been developed further.
The importance of fluctuating alpha effects have been discussed both in the geodynamo context, but also as a general mechanism to explain the phenomenon of what is known as shear dynamos.
Links between solar, astrophysical and geophysical dynamos (R. Arlt, F. Busse, R. Simitev, M. Reshetnyak, E. de Gouveia Dal Pino, V. Duez, S. Sur, A. Bobrick, Xing Wei, M. Mantere, F. del Sordo)
The occurrence of an alpha effect in the absence of any
pseudo-scalars has been discussed in connection with spontaneous
symmetry breaking. New work on the Tayler instability has been
initiated and the possible relevance to magnetars has been
mentioned.
Turbulent fast reconnection and its role on the diffusive
transport of magnetic flux in astrophysical environments were
discussed. Potential applications of this transport to dynamo
problems is foreseen.
Outflow ejection by supernovae in galaxy disks was studied.
Numerical simulations of supernova triggered galactic outflow
formation were performed including realistic galactic disk/coronal
setups for the Milky Way and starburst galaxies, the possibility
of using these setups in magnetic helicity transport studies
related to galactic dynamos has been discussed. The role of
kinectic effects on turbulent dynamo models related to the IGM
using a Kinectic-MHD description was also discussed.
Progress on research on the generation of large scale magnetic
field by strongly-driven chaotic convection in rotating spherical
fluid shells under the assumption of the Boussinesq approximation
has been reported. In addition, self-consistent dynamo models have
been developed to compute maps of various quantities which are of
particular interest, such as magnetic, kinetic and cross helicity,
and discussed the results with other participants.
Thin shell dynamos were investigated with the goal of
understanding as many solar magnetic phenomena as is possible with
numerical simulations of a most simple physically consistent
convection driven dynamo model. With a given ratio of 0.65 between
inner and outer radii of the rotating spherical there are only 4
parameters of the coupled Navier-Stokes equations, heat equation,
and equation of magnetic induction that can be varied: Rayleigh
number R, rotation parameter tau, Prandtl number and magnetic
Prandtl number.
Although the geostrophic differential rotation found in the
simulations clearly differs from the solar differential rotation,
the oscillatory dynamo shares many features with the observed
solar magnetic cycle. The most important new result is the strong
non-axisymmetric (m=1) component of the oscillating magnetic
field, the energy of which far exceeds the energy of the
axisymmetric component. The latter is traditionally assumed to be
the dominant component of the solar magnetic field. The new result
is in good agreement with the phenomenon of active longitudes on
the sun.
In geodynamo, it's believed that Busse rolls generate the alpha
effect, namely the fluid helical motions in cyclonic and
anti-cyclonic convection rolls twist the toroidal field lines to
create the poloidal field lines. An alternative is the precession
which can generate inertial waves arising from the destabilization
of the internal shear layers (the so-called triad resonance) to
induce the alpha effect. The topography or ellipticity can help
the generation of these waves. However, with the spectral code,
it's impossible to calculate for the topography and large
ellipticity. Geodynamo calculations with the pencil code have been
discussed.
Preprints:
As a result of the program, several Nordita preprints have already appeared or are expected to appear:
During the meeting, Koen Kemel defended his licentiate thesis on "Mean-field theory in magneto-hydrodynamics and the generation of magnetic flux concentrations" with Sasha Kosovichev as opponent.
