25 research outputs found
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
Comparisons of Supergranule Characteristics During the Solar Minima of Cycles 22/23 and 23/24
Supergranulation is a component of solar convection that manifests itself on
the photosphere as a cellular network of around 35 Mm across, with a turnover
lifetime of 1-2 days. It is strongly linked to the structure of the magnetic
field. The horizontal, divergent flows within supergranule cells carry local
field lines to the cell boundaries, while the rotational properties of
supergranule upflows may contribute to the restoration of the poloidal field as
part of the dynamo mechanism that controls the solar cycle. The solar minimum
at the transition from cycle 23 to 24 was notable for its low level of activity
and its extended length. It is of interest to study whether the convective
phenomena that influences the solar magnetic field during this time differed in
character to periods of previous minima. This study investigates three
characteristics (velocity components, sizes and lifetimes) of solar
supergranulation. Comparisons of these characteristics are made between the
minima of cycles 22/23 and 23/24 using MDI Doppler data from 1996 and 2008,
respectively. It is found that whereas the lifetimes are equal during both
epochs (around 18 h), the sizes are larger in 1996 (35.9 +/- 0.3 Mm) than in
2008 (35.0 +/- 0.3 Mm), while the dominant horizontal velocity flows are weaker
(139 +/- 1 m/s in 1996; 141 +/- 1 m/s in 2008). Although numerical differences
are seen, they are not conclusive proof of the most recent minimum being
inherently unusual.Comment: 22 pages, 5 figures. Solar Physics, in pres
Active region formation through the negative effective magnetic pressure instability
The negative effective magnetic pressure instability operates on scales
encompassing many turbulent eddies and is here discussed in connection with the
formation of active regions near the surface layers of the Sun. This
instability is related to the negative contribution of turbulence to the mean
magnetic pressure that causes the formation of large-scale magnetic structures.
For an isothermal layer, direct numerical simulations and mean-field
simulations of this phenomenon are shown to agree in many details in that their
onset occurs at the same depth. This depth increases with increasing field
strength, such that the maximum growth rate of this instability is independent
of the field strength, provided the magnetic structures are fully contained
within the domain. A linear stability analysis is shown to support this
finding. The instability also leads to a redistribution of turbulent intensity
and gas pressure that could provide direct observational signatures.Comment: 19 pages, 10 figures, submitted to Solar Physic
Turbulent Compressible Convection with Rotation - Penetration above a Convection Zone
We perform Large eddy simulations of turbulent compressible convection in
stellar-type convection zones by solving the Navi\'{e}r-Stokes equations in
three dimensions. We estimate the extent of penetration into the stable layer
above a stellar-type convection zone by varying the rotation rate
({\boldmath}), the inclination of the rotation vector () and
the relative stability () of the upper stable layer. The computational
domain is a rectangular box in an f-plane configuration and is divided into two
regions of unstable and stable stratification with the stable layer placed
above the convectively unstable layer. Several models have been computed and
the penetration distance into the stable layer above the convection zone is
estimated by determining the position where time averaged kinetic energy flux
has the first zero in the upper stable layer. The vertical grid spacing in all
the model is non-uniform, and is less in the upper region so that the flows are
better resolved in the region of interest. We find that the penetration
distance increases as the rotation rate increases for the case when the
rotation vector is aligned with the vertical axis. However, with the increase
in the stability of the upper stable layer, the upward penetration distance
decreases. Since we are not able to afford computations with finer resolution
for all the models, we compute a number of models to see the effect of
increased resolution on the upward penetration. In addition, we estimate the
upper limit on the upward convective penetration from stellar convective cores.Comment: Accepted for Publication in Asttrophysics & Space Scienc
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
Recent Developments in Helioseismic Analysis Methods and Solar Data Assimilation
MR and AS have received funding from the European Research Council under the European Union’s Seventh Framework Program (FP/2007-2013)/ERC Grant Agreement no. 307117
Large-Eddy Simulations of Magnetohydrodynamic Turbulence in Heliophysics and Astrophysics
We live in an age in which high-performance computing is transforming the way we do science. Previously intractable problems are now becoming accessible by means of increasingly realistic numerical simulations. One of the most enduring and most challenging of these problems is turbulence. Yet, despite these advances, the extreme parameter regimes encountered in space physics and astrophysics (as in atmospheric and oceanic physics) still preclude direct numerical simulation. Numerical models must take a Large Eddy Simulation (LES) approach, explicitly computing only a fraction of the active dynamical scales. The success of such an approach hinges on how well the model can represent the subgrid-scales (SGS) that are not explicitly resolved. In addition to the parameter regime, heliophysical and astrophysical applications must also face an equally daunting challenge: magnetism. The presence of magnetic fields in a turbulent, electrically conducting fluid flow can dramatically alter the coupling between large and small scales, with potentially profound implications for LES/SGS modeling. In this review article, we summarize the state of the art in LES modeling of turbulent magnetohydrodynamic (MHD) ows. After discussing the nature of MHD turbulence and the small-scale processes that give rise to energy dissipation, plasma heating, and magnetic reconnection, we consider how these processes may best be captured within an LES/SGS framework. We then consider several special applications in heliophysics and astrophysics, assessing triumphs, challenges,and future directions
Confirmation of bistable stellar differential rotation profiles
VK: resolve; Karhunen, J.; ReSoLVEContext. Solar-like differential rotation is characterized by a rapidly rotating equator and slower poles. However, theoretical models and numerical simulations can also result in a slower equator and faster poles when the overall rotation is slow. Aims. We study the critical rotational influence under which differential rotation flips from solar-like (fast equator, slow poles) to an anti-solar one (slow equator, fast poles). We also estimate the non-diffusive (Λ effect) and diffusive (turbulent viscosity) contributions to the Reynolds stress. Methods. We present the results of three-dimensional numerical simulations of mildly turbulent convection in spherical wedge geometry. Here we apply a fully compressible setup which would suffer from a prohibitive time step constraint if the real solar luminosity was used. To avoid this problem while still representing the same rotational influence on the flow as in the Sun, we increase the luminosity by a factor of roughly 106 and the rotation rate by a factor of102. We regulate the convective velocities by varying the amount of heat transported by thermal conduction, turbulent diffusion, and resolved convection. Results. Increasing the efficiency of resolved convection leads to a reduction of the rotational influence on the flow and a sharp transition from solar-like to anti-solar differential rotation for Coriolis numbers around 1.3. We confirm the recent finding of a large-scale flow bistability: contrasted with running the models from an initial condition with unprescribed differential rotation, the initialization of the model with certain kind of rotation profile sustains the solution over a wider parameter range. The anti-solar profiles are found to be more stable against perturbations in the level of convective turbulent velocity than the solar-type solutions. Conclusions. Our results may have implications for real stars that start their lives as rapid rotators implying solar-like rotation in the early main-sequence evolution. As they slow down, they might be able to retain solar-like rotation for lower Coriolis numbers, and thus longer in time, before switching to anti-solar rotation. This could partially explain the puzzling findings of anti-solar rotation profiles for models in the solar parameter regime.Peer reviewe
Quantifying the effect of turbulent magnetic diffusion on the growth rate of the magneto-rotational instability
VK: resolve; Karhunen, J.; ReSoLVEContext. In astrophysics, turbulent diffusion is often used in place of microphysical diffusion to avoid resolving the small scales. However, we expect this approach to break down when time and length scales of the turbulence become comparable with other relevant time and length scales in the system. Turbulent diffusion has previously been applied to the magneto-rotational instability (MRI), but no quantitative comparison of growth rates at different turbulent intensities has been performed. Aims. We investigate to what extent turbulent diffusion can be used to model the effects of small-scale turbulence on the kinematic growth rates of the MRI, and how this depends on angular velocity and magnetic field strength. Methods. We use direct numerical simulations in three-dimensional shearing boxes with periodic boundary conditions in the spanwise direction and additional random plane-wave volume forcing to drive a turbulent flow at a given length scale. We estimate the turbulent diffusivity using a mixing length formula and compare with results obtained with the test-field method. Results. It turns out that the concept of turbulent diffusion is remarkably accurate in describing the effect of turbulence on the growth rate of the MRI. No noticeable breakdown of turbulent diffusion has been found, even when time and length scales of the turbulence become comparable with those imposed by the MRI itself. On the other hand, quenching of turbulent magnetic diffusivity by the magnetic field is found to be absent. Conclusions. Turbulence reduces the growth rate of the MRI in the same way as microphysical magnetic diffusion does.Peer reviewe