22 research outputs found
Mean--field electrodynamics: Critical analysis of various analytical approaches to the mean electromotive force
There are various analytical approaches to the mean electromotive force crucial in mean--field electrodynamics, with
and
being velocity and magnetic field fluctuations. In most cases the
traditional approach, restricted to the second--order correlation
approximation, has been used. Its validity is only guaranteed for a range of
conditions, which is narrow in view of many applications, e.g., in
astrophysics. With the intention to have a wider range of applicability other
approaches have been proposed which make use of the so--called
--approximation, reducing correlations of third order in and
to such of second order. After explaining some basic features of the
traditional approach a critical analysis of the approaches of that kind is
given. It is shown that they lead in some cases to results which are in clear
conflict with those of the traditional approach. It is argued that this
indicates shortcomings of the --approaches and poses serious restrictions
to their applicability. These shortcomings do not result from the basic
assumption of the --approximation. Instead, they seem to originate in
some simplifications made in order to derive without really solving
the equations governing and . A starting point for a new
approach is described which avoids the conflict.Comment: 32 pages, no figures; accepted by Geophys. Astrophys. Fluid Dynam. A
quenching formula for \alpha and a section on comparisons with numerical
simulations added; references amended; changes in presentation and languag
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
Properties of - and -modes in hydromagnetic turbulence
With the ultimate aim of using the fundamental or -mode to study
helioseismic aspects of turbulence-generated magnetic flux concentrations, we
use randomly forced hydromagnetic simulations of a piecewise isothermal layer
in two dimensions with reflecting boundaries at top and bottom. We compute
numerically diagnostic wavenumber-frequency diagrams of the vertical velocity
at the interface between the denser gas below and the less dense gas above. For
an Alfv\'en-to-sound speed ratio of about 0.1, a 5% frequency increase of the
-mode can be measured when -, where is the
horizontal wavenumber and is the pressure scale height at the
surface. Since the solar radius is about 2000 times larger than ,
the corresponding spherical harmonic degree would be 6000-8000. For weaker
fields, a -dependent frequency decrease by the turbulent motions becomes
dominant. For vertical magnetic fields, the frequency is enhanced for
, but decreased relative to its nonmagnetic value for
.Comment: 17 pages, 22 figures, Version accepted in MNRA
Scalable communication for high-order stencil computations using CUDA-aware MPI
Modern compute nodes in high-performance computing provide a tremendous level
of parallelism and processing power. However, as arithmetic performance has
been observed to increase at a faster rate relative to memory and network
bandwidths, optimizing data movement has become critical for achieving strong
scaling in many communication-heavy applications. This performance gap has been
further accentuated with the introduction of graphics processing units, which
can provide by multiple factors higher throughput in data-parallel tasks than
central processing units. In this work, we explore the computational aspects of
iterative stencil loops and implement a generic communication scheme using
CUDA-aware MPI, which we use to accelerate magnetohydrodynamics simulations
based on high-order finite differences and third-order Runge-Kutta integration.
We put particular focus on improving intra-node locality of workloads. In
comparison to a theoretical performance model, our implementation exhibits
strong scaling from one to devices at -- efficiency in
sixth-order stencil computations when the problem domain consists of
-- cells.Comment: 17 pages, 15 figure
Interaction of large- and small-scale dynamos in isotropic turbulent flows from GPU-accelerated simulations
Magnetohydrodynamical (MHD) dynamos emerge in many different astrophysical
situations where turbulence is present, but the interaction between large-scale
(LSD) and small-scale dynamos (SSD) is not fully understood. We performed a
systematic study of turbulent dynamos driven by isotropic forcing in isothermal
MHD with magnetic Prandtl number of unity, focusing on the exponential growth
stage. Both helical and non-helical forcing was employed to separate the
effects of LSD and SSD in a periodic domain. Reynolds numbers (Rm) up to
were examined and multiple resolutions used for convergence
checks. We ran our simulations with the Astaroth code, designed to accelerate
3D stencil computations on graphics processing units (GPUs) and to employ
multiple GPUs with peer-to-peer communication. We observed a speedup of
in single-node performance compared to the widely used multi-CPU
MHD solver Pencil Code. We estimated the growth rates both from the averaged
magnetic fields and their power spectra. At low Rm, LSD growth dominates, but
at high Rm SSD appears to dominate in both helically and non-helically forced
cases. Pure SSD growth rates follow a logarithmic scaling as a function of Rm.
Probability density functions of the magnetic field from the growth stage
exhibit SSD behaviour in helically forced cases even at intermediate Rm. We
estimated mean-field turbulence transport coefficients using closures like the
second-order correlation approximation (SOCA). They yield growth rates similar
to the directly measured ones and provide evidence of quenching. Our
results are consistent with the SSD inhibiting the growth of the LSD at
moderate Rm, while the dynamo growth is enhanced at higher Rm.Comment: 22 pages, 23 figures, 2 tables, Accepted for publication in the
Astrophysical Journa
Nonlinear magnetic diffusivity and alpha tensors in helical turbulence
The effect of a dynamo-generated mean magnetic field of Beltrami type on the
mean electromotive force is studied. In the absence of the mean magnetic field
the turbulence is assumed to be homogeneous and isotropic, but it becomes
inhomogeneous and anisotropic with this field. Using the testfield method the
dependence of the alpha and turbulent diffusivity tensors on the magnetic
Reynolds number Rm is determined for magnetic fields that have reached
approximate equipartition with the velocity field. The tensor components are
characterized by a pseudoscalar alpha and a scalar turbulent magnetic
diffusivity etat. Increasing Rm from 2 to 600 reduces etat by a factor ~5,
suggesting that the quenching of etat is, in contrast to the 2-dimensional
case, only weakly dependent on Rm. Over the same range of Rm, however, alpha is
reduced by a factor ~14, which can qualitatively be explained by a
corresponding increase of a magnetic contribution to the alpha effect with
opposite sign. The level of fluctuations of alpha and etat is only 10% and 20%
of the respective kinematic reference values.Comment: 4 pages, 3 figs, ApJL (accepted version
Mean-field diffusivities in passive scalar and magnetic transport in irrotational flows
Certain aspects of the mean-field theory of turbulent passive scalar
transport and of mean-field electrodynamics are considered with particular
emphasis on aspects of compressible fluids. It is demonstrated that the total
mean-field diffusivity for passive scalar transport in a compressible flow may
well be smaller than the molecular diffusivity. This is in full analogy to an
old finding regarding the magnetic mean-field diffusivity in an electrically
conducting turbulently moving compressible fluid. These phenomena occur if the
irrotational part of the motion dominates the vortical part, the P\`eclet or
magnetic Reynolds number is not too large, and, in addition, the variation of
the flow pattern is slow. For both the passive scalar and the magnetic cases
several further analytical results on mean-field diffusivities and related
quantities found within the second-order correlation approximation are
presented, as well as numerical results obtained by the test-field method,
which applies independently of this approximation. Particular attention is paid
to non-local and non-instantaneous connections between the turbulence-caused
terms and the mean fields. Two examples of irrotational flows, in which
interesting phenomena in the above sense occur, are investigated in detail. In
particular, it is demonstrated that the decay of a mean scalar in a
compressible fluid under the influence of these flows can be much slower than
without any flow, and can be strongly influenced by the so-called memory
effect, that is, the fact that the relevant mean-field coefficients depend on
the decay rates themselves.Comment: 13 pages, 10 figures, published on PR
Compressible Test-field Method and Its Application to Shear Dynamos
| openaire: EC/H2020/818665/EU//UniSDyn Funding Information: We acknowledge fruitful and inspiring discussions with Prof. Nishant Singh, Dr. Hongzhe Zhou, Dr. Jonathan Squire, and Prof. Amitava Bhattacharjee, many of which took place in the inspiring atmosphere of the Max Planck Princeton Center for Plasma Physics framework. M.J.K. and M.R. acknowledge the support of the Academy of Finland ReSoLVE Centre of Excellence (grant number 307411). This project has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (Project UniSDyn, grant agreement n:o 818665). A.B. acknowledges support through the Swedish Research Council (Vetenskapsrådet), grant 2019-04234. Publisher Copyright: © 2022. The Author(s). Published by the American Astronomical Society.In this study, we present a compressible test-field method (CTFM) for computing α-effect and turbulent magnetic diffusivity tensors, as well as those relevant for the mean ponderomotive force and mass source, applied to the full MHD equations. We describe the theoretical background of the method and compare it to the quasi-kinematic test-field method and to the previously studied variant working in simplified MHD (SMHD). We present several test cases using velocity and magnetic fields of the Roberts geometry and also compare with the imposed-field method. We show that, for moderate imposed-field strengths, the nonlinear CTFM (nCTFM) gives results in agreement with the imposed-field method. A comparison of different flavors of the nCTFM in the shear dynamo case also yields agreement up to equipartition field strengths. Some deviations between the CTFM and SMHD variants exist. As a relevant physical application, we study nonhelically forced shear flows, which exhibit large-scale dynamo action, and present a reanalysis of low-Reynolds-number, moderate shear systems, where we previously ignored the pressure gradient in the momentum equation and found no coherent shear-current effect. Another key difference is that in the earlier study we used magnetic forcing to mimic small-scale dynamo action, while here it is self-consistently driven by purely kinetic forcing. The kinematic CTFM with general validity forms the core of our analysis. We still find no coherent shear-current effect, but do recover strong large-scale dynamo action that, according to our analysis, is driven by incoherent effects.Peer reviewe