8 research outputs found
Understanding Helical Magnetic Dynamo Spectra with a Nonlinear Four-Scale Theory
Recent MHD dynamo simulations for magnetic Prandtl number demonstrate
that when MHD turbulence is forced with sufficient kinetic helicity, the
saturated magnetic energy spectrum evolves from having a single peak below the
forcing scale to become doubly peaked with one peak at the system (=largest)
scale and one at the forcing scale. The system scale field growth is well
modeled by a recent nonlinear two-scale nonlinear helical dynamo theory in
which the system and forcing scales carry magnetic helicity of opposite sign.
But a two-scale theory cannot model the shift of the small-scale peak toward
the forcing scale. Here I develop a four-scale helical dynamo theory which
shows that the small-scale helical magnetic energy first saturates at very
small scales, but then successively saturates at larger values at larger
scales, eventually becoming dominated by the forcing scale. The transfer of the
small scale peak to the forcing scale is completed by the end of the kinematic
growth regime of the large scale field, and does not depend on magnetic
Reynolds number for large . The four-scale and two-scale theories
subsequently evolve almost identically, and both show significant field growth
on the system and forcing scales that is independent of . In the present
approach, the helical and nonhelical parts of the spectrum are largely
decoupled. Implications for fractionally helical turbulence are discussed.Comment: 19 Pages, LaTex, (includes 4 figs at the end), in press, MNRA
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
Spontaneous formation of flux concentrations in a stratified layer
The negative effective magnetic pressure instability discovered recently in
direct numerical simulations (DNS) may play a crucial role in the formation of
sunspots and active regions in the Sun and stars. This instability is caused by
a negative contribution of turbulence to the effective mean Lorentz force (the
sum of turbulent and non-turbulent contributions) and results in formation of
large-scale inhomogeneous magnetic structures from initial uniform magnetic
field. Earlier investigations of this instability in DNS of stably stratified,
externally forced, isothermal hydromagnetic turbulence in the regime of large
plasma beta are now extended into the regime of larger scale separation ratios
where the number of turbulent eddies in the computational domain is about 30.
Strong spontaneous formation of large-scale magnetic structures is seen even
without performing any spatial averaging. These structures encompass many
turbulent eddies. The characteristic time of the instability is comparable to
the turbulent diffusion time, L^2/eta_t, where eta_t is the turbulent
diffusivity and L is the scale of the domain. DNS are used to confirm that the
effective magnetic pressure does indeed become negative for magnetic field
strengths below the equipartition field. The dependence of the effective
magnetic pressure on the field strength is characterized by fit parameters that
seem to show convergence for larger values of the magnetic Reynolds number.Comment: 14 pages, 8 figures, submitted to special issue "Advances of European
Solar Physics" in Solar Physic
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
Simulations of galactic dynamos
We review our current understanding of galactic dynamo theory, paying
particular attention to numerical simulations both of the mean-field equations
and the original three-dimensional equations relevant to describing the
magnetic field evolution for a turbulent flow. We emphasize the theoretical
difficulties in explaining non-axisymmetric magnetic fields in galaxies and
discuss the observational basis for such results in terms of rotation measure
analysis. Next, we discuss nonlinear theory, the role of magnetic helicity
conservation and magnetic helicity fluxes. This leads to the possibility that
galactic magnetic fields may be bi-helical, with opposite signs of helicity and
large and small length scales. We discuss their observational signatures and
close by discussing the possibilities of explaining the origin of primordial
magnetic fields.Comment: 28 pages, 15 figure, to appear in Lecture Notes in Physics "Magnetic
fields in diffuse media", Eds. E. de Gouveia Dal Pino and A. Lazaria
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