Turbulent viscosity, magnetic diffusivity, and heat conductivity under the influence of rotation and magnetic field

1994 ◽  
Vol 315 (2) ◽  
pp. 157-170 ◽  
Author(s):  
L. L. Kitchatinov ◽  
V. V. Pipin ◽  
G. Rüdiger
Keyword(s):  
Magnetic Field ◽  
Heat Conductivity ◽  
Turbulent Viscosity ◽  
Magnetic Diffusivity

scholarly journals Advection/diffusion of large scale magnetic field in accretion disks

2009 ◽  
Vol 16 (1) ◽  
pp. 77-81 ◽  
Author(s):  
R. V. E. Lovelace ◽  
G. S. Bisnovatyi-Kogan ◽  
D. M. Rothstein
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Turbulent Viscosity ◽  
Pressure Ratio ◽  
Rotational Instability ◽  
Small Scale ◽  
Magnetic Diffusivity ◽  
Large Scale Magnetic Field ◽  
Scale Field ◽  
Large Scale Field

Abstract. Activity of the nuclei of galaxies and stellar mass systems involving disk accretion to black holes is thought to be due to (1) a small-scale turbulent magnetic field in the disk (due to the magneto-rotational instability or MRI) which gives a large viscosity enhancing accretion, and (2) a large-scale magnetic field which gives rise to matter outflows and/or electromagnetic jets from the disk which also enhances accretion. An important problem with this picture is that the enhanced viscosity is accompanied by an enhanced magnetic diffusivity which acts to prevent the build up of a significant large-scale field. Recent work has pointed out that the disk's surface layers are non-turbulent and thus highly conducting (or non-diffusive) because the MRI is suppressed high in the disk where the magnetic and radiation pressures are larger than the thermal pressure. Here, we calculate the vertical (z) profiles of the stationary accretion flows (with radial and azimuthal components), and the profiles of the large-scale, magnetic field taking into account the turbulent viscosity and diffusivity due to the MRI and the fact that the turbulence vanishes at the surface of the disk. We derive a sixth-order differential equation for the radial flow velocity vr(z) which depends mainly on the midplane thermal to magnetic pressure ratio β>1 and the Prandtl number of the turbulence P=viscosity/diffusivity. Boundary conditions at the disk surface take into account a possible magnetic wind or jet and allow for a surface current in the highly conducting surface layer. The stationary solutions we find indicate that a weak (β>1) large-scale field does not diffuse away as suggested by earlier work.

Turbulent dynamo action at low magnetic Reynolds number

1970 ◽  
Vol 41 (2) ◽  
pp. 435-452 ◽  
Author(s):  
H. K. Moffatt
Keyword(s):  
Magnetic Field ◽  
Reynolds Number ◽  
Large Scale ◽  
Isotropic Turbulence ◽  
Magnetic Energy ◽  
Magnetic Reynolds Number ◽  
Dynamo Action ◽  
Ohmic Dissipation ◽  
Magnetic Energy Density ◽  
Magnetic Diffusivity

The effect of turbulence on a magnetic field whose length-scale L is initially large compared with the scale l of the turbulence is considered. There are no external sources for the field, and in the absence of turbulence it decays by ohmic dissipation. It is assumed that the magnetic Reynolds number Rm = u0l/λ (where u0 is the root-mean-square velocity and λ the magnetic diffusivity) is small. It is shown that to lowest order in the small quantities l/L and Rm, isotropic turbulence has no effect on the large-scale field; but that turbulence that lacks reflexional symmetry is capable of amplifying Fourier components of the field on length scales of order Rm−2l and greater. In the case of turbulence whose statistical properties are invariant under rotation of the axes of reference, but not under reflexions in a point, it is shown that the magnetic energy density of a magnetic field which is initially a homogeneous random function of position with a particularly simple spectrum ultimately increases as t−½exp (α2t/2λ3) where α(= O(u02l)) is a certain linear functional of the spectrum tensor of the turbulence. An analogous result is obtained for an initially localized field.

scholarly journals Turbulent viscosity and magnetic Prandtl number from simulations of isotropically forced turbulence

2020 ◽  
Vol 636 ◽  
pp. A93 ◽  
Author(s):  
P. J. Käpylä ◽  
M. Rheinhardt ◽  
A. Brandenburg ◽  
M. J. Käpylä
Keyword(s):  
Magnetic Fields ◽  
Prandtl Number ◽  
Large Scale ◽  
Turbulent Viscosity ◽  
Scale Dependence ◽  
Scale Separation ◽  
Separation Ratio ◽  
Magnetic Prandtl Number ◽  
Magnetic Diffusivity ◽  
Forced Turbulence

Context. Turbulent diffusion of large-scale flows and magnetic fields plays a major role in many astrophysical systems, such as stellar convection zones and accretion discs. Aims. Our goal is to compute turbulent viscosity and magnetic diffusivity which are relevant for diffusing large-scale flows and magnetic fields, respectively. We also aim to compute their ratio, which is the turbulent magnetic Prandtl number, Pmt, for isotropically forced homogeneous turbulence. Methods. We used simulations of forced turbulence in fully periodic cubes composed of isothermal gas with an imposed large-scale sinusoidal shear flow. Turbulent viscosity was computed either from the resulting Reynolds stress or from the decay rate of the large-scale flow. Turbulent magnetic diffusivity was computed using the test-field method for a microphysical magnetic Prandtl number of unity. The scale dependence of the coefficients was studied by varying the wavenumber of the imposed sinusoidal shear and test fields. Results. We find that turbulent viscosity and magnetic diffusivity are in general of the same order of magnitude. Furthermore, the turbulent viscosity depends on the fluid Reynolds number (Re) and scale separation ratio of turbulence. The scale dependence of the turbulent viscosity is found to be well approximated by a Lorentzian. These results are similar to those obtained earlier for the turbulent magnetic diffusivity. The results for the turbulent transport coefficients appear to converge at sufficiently high values of Re and the scale separation ratio. However, a weak trend is found even at the largest values of Re, suggesting that the turbulence is not in the fully developed regime. The turbulent magnetic Prandtl number converges to a value that is slightly below unity for large Re. For small Re we find values between 0.5 and 0.6 but the data are insufficient to draw conclusions regarding asymptotics. We demonstrate that our results are independent of the correlation time of the forcing function. Conclusions. The turbulent magnetic diffusivity is, in general, consistently higher than the turbulent viscosity, which is in qualitative agreement with analytic theories. However, the actual value of Pmt found from the simulations (≈0.9−0.95) at large Re and large scale separation ratio is higher than any of the analytic predictions (0.4−0.8).

Kinetic Theory for Mixtures of Dilute Gases of Linear Rotating Molecules II. The Senftleben-Beenakker Effect of the Heat Conductivity

1972 ◽  
Vol 27 (10) ◽  
pp. 1383-1393 ◽  
Author(s):  
W. E. Köhler ◽  
H. H. Raum
Keyword(s):  
Magnetic Field ◽  
Cross Sections ◽  
Heat Conductivity ◽  
Noble Gas ◽  
Homogeneous Magnetic Field ◽  
Starting Point ◽  
Order Of Magnitude ◽  
Molecular Distribution Function ◽  
Transport Relaxation ◽  
Kinetic Treatment

Abstract The system of transport relaxation equations obtained from the linearized Waldmann-Snider equation is the starting point for the kinetic treatment of the heat conductivity for mixtures of linear diamagnetic molecules in an external homogeneous magnetic field. The connection of the occurring collision integrals with certain molecular cross sections is discussed and order of magnitude considerations are made for molecules with small nonsphericity of their interaction. With the Kagan polarization as the decisive rotational angular momentum anisotropy term in the molecular distribution function, an expression for the heat conductivity ini the presence of a magnetic field is derived for mixtures with an arbitrary number of components. The mole fraction dependence of the saturation values is studied for binary mixtures of rotating molecules and noble gas atoms for a simplified model. As an example, the system o-D2/He is considered.

scholarly journals Galactic Dynamics and Magnetic Field Amplification

1993 ◽  
Vol 157 ◽  
pp. 395-401 ◽  
Author(s):  
Harald Lesch
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Magnetic Fields ◽  
Time Scale ◽  
Numerical Models ◽  
Momentum Transport ◽  
Angular Momentum Transport ◽  
Field Amplification ◽  
Gravitational Instabilities ◽  
Magnetic Diffusivity

Stimulated by recent high frequency radio polarization measurements of M83 and M51, we consider the influence of non-axisymmetric features (bars, spiral arms, etc…) on galactic magnetic fields. The time scale for the field amplification due to the non-axisymmetric velocity field is related to the time scale of angular momentum transport in the disk by the non-axisymmetric features. Due to its dissipational character (cooling and angular momentum transport) the gas plays a major role for the excitation of non-axisymmetric instabilities. Since it is the gaseous component of the interstellar gas in which magnetic field amplification takes place we consider the interplay of gasdynamical processes triggered by gravitational instabilities and magnetic fields. A comparison with the time scale for dynamo action in a disk from numerical models for disk dynamos gives the result that field amplification by non-axisymmetric features is faster in galaxies like M83 (strong bar) and M51 (compagnion and very distinct spiral structure), than amplification by an axisymmetric dynamo. Furthermore, we propose that axisymmetric gravitational instabilities may provide the turbulent magnetic diffusivity ηT. Based on standard galaxy models we obtain a radially dependent diffusivity whose numerical value rises from 1025cm2s−1 to 1027cm2s−1, declining for large radii.

scholarly journals Optimization of surface flux transport models for the solar polar magnetic field

2019 ◽  
Vol 632 ◽  
pp. A87 ◽  
Author(s):  
K. Petrovay ◽  
M. Talafha
Keyword(s):  
Magnetic Field ◽  
Solar Cycle ◽  
Parameter Space ◽  
Large Scale ◽  
Surface Flux ◽  
Supporting Evidence ◽  
Flux Transport ◽  
Polar Magnetic Field ◽  
Flow Profiles ◽  
Magnetic Diffusivity

Context. The choice of free parameters in surface flux transport (SFT) models describing the evolution of the large-scale poloidal magnetic field of the Sun is critical for the correct reproduction of the polar magnetic flux built up during a solar cycle, which is known to be a good predictor of the amplitude of the upcoming cycle. Aims. For an informed choice of parameters it is important to understand the effects of and interplay among the various parameters and to optimize the models for the polar magnetic field. Methods. Here we present the results of a large-scale systematic study of the parameter space in an SFT model where the source term representing the net effect of tilted flux emergence was chosen to represent a typical, average solar cycle as described by observations. Results. Comparing the results with observational constraints on the spatiotemporal variation of the polar magnetic field, as seen in magnetograms for the last four solar cycles, we mark allowed and excluded regions in the 3D parameter space defined by the flow amplitude u0, the magnetic diffusivity η and the decay time scale τ, for three different assumed meridional flow profiles. Conclusions. Without a significant decay term in the SFT equation (i.e., for τ >  10 yr) the global dipole moment reverses too late in the cycle for all flow profiles and parameters, providing independent supporting evidence for the need of a decay term, even in the case of identical cycles. An allowed domain is found to exist for τ values in the 5–10 yr range for all flow profiles considered. Generally higher values of η (500–800 km2 s−1) are preferred though some solutions with lower η are still allowed.

Electric and magnetic field effects on the heat conductivity of gaseous NF3

1970 ◽  
Vol 31 (6) ◽  
pp. 304-305 ◽  
Author(s):  
J.J. De Groot ◽  
L.J.F. Hermans ◽  
C.J. Van Den Meijdenberg ◽  
J.J.M. Beenakker
Keyword(s):  
Magnetic Field ◽  
Heat Conductivity ◽  
Magnetic Field Effects ◽  
Field Effects ◽  
Electric And Magnetic Field

Magneto-thermo-elastic plane waves

1965 ◽  
Vol 61 (4) ◽  
pp. 939-944 ◽  
Author(s):  
C. M. Purushothama
Keyword(s):  
Magnetic Field ◽  
Wave Propagation ◽  
Shear Wave ◽  
Wave Velocity ◽  
Compression Wave ◽  
Thermal Field ◽  
Plane Waves ◽  
Elastic Plane ◽  
Magnetic Diffusivity ◽  
The Magnetic Field

AbstractThe combined effects of uniform thermal and magnetic fields on the propagation of plane waves in a homogeneous, initially unstressed, electrically conducting elastic medium have been investigated.When the magnetic field is parallel to the direction of wave propagation, the compression wave is purely thermo-elastic and the shear wave is purely magneto-elastic in nature. For a transverse magnetic field, the shear waves remain elastic whereas the compression wave assumes magneto-thermo-elastic character due to the coupling of all the three fields—mechanical, magnetic and thermal. In the general case, the waves polarized in the plane of the direction of wave propagation and the magnetic field are not only coupled but are also influenced by the thermal field, once again exhibiting the coupling of the three fields. The shear wave polarized transverse to the plane retains its magneto-elastic character.Notation.Hi = primary magnetic field components,ht = induced magnetic field components,To = initial thermal field,θ = induced thermal field,C = compression wave velocity.S = shear wave velocity,ui = displacement components,cv = specific heat at constant volume,k = thermal conductivity,η = magnetic diffusivity,μe = magnetic permeability,λ, μ = Lamé's constants,β = ratio of coefficient of volume expansion to isothermal compressibility.

scholarly journals Magnetic Flux Transport in Protostellar Accretion Disks

1997 ◽  
Vol 163 ◽  
pp. 692-692
Author(s):  
John Contopoulos ◽  
Arieh Königl
Keyword(s):  
Magnetic Field ◽  
Angular Momentum ◽  
Accretion Disks ◽  
Large Scale ◽  
Turbulent Viscosity ◽  
Flux Transport ◽  
Disk Structure ◽  
Large Scale Magnetic Field ◽  
Field Lines ◽  
Open Magnetic Field

AbstractCentrifugally driven winds from the surfaces of magnetized accretion disks are a leading candidate for the origin of bipolar outflows and have also been recognized as an attractive mechanism for removing the angular momentum of the accreted matter. The origin of the open magnetic field lines that thread the disk in this scenario is, however, still uncertain. One possibility is that the field lines are transported through the disk, but previous studies have shown that this process is inefficient in disks with turbulent viscosity and diffusivity. Here we examine whether the efficiency can be increased if angular momentum is transported from the disk surfaces by large-scale magnetic fields instead of radially by viscous stresses. In this picture, the removal of angular momentum is associated with the establishment of a global poloidal electric current driven by the radial EMF in the disc, and it does not necessarily need to involve super-Alfvénic outflows. We address this problem in the context of protostellar systems and present representative solutions of the time evolution of a resistive disk that is initially threaded by a uniform vertical field anchored at a large distance from its surfaces. We assume that the angular momentum transport in the disk is controlled by the large-scale magnetic field and take into account the influence of the field on the disk structure.

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