Lagrangian approach to the mean-field electrodynamics for turbulent fluids with arbitrary conductivities

1989 ◽  
Vol 208 ◽  
pp. 115-126 ◽  
Author(s):  
L. L. Kichatinov
Keyword(s):  
Turbulent Flow ◽  
Mean Field ◽  
Reynolds Numbers ◽  
Convective Transport ◽  
Lagrangian Approach ◽  
Compressible Turbulence ◽  
Magnetic Diffusivity ◽  
Alpha Effect ◽  
The Mean ◽  
Turbulent Fluids

A modification is made to the traditional Lagrangian approach to the derivation of the mean EMF of turbulent fluids which allows for finite conductivities. Consideration is confined to the case of homogeneous, isotropic but generally mirrornon-invariant and compressible turbulence. The eddy magnetic diffusivity and the coefficient α of the alpha-effect are expressed in terms of statistical moments of displacements of adjacent particles which undergo convective transport and microscopic diffusion in a turbulent flow. These expressions, being valid for arbitrary conductivities, reproduce known results in the cases of both very large and very small magnetic Reynolds numbers. Difficulties and advantages of the use of the results obtained for evaluations of the mean EMF are discussed.

scholarly journals Electrodynamics of turbulent fluids with fluctuating electric conductivity

2020 ◽  
Vol 86 (3) ◽  
Author(s):  
G. Rüdiger ◽  
M. Küker ◽  
P. J. Käpylä
Keyword(s):  
Magnetic Field ◽  
Large Scale ◽  
Mean Field ◽  
Outer Core ◽  
Cycle Times ◽  
Solar Convection ◽  
Magnetic Diffusivity ◽  
Large Scale Magnetic Field ◽  
Alpha Effect ◽  
Turbulent Fluids

Consequences of fluctuating microscopic conductivity in mean-field electrodynamics of turbulent fluids are formulated and discussed. If the conductivity fluctuations are assumed to be uncorrelated with the velocity fluctuations then only the turbulence-originated magnetic diffusivity of the fluid is reduced and the decay time of a large-scale magnetic field or the cycle times of oscillating turbulent dynamo models are increased. If, however, the fluctuations of conductivity and flow in a certain well-defined direction are correlated, an additional diamagnetic pumping effect results, transporting the magnetic field in the opposite direction to the diffusivity flux vector $\langle \unicode[STIX]{x1D702}^{\prime }\boldsymbol{u}^{\prime }\rangle$ . In the presence of global rotation, even for homogeneous turbulence fields, an alpha effect appears. If the characteristic values of the outer core of the Earth or the solar convection zone are applied, the dynamo number of the new alpha effect does not reach supercritical values to operate as an $\unicode[STIX]{x1D6FC}^{2}$ -dynamo but oscillating $\unicode[STIX]{x1D6FC}\unicode[STIX]{x1D6FA}$ -dynamos with differential rotation are not excluded.

scholarly journals Filaments and the Solar Dynamo

1998 ◽  
Vol 167 ◽  
pp. 406-414
Author(s):  
N. Seehafer
Keyword(s):  
Mean Field ◽  
Decisive Role ◽  
Dynamo Theory ◽  
Simultaneous Generation ◽  
Alpha Effect ◽  
Generation Region ◽  
The Mean ◽  
Numerical Bifurcation ◽  
Dynamo Effect

AbstractFilaments are a global phenomenon and their formation, structure and dynamics are determined by magnetic fields. So they are an important signature of the solar magnetism. The central mechanism in traditional mean-field dynamo theory is the alpha effect and it is a major result of this theory that the presence of kinetic or magnetic helicities is at least favourable for the effect. Recent studies of the magnetohydrodynamic equations by means of numerical bifurcation-analysis techniques have confirmed the decisive role of helicity for a dynamo effect. The alpha effect corresponds to the simultaneous generation of magnetic helicities in the mean field and in the fluctuations, the generation rates being equal in magnitude and opposite in sign. In the case of statistically stationary and homogeneous fluctuations, in particular, the alpha effect can increase the energy in the mean magnetic field only under the condition that also magnetic helicity is accumulated there. Generally, the two helicities generated by the alpha effect, that in the mean field and that in the fluctuations, have either to be dissipated in the generation region or to be transported out of this region. The latter may lead to the appearance of helicity in the atmosphere, in particular in filaments, and thus provide valuable information on dynamo processes inaccessible to in situ measurements.

The diffusion behind a line source in homogeneous turbulence

1954 ◽  
Vol 224 (1159) ◽  
pp. 487-512 ◽  
Keyword(s):  
Turbulent Flow ◽  
Decay Time ◽  
Molecular Diffusion ◽  
Initial Period ◽  
Reynolds Numbers ◽  
Particle Diffusion ◽  
Velocity Correlation ◽  
Rate Of Spread ◽  
Heated Wire ◽  
The Mean

The theory of turbulent diffusion by continuous movements relates the mean particle diffusion from a fixed source to the Lagrangian velocity correlation function, and measure­ments of the diffusion of heat behind a thin heated wire in a uniform turbulent flow have been used to compute this correlation, assuming that the processes of diffusion by con­tinuous movements and molecular conduction are statistically independent. A series of measurements both of the mean temperatures and the temperature fluctuations in the wake of a thin heated wire has been made in the uniform turbulent flow behind bi-plane grids, for grid Reynolds numbers between 2700 and 21000 and within the initial period of decay of the turbulence. In these measurements, the rate of spread of the heat wake was determined in two ways, directly from measurements of the turbulent transport of heat and by numerical differentiation of widths computed from observations of mean temperature. The extent of the accelerated diffusion of heat, which is caused by intensification of the temperature gradients by the turbulent motion, can be computed from the measurements of lateral temperature correlations in the flow, and was found to be comparable with the total diffusion. Both the total diffusion process and the process of accelerated molecular dif­fusion are very nearly self-preserving during decay in the initial period, with a time scale that varies as the decay time and a velocity scale varying inversely as the square root of the decay time, which is consistent with the observed self-preservation of Eulerian correlations. The rate of spread of the heat wake is simply related to the particle diffusion only for short diffusion times at ordinary Reynolds numbers, and the mean-square particle accelera­tion can be computed. The results are significantly larger than those found by other workers who have neglected the additional spread of the wake by accelerated molecular diffusion.

Diffusion of passive-scalar and magnetic fields by helical turbulence

1976 ◽  
Vol 77 (4) ◽  
pp. 753-768 ◽  
Author(s):  
Robert H. Kraichnan
Keyword(s):  
Magnetic Field ◽  
Rapid Development ◽  
Passive Scalar ◽  
Time Correlation ◽  
Response Functions ◽  
Helical Turbulence ◽  
Magnetic Diffusivity ◽  
Alpha Effect ◽  
The Mean ◽  
The Difference

Computer simulations of fluid-element trajectories in mirror-symmetric and maximally helical turbulence are used to evaluate Moffatt's (1974) formulae for the magnetic diffusivity η(t) and the coefficient κ(t) of the alpha-effect. The passive-scalar diffusivity κ(t) and the mean response functions of scalar and magnetic field wave-vector modes are also computed. The velocity field is normal, stationary, homogeneous and isotropic with spectrum $E(k) = \frac{3}{2}v^2_0\delta(k - k_0)$ and time correlation exp [−1/2ω2/0(t-t)2]. The cases ω0 = O (frozen turbulence), ω = vo k0 and ω0 = 2v0 k0 are followed to t = 4/v0 k0. In the ω0 > 0 cases with maximal helicity, κ(t) and a(t) approach steady-state values of order vo/k0 and v0, respectively. They behave anomalously for ω0 = 0. In the mirror-symmetric: cases, q(t) and κ(t) differ very little from each other. At all the ω0 values, is bigger in the helical than in the mirror-symmetric case. The difference is marked for ω0 = 0. The simulation results imply that κ(t) becomes negative in non-normal mirror-symmetric turbulence with strong helicity fluctuations that persist over several correlation lengths and times. The computations of response functions indicate that asymptotic expressions for these functions, valid for k [Lt ]; k0, retain good accuracy for k ∼ k0. The mean-square magnetic field is found to grow exponentially, and its kurtosis also grows apidly with t, indicating rapid development of a highly intermittent distribution of magnetic field.

scholarly journals The nature of mean-field generation in three classes of optimal dynamos

2020 ◽  
Vol 86 (1) ◽  
Author(s):  
Axel Brandenburg ◽  
Long Chen
Keyword(s):  
Magnetic Field ◽  
Growth Rate ◽  
Boundary Conditions ◽  
Magnetic Energy ◽  
Mean Field ◽  
Dynamo Action ◽  
Magnetic Diffusivity ◽  
The Mean ◽  
The Magnetic Field ◽  
Mean Field Dynamo

In recent years, several optimal dynamos have been discovered. They minimize the magnetic energy dissipation or, equivalently, maximize the growth rate at a fixed magnetic Reynolds number. In the optimal dynamo of Willis (Phys. Rev. Lett., vol. 109, 2012, 251101), we find mean-field dynamo action for planar averages. One component of the magnetic field grows exponentially while the other decays in an oscillatory fashion near onset. This behaviour is different from that of an $\unicode[STIX]{x1D6FC}^{2}$ dynamo, where the two non-vanishing components of the planar averages are coupled and have the same growth rate. For the Willis dynamo, we find that the mean field is excited by a negative turbulent magnetic diffusivity, which has a non-uniform spatial profile near onset. The temporal oscillations in the decaying component are caused by the corresponding component of the diffusivity tensor being complex when the mean field is decaying and, in this way, time dependent. The growing mean field can be modelled by a negative magnetic diffusivity combined with a positive magnetic hyperdiffusivity. In two other classes of optimal dynamos of Chen et al. (J. Fluid Mech., vol. 783, 2015, pp. 23–45), we find, to some extent, similar mean-field dynamo actions. When the magnetic boundary conditions are mixed, the two components of the planar averaged field grow at different rates when the dynamo is 15 % supercritical. When the mean magnetic field satisfies homogeneous boundary conditions (where the magnetic field is tangential to the boundary), mean-field dynamo action is found for one-dimensional averages, but not for planar averages. Despite having different spatial profiles, both dynamos show negative turbulent magnetic diffusivities. Our finding suggests that negative turbulent magnetic diffusivities may support a broader class of dynamos than previously thought, including these three optimal dynamos.

scholarly journals A galaxy dynamo by Supernova-driven interstellar turbulence

2008 ◽  
Vol 4 (S259) ◽  
pp. 81-86 ◽  
Author(s):  
Oliver Gressel ◽  
Udo Ziegler ◽  
Detlef Elstner ◽  
Günther Rüdiger
Keyword(s):  
Magnetic Field ◽  
Mean Field ◽  
Reynolds Numbers ◽  
Disk Galaxies ◽  
Dynamo Action ◽  
Quasilinear Theory ◽  
Interstellar Turbulence ◽  
Field Amplification ◽  
Interstellar Plasma ◽  
The Mean

AbstractSupernovae are the dominant energy source for driving turbulence within the interstellar plasma. Until recently, their effects on magnetic field amplification in disk galaxies remained a matter of speculation. By means of self-consistent simulations of supernova-driven turbulence, we find an exponential amplification of the mean magnetic field on timescales of a few hundred million years. The robustness of the observed fast dynamo is checked at different magnetic Reynolds numbers, and we find sustained dynamo action at moderate Rm. This indicates that the mechanism might indeed be of relevance for the real ISM.Sensing the flow via passive tracer fields, we infer that SNe produce a turbulent α effect which is consistent with the predictions of quasilinear theory. To lay a foundation for global mean-field models, we aim to explore the scaling of the dynamo tensors with respect to the key parameters of our simulations. Here we give a first account on the variation with the supernova rate.

scholarly journals Lagrangian approach to the semirelativistic electron dynamics in the mean-field approximation

2013 ◽  
Vol 88 (3) ◽  
Author(s):  
Anant Dixit ◽  
Yannick Hinschberger ◽  
Jens Zamanian ◽  
Giovanni Manfredi ◽  
Paul-Antoine Hervieux
Keyword(s):  
Mean Field ◽  
Field Approximation ◽  
Lagrangian Approach ◽  
Mean Field Approximation ◽  
Electron Dynamics ◽  
The Mean

scholarly journals The Alpha-Effect in Galaxies is Highly Anisotropic

1990 ◽  
Vol 140 ◽  
pp. 113-114
Author(s):  
G. Rüdiger
Keyword(s):  
Large Scale ◽  
Rotation Axis ◽  
Mean Field ◽  
Dynamo Model ◽  
Mean Flow ◽  
Dynamo Theory ◽  
Input Quantity ◽  
Alpha Effect ◽  
The Mean ◽  
Mean Field Dynamo

Besides the mean flow the alpha is the other input quantity for any mean-field dynamo model. It describes the generation of turbulent electromotive force <u × B> from a large-scale field <B> for a given turbulence. The necessary helicity of the turbulence results from the joint action of Coriolis force and density stratification. The standard estimate of 1 km/s for alpha in galaxies is a surely well-established approximation. One of the essentials, however, remains open. Due to the extremely anisotropic structure of disks the tensorial character of alpha can no longer be ignored. In stellar applications anisotropy in the α-tensor leads to a preferred excitation of non-axisymmetric magnetic fields. That is true for α2 -dynamos if the alpha parallel to the rotation axis, α||, is much smaller than that in the equatorial plane, α⊥. The idea is that also for disk-like configurations a similar behaviour makes the existence of the observed large-scale non-axisymmetric magnetic BSS modes understandable within the frame of the mean-field dynamo theory.

Alternate Scales for Turbulent Flow in Transitional Rough Pipes: Universal Log Laws

2006 ◽  
Vol 129 (1) ◽  
pp. 80-90 ◽  
Author(s):  
Noor Afzal ◽  
Abu Seena
Keyword(s):  
Reynolds Number ◽  
Velocity Profile ◽  
Turbulent Flow ◽  
Friction Factor ◽  
Friction Velocity ◽  
Strong Support ◽  
Reynolds Numbers ◽  
Momentum Theory ◽  
The Mean ◽  
Pipe Roughness

In transitional rough pipes, the present work deals with alternate four new scales, the inner wall transitional roughness variable ζ=Z+∕ϕ, associated with a particular roughness level, defined by roughness scale ϕ connected with roughness function ▵U+, the roughness friction Reynolds number Rϕ (based on roughness friction velocity), and roughness Reynolds number Reϕ (based on roughness average velocity) where the mean turbulent flow, little above the roughness sublayer, does not depend on pipes transitional roughness. In these alternate variables, a two layer mean momentum theory is analyzed by the method of matched asymptotic expansions for large Reynolds numbers. The matching of the velocity profile and friction factor by Izakson-Millikan-Kolmogorov hypothesis gives universal log laws that are explicitly independent of pipe roughness. The data of the velocity profile and friction factor on transitional rough pipes provide strong support to universal log laws, having the same constants as for smooth walls. There is no universality of scalings in traditional variables and different expressions are needed for various types of roughness, as suggested, for example, with inflectional-type roughness, monotonic Colebrook-Moody roughness, etc. In traditional variables, the roughness scale, velocity profile, and friction factor prediction for inflectional pipes roughness are supported very well by experimental data.

scholarly journals Turbulent diffusion and galactic magnetism

2009 ◽  
Vol 5 (H15) ◽  
pp. 432-433 ◽  
Author(s):  
Axel Brandenburg ◽  
Fabio Del Sordo
Keyword(s):  
Turbulent Diffusion ◽  
Mean Field ◽  
Reynolds Numbers ◽  
Field Method ◽  
Test Field ◽  
Expansion Waves ◽  
Magnetic Diffusivity ◽  
Spherical Expansion ◽  
Mean Field Dynamo

AbstractUsing the test-field method for nearly irrotational turbulence driven by spherical expansion waves it is shown that the turbulent magnetic diffusivity increases with magnetic Reynolds numbers. Its value levels off at several times the rms velocity of the turbulence multiplied by the typical radius of the expansion waves. This result is discussed in the context of the galactic mean-field dynamo.

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