Berechnung der mittleren Lorentz-Feldstärke  für ein elektrisch leitendes Medium in turbulenter, durch Coriolis-Kräfte beeinflußter Bewegung

Steenbeck, M.; Krause, F.; Rädler, K.-H.

doi:10.1515/zna-1966-0401

Cited by 765 publications

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“…(26) reproduces the momentous result by Steenbeck, Krause & Rädler (1966). Due to the Coriolis force there is now (at least locally) a preference of either right-handed or left-handed helical patterns in the turbulent flow.…”

Section: A More Realistic Examplesupporting

confidence: 75%

“…The occurrence of the electromotive force αB is called "α effect". It has been first considered by Steenbeck, Krause & Rädler (1966) in a slightly different context (see Sect. 2.3).…”

Section: A Simple Examplementioning

confidence: 99%

“…The α effect allows dynamo action. The first paper on this topic has been published by Steenbeck, Krause, and Rädler in 1966 (unfortunately only in German language). Since then meanfield electrodynamics and, more general, mean-field magnetohydrodynamics have been elaborated in great detail and dynamo models have been proposed for the Sun, planets, several types of stars and for galaxies.…”

Section: Introductionmentioning

confidence: 99%

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Mean‐field dynamos: The old concept and some recent developments

Rädler

2014

Astron Nachr

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This article elucidates the basic ideas of electrodynamics and magnetohydrodynamics of mean fields in turbulently moving conducting fluids. It is stressed that the connection of the mean electromotive force with the mean magnetic field and its first spatial derivatives is in general neither local nor instantaneous and that quite a few claims concerning pretended failures of the mean-field concept result from ignoring this aspect. In addition to the mean-field dynamo mechanisms of α 2 and αΩ type several others are considered. Much progress in mean-field electrodynamics and magnetohydrodynamics results from the test-field method for calculating the coefficients that determine the connection of the mean electromotive force with the mean magnetic field. As an important example the memory effect in homogeneous isotropic turbulence is explained. In magnetohydrodynamic turbulence there is the possibility of a mean electromotive force that is primarily independent of the mean magnetic field and labeled as Yoshizawa effect. Despite of many efforts there is so far no convincing comprehensive theory of α quenching, that is, the reduction of the α effect with growing mean magnetic field, and of the saturation of mean-field dynamos. Steps toward such a theory are explained. Finally, some remarks on laboratory experiments with dynamos are made.

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Section: A More Realistic Examplesupporting

confidence: 75%

“…The occurrence of the electromotive force αB is called "α effect". It has been first considered by Steenbeck, Krause & Rädler (1966) in a slightly different context (see Sect. 2.3).…”

Section: A Simple Examplementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Mean‐field dynamos: The old concept and some recent developments

Rädler

2014

Astron Nachr

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“…With the development of mean-field theory (Parker 1955;Steenbeck et al 1966), this complicated threedimensional process became amenable to simpler analytic and numerical treatments in one and two dimensions.…”

Section: Introductionmentioning

confidence: 99%

Analytic solution of an oscillatory migratoryα²stellar dynamo

Brandenburg

2017

A&A

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Context. Analytic solutions of the mean-field induction equation predict a nonoscillatory dynamo for homogeneous helical turbulence or constant α effect in unbounded or periodic domains. Oscillatory dynamos are generally thought impossible for constant α. Aims. We present an analytic solution for a one-dimensional bounded domain resulting in oscillatory solutions for constant α, but different (Dirichlet and von Neumann or perfect conductor and vacuum) boundary conditions on the two boundaries. Methods. We solve a second order complex equation and superimpose two independent solutions to obey both boundary conditions. Results. The solution has time-independent energy density. On one end where the function value vanishes, the second derivative is finite, which would not be correctly reproduced with sine-like expansion functions where a node coincides with an inflection point. The field always migrates away from the perfect conductor boundary toward the vacuum boundary, independently of the sign of α. Conclusions. The obtained solution may serve as a benchmark for numerical dynamo experiments and as a pedagogical illustration that oscillatory migratory dynamos are possible with constant α.

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“…Nevertheless, subsequent progress in modeling the solar dynamo appears to have been suspended until the foundations of a mean-field treatment of the induction equation were developed by Steenbeck et al, (1966). In the following years, a large number of models were computed covering mostly aspects of the solar dynamo (Steenbeck & Krause, 1969a;Parker, 1970a;Parker, 1970b;Parker, 1970c;Parker, 1971b;Parker, 1971d; Simulations of astrophysical dynamos 403 1971f), but in some cases also terrestrial dynamos (Steenbeck & Krause, 1969b;Parker, 1971c) and the galactic dynamo (Parker, 1971a;Parker, 1971e;Vainshtein & Ruzmaikin, 1971;Vainshtein & Ruzmaikin, 1972).…”

Section: Introductionmentioning

confidence: 99%

Simulations of astrophysical dynamos

Brandenburg

2010

Proc. IAU

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Abstract. Numerical aspects of dynamos in periodic domains are discussed. Modifications of the solutions by numerically motivated alterations of the equations are being reviewed using the examples of magnetic hyperdiffusion and artificial diffusion when advancing the magnetic field in its Euler potential representation. The importance of using integral kernel formulations in mean-field dynamo theory is emphasized in cases where the dynamo growth rate becomes comparable with the inverse turnover time. Finally, the significance of microscopic magnetic Prandtl number in controlling the conversion from kinetic to magnetic energy is highlighted.

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Berechnung der mittleren Lorentz-Feldstärke für ein elektrisch leitendes Medium in turbulenter, durch Coriolis-Kräfte beeinflußter Bewegung

Cited by 765 publications

References 0 publications

Mean‐field dynamos: The old concept and some recent developments

Mean‐field dynamos: The old concept and some recent developments

Analytic solution of an oscillatory migratoryα²stellar dynamo

Simulations of astrophysical dynamos

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Berechnung der mittleren Lorentz-Feldstärke für ein elektrisch leitendes Medium in turbulenter, durch Coriolis-Kräfte beeinflußter Bewegung

Cited by 765 publications

References 0 publications

Mean‐field dynamos: The old concept and some recent developments

Mean‐field dynamos: The old concept and some recent developments

Analytic solution of an oscillatory migratoryα2stellar dynamo

Simulations of astrophysical dynamos

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Analytic solution of an oscillatory migratoryα²stellar dynamo