Linear and non-linear dynamos associated with ABC flows

Galanti, Barak; Sulem, P. L.; Pouquet, A.

doi:10.1080/03091929208229056

Cited by 143 publications

(73 citation statements)

References 19 publications

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“…Eq. (1)] is negative, thus opposite in sign to the kinetic helicity, as also found by Galanti et al (1992).…”

Section: Bifurcation Analysis Of a Magnetofluid With Helical Forcingsupporting

confidence: 61%

Filaments and the Solar Dynamo

Seehafer

1998

International Astronomical Union Colloquium

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Abstract.Filaments 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.

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“…Eq. (1)] is negative, thus opposite in sign to the kinetic helicity, as also found by Galanti et al (1992).…”

Section: Bifurcation Analysis Of a Magnetofluid With Helical Forcingsupporting

confidence: 61%

Filaments and the Solar Dynamo

Seehafer

1998

International Astronomical Union Colloquium

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“…The hydrodynamic stability of the ABC flow has been studied by Podvigina & Pouquet (1994) who found that for values of fluid Reynolds number above a critical one (Re c = 13) the ABC flow destabilizes, first to time dependent but still smooth states, and then to a turbulent state. In our simulation, the definition of the Reynolds numbers is the same as in Galanti et al (1992).…”

Section: Flow Considerationsmentioning

confidence: 99%

Dynamo action in turbulent flows

Archontis

Dorch²,

Nordlund³

2003

A&A

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Abstract. We present results from numerical simulations of nonlinear MHD dynamo action produced by three-dimensional flows that become turbulent for high values of the fluid Reynolds number. The magnitude of the forcing function driving the flow is allowed to evolve with time in such way as to maintain an approximately constant velocity amplitude (and average kinetic energy) when the flow becomes hydrodynamically unstable. It is found that the saturation level of the dynamo increases with the fluid Reynolds number (at constant magnetic Prandtl number), and that the average growth rate approaches an asymptotic value for high fluid Reynolds number. The generation and destruction of magnetic field is examined during the laminar and turbulent phase of the flow and it is found that in the neighborhood of strong magnetic flux "cigars" Joule dissipation is balanced by the work done against the Lorentz force, while the steady increase of magnetic energy occurs mainly through work done in the weak part of the magnetic field.

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“…In kinematic dynamo studies using the ABC flow with A = B = C cigar-like concentrations of the magnetic field about velocity stagnation points were observed [15,17]. The ABC flow with A = B = C has eight stagnation points, which are unstable fixed points of the flow v. The corresponding eigenvalues are real and have signs (+, −, −) or (−, +, +).…”

Section: Branch Stability Intervalmentioning

confidence: 97%

“…in the NSE and applying periodic boundary conditions with period 2π in all three spatial directions, Galanti et al [15] investigated the system of the MHD equations [Eqs. (1)- (3)].…”

Section: Pure Abc Forcingmentioning

confidence: 99%