Kinematic dynamo in random flow

Molchanov, Stanislav; Ruzmaikin, A.; Соколов, Д. Д.

doi:10.1070/pu1985v028n04abeh003869

Cited by 88 publications

(39 citation statements)

References 34 publications

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“…The particular case of delta-correlated flows has attracted quite some attention in dynamo theory (Moffatt 1978;Krause & Rädler 1980;Molchanov et al 1985), as it allows calculations of alpha and beta tensors. In that case, the correlation time scale can no longer be used to non-dimensionalise the induction equation (T = 0) and the infinite root mean square (r.m.s.)…”

Section: Delta-correlated Flowsmentioning

confidence: 99%

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Stokes drift dynamos

Herreman

Lesaffre²

2011

J. Fluid Mech.

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Fluid particles can have a mean motion in time, even when the Eulerian mean flow disappears everywhere in space. In the present article, we demonstrate that this phenomenon, known as the Stokes drift, plays an essential role in the problem of magnetic field generation by fluctuation flows (kinematic dynamo) at high Rm. At leading order, the dynamo is generated by the Stokes drift that acts as if it were a mean flow. This result is derived from a mean-field dynamo theory in terms of time averages, which reveals how classical expressions for alpha and beta tensors actually recombine into a single Stokes drift contribution. In a test case, we find fluctuation flows that have a G. O. Roberts flow as Stokes drift and this allows to confront our model to direct integration of the induction equation. We find an excellent quantitative agreement between the prediction of our model and the results of our simulations. We finally apply our Stokes drift model to prove that a broad class of inertial waves in rapidly rotating flows cannot drive a dynamo.

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Section: Delta-correlated Flowsmentioning

confidence: 99%

“…If we now have some initial magnetic field b 0 (a), the Cauchy solution gives the magnetic field at any time (see, for example, Molchanov, Ruzmaikin & Sokolov (1985)) in terms of the trajectories only b L (a, t) = b 0 (a) · ∇ a x(a, t).…”

Section: Stokes Drift and Frozen Flux Limitmentioning

confidence: 99%

Stokes drift dynamos

Herreman

Lesaffre²

2011

J. Fluid Mech.

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“…Other significant categories may be distinguished. Molchanov et al (1985) have introduced the idea of an "intermediate" dynamo. This is fast but, as R increases, the mode to which (3.6) applies changes.…”

Section: Dynamo Typ Esmentioning

confidence: 99%

Dynamo Theory

Roberts¹,

Soward²

1992

Annu. Rev. Fluid Mech.

226

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“…They could be generated by dynamo amplification of weak seed fields. A particularly generic dynamo is the fluctuation or small-scale dynamo (Kazantsev 1967;Molchanov et al 1985;Zeldovich et al 1990; Kulsrud & Anderson 1992;Subramanian 1997Subramanian , 1999Rogachevskii & Kleeorin 1997;Brandenburg & Subramanian 2005;Cho et al 2009;Federrath et al 2011;Tobias et al 2011;Sur et al 2012;Brandenburg et al 2012;Bhat & Subramanian 2013). Here, turbulence in a conducting plasma, with even a modest magnetic Reynolds number (R M > R crit ∼ 30-500), leads to the amplification of magnetic fields on the fast eddy turnover timescale, usually much smaller than the age of the astrophysical system (Haugen et al 2004;Schekochihin et al 2004Schekochihin et al , 2005Malyshkin & Boldyrev 2010;Schober et al 2012).…”

Section: Introductionmentioning

confidence: 99%

Fluctuation Dynamo at Finite Correlation Times and the Kazantsev Spectrum

Bhat¹,

Subramanian²

2014

ApJ

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Fluctuation dynamos are generic to astrophysical systems. The only analytical model of the fluctuation dynamo is the Kazantsev model which assumes a velocity field that is delta-correlated in time. We derive a generalized model of fluctuation dynamos with finite correlation time, τ , using renovating flows. For τ → 0, we recover the standard Kazantsev equation for the evolution of longitudinal magnetic correlation, M L . To the next order in τ , the generalized equation involves third and fourth spatial derivatives of M L . It can be recast to one with at most second derivatives of M L using the Landau-Lifschitz approach. Remarkably, we then find that the magnetic power spectrum remains the Kazantsev spectrum of M(k) ∝ k 3/2 , in the large k limit, independent of τ .

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Kinematic dynamo in random flow

Cited by 88 publications

References 34 publications

Stokes drift dynamos

Stokes drift dynamos

Dynamo Theory

Fluctuation Dynamo at Finite Correlation Times and the Kazantsev Spectrum

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