Dynamo action in flows with cat's eyes

Courvoisier, Alice; Gilbert, Andrew D.; Ponty, Yannick

doi:10.1080/03091920500334159

Cited by 10 publications

(5 citation statements)

References 26 publications

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“…This differs from the situation for flows where the cells have a cats-eye topology, where there appear to be distinct sets of branches that do not interact. 13 The flows we are considering have less symmetry than both these flows and the Roberts flow, and one would therefore not expect to find a sharp distinction between flows of largeand small-scale type since there are no symmetries to distinguish. Nonetheless, the smoothness of the transition was more marked than we were expecting.…”

Section: Discussionmentioning

confidence: 96%

From large-scale to small-scale dynamos in a spherical shell

2012

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Kinematic dynamo action in a spherical shell is studied with a small-scale cellular prescribed velocity field. Three velocity fields are considered, all of which are axisymmetric and have a large-scale separation between the shell size and the dominant scale of the motion. The first flow is steady and strongly helical, so that a mean field dynamo might be expected. We find that indeed large-scale dynamo action is obtained at onset, but that the dynamo is of small-scale type at large magnetic Reynolds number Rm, where advection processes dominate and the magnetic field is generated on the scale of the cells in the flow. We study the transition between these two dynamo processes and find a gradual transition as Rm is increased, where the energy is slowly passed from the large scales to the small scales as the two dynamo processes morph into one another. The second flow, a time-dependent version of the first, produces almost identical results, but the transition appears to occur at smaller Rm than in the steady case and there is some evidence of fast dynamo action as Rm becomes large. The third flow, a nonhelical variant of the first flow, is also studied, and small-scale dynamo action was found at onset in this case, with a much larger critical value of Rm for growth of the magnetic field.

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Section: Discussionmentioning

confidence: 96%

From large-scale to small-scale dynamos in a spherical shell

2012

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“…the flow properties are continuously changed from those of the circularly polarized to those of the cat's-eye flow. The structure of these flows has been thoroughly analyzed by Galloway (2012) and Courvoisier et al (2005), respectively, see also references therein. The computations of Tanner and Hughes (2003) show the flow structure as δ is varied.…”

Section: Model Flow and Lagrangian Passive Vector Equationsmentioning

confidence: 99%

“…Although a big concern of magnetohydrodynamics (MHD) is in the saturation mechanisms and the dynamic regime in which the magnetic field and the flow properties are tightly coupled, the kinematic approach is still used to understand how a flowfield promotes the dynamo effect (Kaplan et al 2012, McWilliams 2012, Bouya and Dormy 2013, Hughes and Proctor 2013. In the kinematic model, the flowfield is given-most often analytically-and used to derive the magnetic field from the induction equation; see for instance Courvoisier et al (2005) and Galloway (2012) for a review of the most current model flows. Now, while the passive vector alignments have been investigated in turbulent flows (Ohkitani 2002, Tsinober andGalanti 2003), it appears that a few studies devoted to the dynamo effect specifically deal with the alignment properties of the magnetic field vector (Brandenburg 1995, Polygiannakis andMoussas 1999).…”

Section: Introductionmentioning

confidence: 99%

Effect of orientation dynamics on the growth of a passive vector in a family of model flows

Gonzalez¹

2013

Fluid Dyn. Res.

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The stretching properties of a parameterized model flow used to study the fast dynamo (Tanner and Hughes 2003 Astrophys. J. 586 685-91) are analyzed by paying special attention to the dependence of the growth rate of a passive vector on its orientation with respect to strain principal axes. More specifically, the study brings out that, rather than strain intensity, it is the dynamics of orientation resulting from the alternating tilting of the strain principal axes that explains the evolution of the passive vector mean growth rate in this class of flows. On a more general level, this view of stretching may bring an alternative understanding of the growth mechanisms of vectors such as the magnetic field vector.

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“…Simple steady cellular flows that take the form u(x, y) and possess just one spatial scale have been utilized in studies of transport coefficients over many years; these date back to the pioneering work of Roberts (1970), with subsequent modifications by, for example, Plunian & Rädler (2002), Childress & Soward (1989) and Courvoisier, Gilbert & Ponty (2005). The natural extension to time-periodic flows of the form u(x, y, t) has been considered by, for example, Majda & Kramer (1999) for scalar diffusion and by Courvoisier, Hughes & Tobias (2006) and Rädler & Brandenburg (2009) for the α-effect.…”

Section: Introductionmentioning

confidence: 99%

Mean induction and diffusion: the influence of spatial coherence

2009

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Within the same framework we calculate the mean induction of a magnetic field and the mean diffusivity of a passive scalar, for two families of flows in which the degree of spatial decorrelation can be systematically adjusted. We investigate the dependence of these quantities both on the spatial decoherence and on the molecular diffusivity. We demonstrate that for flows with similar global properties, the mean induction is dramatically reduced as the flows become less spatially correlated; the mean diffusivity, on the other hand, shows no significant or systematic variation.

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Dynamo action in flows with cat's eyes

Abstract: Geophysical and Astrophysical Fluid Dynamics, 99, pp. 413-429, http://dx.doi.org./10.1080/03091920500334159International audienc

Cited by 10 publications

References 26 publications

From large-scale to small-scale dynamos in a spherical shell

From large-scale to small-scale dynamos in a spherical shell

Effect of orientation dynamics on the growth of a passive vector in a family of model flows

Mean induction and diffusion: the influence of spatial coherence

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