Magnetic material in mean-field dynamos driven by small scale helical flows

Abstract

We perform kinematic simulations of dynamo action driven by a helical small scale flow of a conducting fluid in order to deduce mean-field properties of the combined induction action of small scale eddies. We examine two different flow patterns in the style of the G O Roberts flow but with a mean vertical component and with internal fixtures that are modelled by regions with vanishing flow. These fixtures represent either rods that lie in the center of individual eddies, or internal dividing walls that provide a separation of the eddies from each other. The fixtures can be made of magnetic material with a relative permeability larger than one which can alter the dynamo behavior. The investigations are motivated by the widely unknown induction effects of the forced helical flow that is used in the core of liquid sodium cooled fast reactors, and from the key role of soft iron impellers in the von-Kármán-sodium dynamo. For both examined flow configurations the consideration of magnetic material within the fluid flow causes a reduction of the critical magnetic Reynolds number of up to 25%. The development of the growth-rate in the limit of the largest achievable permeabilities suggests no further significant reduction for even larger values of the permeability. In order to study the dynamo behavior of systems that consist of tens of thousands of helical cells we resort to the mean-field dynamo theory (Krause and Rädler 1980 Mean-field Magnetohydrodynamics and Dynamo Theory (Oxford: Pergamon)) in which the action of the small scale flow is parameterized in terms of an αand β-effect. We compute the relevant elements of the αand the Content from this work may be used under the terms of the Creative Commons Attribution 3.0 licence. Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.

Helical bottleneck effect in 3D homogeneous isotropic turbulence

“…As shown above (see figure 1, left panel), the energy accumulation can occur near the dissipative range, which explains the bottleneck effect. It may be responsible for the slope of the experimentally obtained energy spectrum in the background the Kármán swirling flow (López-Caballero and Burguete 2013), where helicity was intensively injected into small scales by the blades of rotating discs (Giesecke et al 2014). The helicity effect at the large scale (see figure 1, right panel) can be interpreted as a reduction of the turbulent viscosity, which is consistent with our phenomenology.…”

Turbulence Reduces Magnetic Diffusivity in a Liquid Sodium Experiment

“…The much lower amplitude of β in the DNS is due to a Reynolds number 300 times smaller than that in the experiment, suggesting that β may scale with Re 2 (but see the Erratum below). Although negative β values, and hence reduced magnetic diffusivity, are not unexpected [16][17][18][19], it is the first time that they are observed in experiment. Our DTS experiment combines a strong imposed magnetic field and strong rotation.…”

Hindered Energy Cascade in Highly Helical Isotropic Turbulence

“…For example, we suggest that the helical bottleneck effect could be responsible for steepening the experimentally obtained energy spectrum in a von Kármán swirling flow [23]. In that experiment, the helicity was intensively injected by the blades at smaller scales than the scale of energy injection by rotating discs [29]. Another applicable situation might be a flow with shear generated helicity, which is favorable for development and intensification of tropical cyclones [19,30].…”