The Inverse Cascade and Nonlinear Alpha-Effect in Simulations of Isotropic Helical Hydromagnetic Turbulence

By Axel Brandenburg. 2000

525 citations recorded by the source corpus.

A numerical model of isotropic homogeneous turbulence with helical forcing is investigated. The resulting flow, which is essentially the prototype of the α2 dynamo of mean field dynamo theory, produces strong dynamo action with an additional large-scale field on the scale of the box (at wavenumber k = 1; forcing is at k = 5). This large-scale field is nearly force free and exceeds the equipartition value. As the magnetic Reynolds number Rm increases, the saturation field strength and the growth rate of the dynamo increase. However, the time it takes to build up the large-scale field from equipartition to its final superequipartition value increases with magnetic Reynolds number. The large-scale field generation can be identified as being due to nonlocal interactions originating from the forcing scale, which is characteristic of the α-effect. Both α and turbulent magnetic diffusivity ηt are determined simultaneously using numerical experiments where the mean field is modified artificially. Both quantities are quenched in an Rm-dependent fashion. The evolution of the energy of the mean field matches that predicted by an α2 dynamo model with similar α and ηt quenchings. For this model an analytic solution is given that matches the results of the simulations. The simulations are numerically robust in that the shape of the spectrum at large scales is unchanged when changing the resolution from 303 to 1203 mesh points, or when increasing the magnetic Prandtl number (viscosity/magnetic diffusivity) from 1 to 100. Increasing the forcing wavenumber to 30 (i.e., increasing the scale separation) makes the inverse cascade effect more pronounced, although it remains otherwise qualitatively unchanged.

Subfields: Astronomy and Astrophysics, Molecular Biology, Oceanography

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Citations in the corpus

Global simulations of axisymmetric radiative black hole accretion discs in general relativity with a mean-field magnetic dynamo (2014, background): “The evolution of the mean magnetic field may be described under the mean field theory by the following equation (Brandenburg 2001), ∂ ∂t ~B = α∇ × ~B + η∇2~B, (31) where α and η, are the dynamo, and magnetic diffusivity coefficients, respectively.”
Astrophysical magnetic fields and nonlinear dynamo theory (2004, methodology): “[4] the flow was forced at an intermediate wavenumber, k ≈ kf = 5, while the smallest wavenumber in the computational domain corresponds to k = k1 = 1.”
Simulations of the Small-Scale Turbulent Dynamo (2003, background): “A natural step beyond Prm ¼ 1 is to look at Prandtl numbers above, but of the order of, unity (Meneguzzi et al. 1981; Chou 2001; Brandenburg 2001; Maron & Blackman 2002; Maron et al. 2004; Archontis et al. 2003a, 2003b; Haugen et al. 2004; our run B in x 5) more or less in the hope that essential…”
The solar magnetic field (2006, background): “This represents a relevant constraint on dynamo models for the Sun, since the 11/22-year period of the solar cycle is very much shorter than the resistive time scale based upon (microscopic) diffusion [155,156].”
Solar Dynamo Theory (2014, background): “It is also possible to bypass the helicity conservation constraints by having the dynamo produce helicity of opposite signs at large and small spatial scales (Brandenburg 2001).”
Dynamic Nonlinearity in Large-Scale Dynamos with Shear (2002, background): “Sim - ulationswith thesam esinusoidal pro le(Brandenburg 2001b) have shown that the resulting large scale eld varies m ostly in the x direction, which is incom patible with the present m odel.”
The Case for a Distributed Solar Dynamo Shaped by Near-Surface Shear (2005, background): “Second, at high magnetic Reynolds numbers the large scale dynamo time scale tends to be constrained by magnetic helicity conservation (Brandenburg 2001).”
SUSTAINED MAGNETOROTATIONAL TURBULENCE IN LOCAL SIMULATIONS OF STRATIFIED DISKS WITH ZERO NET MAGNETIC FLUX (2009, result): “This result differs from simulations of helically driven turbulence where the kinetic and magnetic energy have comparable amplitude at all but the lowest k where magnetic energy dominates (see, e.g., Brandenburg 2001).”
Statistical theory of magnetohydrodynamic turbulence: recent results (2004, methodology): “The above observation explains the numerical findings of Brandenburg[22] discussed above.”
Fluctuation dynamo and turbulent induction at low magnetic Prandtl numbers (2007, background): “Numerical experiments have, therefore, played a crucial role in building up the case for the turbulent dynamo (e.g., Galloway & Proctor 1992, Meneguzzi et al. 1981, Cattaneo 1999, Brandenburg 2001).”
Magnetic Field Generation in Fully Convective Rotating Spheres (2004, background): “This results in a normalized growth rate λτ = 0.08, which is comparable to the values for both helically and nonhelically forced turbulence simulations where λτ = 0.03–0.1, see Brandenburg (2001) and Haugen et al. (2004), respectively.”