Dynamic Nonlinearity in Large-Scale Dynamos with Shear

By Eric G. Blackman, Axel Brandenburg. 2002

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We supplement the mean field dynamo growth equation with the total magnetic helicity evolution equation. This provides an explicitly time-dependent model for α-quenching in dynamo theory. For dynamos without shear, this approach accounts for the observed large-scale field growth and saturation in numerical simulations. After a significant kinematic phase, the dynamo is resistively quenched, i.e., the saturation time depends on the microscopic resistivity. This is independent of whether or not the turbulent diffusivity is resistively quenched. We find that the approach is also successful for dynamos that include shear and exhibit migratory waves (cycles). In this case, however, whether or not the cycle period remains of the order of the dynamical timescale at large magnetic Reynolds numbers does depend on how the turbulent magnetic diffusivity quenches. Since this is unconstrained by magnetic helicity conservation, the diffusivity is currently an input parameter. Comparison with current numerical experiments suggests a turbulent diffusivity that depends only weakly on the magnetic Reynolds number, but higher resolution simulations are needed.

Subfields: Astronomy and Astrophysics, Molecular Biology, Oceanography

View Paper: https://www.semanticscholar.org/paper/8a17aa2711a779fd14f88f67a867fe6a1cd63e84

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Citations in the corpus

Astrophysical magnetic fields and nonlinear dynamo theory (2004, methodology): “As mentioned earlier [6], the kf factor may be attenuated by a R m factor to account for the fact that for a k−5/3 energy spectrum the 〈 j · b〉 term will 35 pick up contributions from smaller scales.”
Dynamo Models of the Solar Cycle (2005, background): “A number of authors have attempted to bypass the shortcomings of α-quenching by introducing into dynamo models an additional, physically-inspired partial differential equation for the α-coefficient itself (e.g., Kleeorin et al., 1995; Blackman and Brandenburg, 2002, and references therein).”
Solar Dynamo Theory (2014, background): “…forced “toy” flow, Cattaneo & Hughes (1996) carried out a series of numerical experiments at varying magnetic Reynolds number Rm and found that their results did not fit Equation 33, but rather the closely related form αi j (〈B〉) → αi j1 + Rm(〈B〉2/B2eq) (34) (see also Blackman & Brandenburg 2002).”