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Register a new userNumerical Simulations of Kinematic Dynamo Action
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Vasilis Archontis
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Numerical simulations of kinematic dynamo action in steady and 3-d ABC flows are presented with special focus on growth rates and multiple periods of the prescribed velocity field. It is found that the difference in growth rate is due to differences in the recycling of the weakest part of the magnetic field. Differences in the topology in cases with and without stagnation points in the imposed velocity field are also investigated, and it is found that the cigar-like structures that develop in the classical A=B=C dynamos, are replaced by ribbon structures in cases where the flow is without stagnation points.
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We present a three--pronged numerical approach to the dynamo problem at low magnetic Prandtl numbers $P_M$. The difficulty of resolving a large range of scales is circumvented by combining Direct Numerical Simulations, a Lagrangian-averaged model, and Large-Eddy Simulations (LES). The flow is generated by the Taylor-Green forcing; it combines a well defined structure at large scales and turbulent fluctuations at small scales. Our main findings are: (i) dynamos are observed from $P_M=1$ down to $P_M=10^{-2}$; (ii) the critical magnetic Reynolds number increases sharply with $P_M^{-1}$ as turbulence sets in and then saturates; (iii) in the linear growth phase, the most unstable magnetic modes move to small scales as $P_M$ is decreased and a Kazantsev $k^{3/2}$ spectrum develops; then the dynamo grows at large scales and modifies the turbulent velocity fluctuations.
Numerical simulations of forced turbulence in elongated shearing boxes are carried out to demonstrate that a nonhelical turbulence in conjunction with a linear shear can give rise to a mean-field dynamo. Exponential growth of magnetic field at scales larger than the outer (forcing) scale of the turbulence is found. Over a range of values of the shearing rate S spanning approximately two orders of magnitude, the growth rate of the magnetic field is proportional to the imposed shear, gamma ~ S, while the characteristic spatial scale of the field is l_b ~ S^(-1/2). The effect is quite general: earlier results for the nonrotating case by Yousef et al. 2008 (PRL 100, 184501) are extended to shearing boxes with Keplerian rotation; it is also shown that the shear dynamo mechanism operates both below and above the threshold for the fluctuation dynamo. The apparently generic nature of the shear dynamo effect makes it an attractive object of study for the purpose of understanding the generation of magnetic fields in astrophysical systems.
In this paper we address a discrepancy between the surface flux evolution in a 3D kinematic dynamo model and a 2D surface flux transport model that has been closely calibrated to the real Sun. We demonstrate that the difference is due to the connectivity of active regions to the toroidal field at the base of the convection zone, which is not accounted for in the surface-only model. Initially, we consider the decay of a single active region, firstly in a simplified Cartesian 2D model and subsequently the full 3D model. By varying the turbulent diffusivity profile in the convection zone, we find that increasing the diffusivity - so that active regions are more rapidly disconnected from the base of the convection zone - improves the evolution of the surface field. However, if we simulate a full solar cycle, we find that the dynamo is unable to sustain itself under such an enhanced diffusivity. This suggests that in order to accurately model the solar cycle, we must find an alternative way to disconnect emerging active regions, whilst conserving magnetic flux.
Core convection and dynamo activity deep within rotating A-type stars of 2 solar masses are studied with 3--D nonlinear simulations. Our modeling considers the inner 30% by radius of such stars, thus capturing within a spherical domain the convective core and a modest portion of the surrounding radiative envelope. The MHD equations are solved using the ASH code to examine turbulent flows and magnetic fields, both of which exhibit intricate time dependence. By introducing small seed magnetic fields into our progenitor hydrodynamic models rotating at one and four times the solar rate, we assess here how the vigorous convection can amplify those fields and sustain them against ohmic decay. Dynamo action is indeed realized, ultimately yielding magnetic fields that are in energy equipartion with the flow. Such magnetism reduces the differential rotation obtained in the progenitors, partly by Maxwell stresses that transport angular momentum poleward and oppose the Reynolds stresses in the latitudinal balance. In contrast, in the radial direction we find that the Maxwell and Reynolds stresses may act together to transport angular momentum. The central columns of slow rotation established in the progenitors are weakened, with the differential rotation waxing and waning in strength as the simulations evolve. We assess the morphology of the flows and magnetic fields, their complex temporal variations, and the manner in which dynamo action is sustained. Differential rotation and helical convection are both found to play roles in giving rise to the magnetic fields. The magnetism is dominated by strong fluctuating fields throughout the core, with the axisymmetric (mean) fields there relatively weak.
A hypothesis for sunspot formation is the buoyant emergence of magnetic flux tubes created by the strong radial shear at the tachocline. In this scenario, the magnetic field has to exceed a threshold value before it becomes buoyant and emerges through the whole convection zone. We follow the evolution of a random seed magnetic field with the aim of study under what conditions it is possible to excite the dynamo instability and whether the dynamo generated magnetic field becomes buoyantly unstable and emerges to the surface as expected in the flux-tube context. We perform numerical simulations of compressible turbulent convection that include a vertical shear layer. Like the solar tachocline, the shear is located at the interface between convective and stable layers. We find that shear and convection are able to amplify the initial magnetic field and form large-scale elongated magnetic structures. The magnetic field strength depends on several parameters such as the shear amplitude, the thickness and location of the shear layer, and the magnetic Reynolds number ($Rm$). Whenever the toroidal magnetic field reaches amplitudes greater a threshold value which is close to the equipartition value, it becomes buoyant and rises into the convection zone where it expands and forms mushroom shape structures. Some events of emergence, i.e. those with the largest amplitudes of the initial field, are able to reach the very uppermost layers of the domain. These episodes are able to modify the convective pattern forming either broader convection cells or convective eddies elongated in the direction of the field. However, in none of these events the field preserves its initial structure.
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