The alpha effect in rotating convection with sinusoidal shear

Using three-dimensional convection simulations it is shown that a sinusoidal variation of horizontal shear leads to a kinematic \alpha effect with a similar sinusoidal variation. The effect exists even for weak stratification and arises owing to the inhomogeneity of turbulence and the presence of impenetrable vertical boundaries. This system produces large-scale magnetic fields that also show a sinusoidal variation in the streamwise direction. It is argued that earlier investigations overlooked these phenomena partly because of the use of horizontal averaging and also because measurements of \alpha using an imposed field combined with long time averages give erroneous results. It is demonstrated that in such cases the actual horizontally averaged mean field becomes non-uniform. The turbulent magnetic diffusion term resulting from such non-uniform fields can then no longer be neglected and begins to balance the \alpha effect.Comment: 9 pages, 10 figures, published versio

Local models of stellar convection II: Rotation dependence of the mixing length relations

We study the mixing length concept in comparison to three-dimensional numerical calculations of convection with rotation. In a limited range, the velocity and temperature fluctuations are linearly proportional to the superadiabaticity, as predicted by the mixing length concept and in accordance with published results. The effects of rotation are investigated by varying the Coriolis number, Co = 2 Omega tau, from zero to roughly ten, and by calculating models at different latitudes. We find that \alpha decreases monotonically as a function of the Coriolis number. This can be explained by the decreased spatial scale of convection and the diminished efficiency of the convective energy transport, the latter of which leads to a large increase of the superadibaticity, \delta = \nabla - \nabla_ad as function of Co. Applying a decreased mixing length parameter in a solar model yields very small differences in comparison to the standard model within the convection zone. The main difference is the reduction of the overshooting depth, and thus the depth of the convection zone, when a non-local version of the mixing length concept is used. Reduction of \alpha by a factor of roughly 2.5 is sufficient to reconcile the difference between the model and helioseismic results. The numerical results indicate reduction of \alpha by this order of magnitude.Comment: Final published version, 8 pages, 9 figure

New scaling for the alpha effect in slowly rotating turbulence

Using simulations of slowly rotating stratified turbulence, we show that the alpha effect responsible for the generation of astrophysical magnetic fields is proportional to the logarithmic gradient of kinetic energy density rather than that of momentum, as was previously thought. This result is in agreement with a new analytic theory developed in this paper for large Reynolds numbers. Thus, the contribution of density stratification is less important than that of turbulent velocity. The alpha effect and other turbulent transport coefficients are determined by means of the test-field method. In addition to forced turbulence, we also investigate supernova-driven turbulence and stellar convection. In some cases (intermediate rotation rate for forced turbulence, convection with intermediate temperature stratification, and supernova-driven turbulence) we find that the contribution of density stratification might be even less important than suggested by the analytic theory.Comment: 10 pages, 9 figures, revised version, Astrophys. J., in pres

Reynolds stresses from hydrodynamic turbulence with shear and rotation

To study the Reynolds stresses which describe turbulent momentum transport from turbulence affected by large-scale shear and rotation. Three-dimensional numerical simulations are used to study turbulent transport under the influences of large-scale shear and rotation in homogeneous, isotropically forced turbulence. We study three cases: one with only shear, and two others where in addition to shear, rotation is present. These cases differ by the angle (0 or 90\degr) the rotation vector makes with respect to the z-direction. Two subsets of runs are performed with both values of \theta where either rotation or shear is kept constant. When only shear is present, the off-diagonal stress can be described by turbulent viscosity whereas if the system also rotates, nondiffusive contributions (\Lambda-effect) to the stress can arise. Comparison of the direct simulations are made with analytical results from a simple closure model. We find that the turbulent viscosity is of the order of the first order smoothing result in the parameter regime studied and that for sufficiently large Reynolds numbers the Strouhal number, describing the ratio of correlation to turnover times, is roughly 1.5. This is consistent with the closure model based on the minimal tau-approximation which produces a reasonable fit to the simulation data for similar Strouhal numbers. In the cases where rotation is present, separating the diffusive and nondiffusive components of the stress turns out to be challenging but taking the results at face value, we can obtain nondiffusive contributions of the order of 0.1 times the turbulent viscosity. We also find that the simple closure model is able to reproduce most of the qualitative features of the numerical results provided that the Strouhal number is of the order of unity.Comment: 19 pages, 12 figures, published versio

Magnetoconvection and dynamo coefficients III: alpha-effect and magnetic pumping in the rapid rotation regime

Aims. The alpha- and gamma-effects, which are responsible for the generation and turbulent pumping of large scale magnetic fields, respectively, due to passive advection by convection are determined in the rapid rotation regime corresponding to the deep layers of the solar convection zone. Methods. A 3D rectangular local model is used for solving the full set of MHD equations in order to compute the electromotive force (emf), E = , generated by the interaction of imposed weak gradient-free magnetic fields and turbulent convection with varying rotational influence and latitude. By expanding the emf in terms of the mean magnetic field, E_i = a_ij , all nine components of a_ij are computed. The diagonal elements of a_ij describe the alpha-effect, whereas the off-diagonals represent magnetic pumping. The latter is essentially the advection of magnetic fields by means other than the underlying large-scale velocity field. Comparisons are made to analytical expressions of the coefficients derived under the first-order smoothing approximation (FOSA). Results. In the rapid rotation regime the latitudinal dependence of the alpha-components responsible for the generation of the azimuthal and radial fields does not exhibit a peak at the poles, as is the case for slow rotation, but at a latitude of about 30 degrees. The magnetic pumping is predominantly radially down- and latitudinally equatorward as in earlier studies. The numerical results compare surprisingly well with analytical expressions derived under first-order smoothing, although the present calculations are expected to lie near the limits of the validity range of FOSA.Comment: 14 pages, 12 figures, accepted for publication in Astronomy & Astrophysic

Large-scale dynamos in turbulent convection with shear

(abridged) Aims: Three-dimensional numerical simulations of penetrative compressible convection with uniform horizontal shear are used to study dynamo action and the generation of large-scale magnetic fields. Methods: We consider cases where the magnetic Reynolds number is either marginal or moderately supercritical with respect to small-scale dynamo action in the absence of shear and rotation. The effects of magnetic helicity fluxes are studied by comparing results for the magnetic field with open and closed boundaries. Results: Without shear no large-scale dynamos are found even if the ingredients necessary for the alpha-effect (rotation and stratification) are present in the system. When uniform horizontal shear is added, a large-scale magnetic field develops, provided the boundaries are open. In this case the mean magnetic field contains a significant fraction of the total field. For those runs where the magnetic Reynolds number is between 60 and 250, small-scale dynamo is expected to be excited, but the field distribution is found to be similar to cases with smaller magnetic Reynolds number where the small-scale dynamo is not excited. In the case of closed (perfectly conducting) boundaries, magnetic helicity fluxes are suppressed and no large-scale fields are found. Similarly, poor large-scale field development is seen when vertical shear is used in combination with periodic boundary conditions in the horizontal directions. If, however, open (normal-field) boundary conditions are used in the x-direction, a large-scale field develops. These results support the notion that shear not only helps to generate the field, but it also plays a crucial role in driving magnetic helicity fluxes out of the system along the isocontours of shear, thereby allowing efficient dynamo action.Comment: 10 pages, 19 figures, accepted for publication in Astron. Astrophy

Alpha effect and turbulent diffusion from convection

(abridged) Aims: To study turbulent transport coefficients that describe the evolution of large-scale magnetic fields in turbulent convection. Methods: We use the test field method together with 3D numerical simulations of turbulent convection with shear and rotation to compute turbulent transport coefficients describing the evolution of large-scale magnetic fields in mean-field theory in the kinematic regime. 1D mean-field models are used with the derived turbulent transport coefficients to compare with direct simulations. Results: The alpha-effect increases monotonically as rotation increases. Turbulent diffusivity, eta_t, is proportional to the square of the turbulent vertical velocity. Whereas eta_t decreases approximately inversely proportional to the wavenumber of the field, the alpha-effect and turbulent pumping show a more complex behaviour. In the presence of shear and no rotation a small alpha-effect is induced which does not seem to show any consistent trend as a function of shear. If the shear is large enough, this small alpha is able to excite a dynamo in the mean-field model. The coefficient responsible for driving the shear-current effect shows several sign changes as a function of depth but is also able to contribute to dynamo action in the mean-field model. The growth rates in these cases are well below those in direct simulations suggesting that an incoherent alpha-shear dynamo may also act in them. If both rotation and shear are present, the alpha-effect is more pronounced. The combination of the shear-current and Omega x J-effects is also stronger than in the case of shear only, but subdominant to the alpha-shear dynamo. The results of direct simulations are consistent with mean-field models where all of these effects are taken into account without the need to invoke incoherent effects.Comment: 14 pages, 14 figures, minor changes to match with the published versio

A solar mean field dynamo benchmark

ABSTRACT Context. The solar magnetic activity and cycle are linked to an internal dynamo. Numerical simulations are an efficient and accurate tool to investigate such intricate dynamical processes. Aims. We present the results of an international numerical benchmark study based on two-dimensional axisymmetric mean field solar dynamo models in spherical geometry. The purpose of this work is to provide the scientific community with reference cases that can be analyzed in detail and that can help in further development and validation of numerical codes that solve such kinematic problems. Methods. The results of eight numerical codes solving the induction equation in the framework of mean field theory are compared for three increasingly computationally intensive models of the solar dynamo: an αΩ dynamo with constant magnetic diffusivity, an αΩ dynamo with magnetic diffusivity sharply varying with depth and an example of a flux-transport Babcock-Leighton dynamo which includes a non-local source term and one large single cell of meridional circulation per hemisphere. All cases include a realistic profile of differential rotation and thus a sharp tachocline. Results. The most important finding of this study is that all codes agree quantitatively to within less than a percent for the αΩ dynamo cases and within a few percents for the flux-transport case. Both the critical dynamo numbers for the onset of dynamo action and the corresponding cycle periods are reasonably well recovered by all codes. Detailed comparisons of butterfly diagrams and specific cuts of both toroidal and poloidal fields at given latitude and radius confirm the good quantitative agreement. Conclusions. We believe that such a benchmark study will be a very useful tool for the scientific community since it provides detailed standard cases for comparison and reference