Testing turbulent closure models with convection simulations

We compare simple analytical closure models of homogeneous turbulent Boussinesq convection for stellar applications with three-dimensional simulations. We use simple analytical closure models to compute the fluxes of angular momentum and heat as a function of rotation rate measured by the Taylor number. We also investigate cases with varying angles between the angular velocity and gravity vectors, corresponding to locating the computational domain at different latitudes ranging from the pole to the equator of the star. We perform three-dimensional numerical simulations in the same parameter regimes for comparison. The free parameters appearing in the closure models are calibrated by two fitting methods using simulation data. Unique determination of the closure parameters is possible only in the non-rotating case or when the system is placed at the pole. In the other cases the fit procedures yield somewhat differing results. The quality of the closure is tested by substituting the resulting coefficients back into the closure model and comparing with the simulation results. To eliminate the possibilities that the results obtained depend on the aspect ratio of the simulation domain or suffer from too small Rayleigh numbers we performed runs varying these parameters. The simulation data for the Reynolds stress and heat fluxes broadly agree with previous compressible simulations. The closure works fairly well with slow and fast rotation but its quality degrades for intermediate rotation rates. We find that the closure parameters depend not only on rotation rate but also on latitude. The weak dependence on Rayleigh number and the aspect ratio of the domain indicates that our results are generally validComment: 21 pages, 9 figures, submitted to Astron. Nach

Lambda-effect from forced turbulence simulations

Aims: We determine the components of the $\Lambda$-effect tensor that quantifies the contributions to the turbulent momentum transport even for uniform rotation. Methods: Three-dimensional numerical simulations are used to study turbulent transport in triply periodic cubes under the influence of rotation and anisotropic forcing. Comparison is made with analytical results obtained via the so-called minimal tau-approximation. Results: In the case where the turbulence intensity in the vertical direction dominates, the vertical stress is always negative. This situation is expected to occur in stellar convection zones. The horizontal component of the stress is weaker and exhibits a maximum at latitude 30 degrees - regardless of how rapid the rotation is. The minimal tau-approximation captures many of the qualitative features of the numerical results, provided the relaxation time tau is close to the turnover time, i.e. the Strouhal number is of order unity.Comment: 20 pages, 14 figures, accepted for publication in Astronomy & Astrophysic

The alpha effect with imposed and dynamo-generated magnetic fields

Estimates for the nonlinear alpha effect in helical turbulence with an applied magnetic field are presented using two different approaches: the imposed-field method where the electromotive force owing to the applied field is used, and the test-field method where separate evolution equations are solved for a set of different test fields. Both approaches agree for stronger fields, but there are apparent discrepancies for weaker fields that can be explained by the influence of dynamo-generated magnetic fields on the scale of the domain that are referred to as meso-scale magnetic fields. Examples are discussed where these meso-scale fields can lead to both drastically overestimated and underestimated values of alpha compared with the kinematic case. It is demonstrated that the kinematic value can be recovered by resetting the fluctuating magnetic field to zero in regular time intervals. It is concluded that this is the preferred technique both for the imposed-field and the test-field methods.Comment: 10 pages, 8 figures, published versio

Oscillatory large-scale dynamos from Cartesian convection simulations

Peer reviewe

Open and closed boundaries in large-scale convective dynamos

9 pages, 7 figures, submitted to Astron. AstrophysEarlier work has suggested that large-scale dynamos can reach and maintain equipartition field strengths on a dynamical time scale only if magnetic helicity of the fluctuating field can be shed from the domain through open boundaries. To test this scenario in convection-driven dynamos by comparing results for open and closed boundary conditions. Three-dimensional numerical simulations of turbulent compressible convection with shear and rotation are used to study the effects of boundary conditions on the excitation and saturation level of large-scale dynamos. Open (vertical field) and closed (perfect conductor) boundary conditions are used for the magnetic field. The contours of shear are vertical, crossing the outer surface, and are thus ideally suited for driving a shear-induced magnetic helicity flux. We find that for given shear and rotation rate, the growth rate of the magnetic field is larger if open boundary conditions are used. The growth rate first increases for small magnetic Reynolds number, Rm, but then levels off at an approximately constant value for intermediate values of Rm. For large enough Rm, a small-scale dynamo is excited and the growth rate in this regime increases proportional to Rm^(1/2). In the nonlinear regime, the saturation level of the energy of the mean magnetic field is independent of Rm when open boundaries are used. In the case of perfect conductor boundaries, the saturation level first increases as a function of Rm, but then decreases proportional to Rm^(-1) for Rm > 30, indicative of catastrophic quenching. These results suggest that the shear-induced magnetic helicity flux is efficient in alleviating catastrophic quenching when open boundaries are used. The horizontally averaged mean field is still weakly decreasing as a function of Rm even for open boundaries.Peer reviewe