220 research outputs found
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 -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
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
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