252 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
Effects of Rotation and Input Energy Flux on Convective Overshooting
We study convective overshooting by means of local 3D convection
calculations. Using a mixing length model of the solar convection zone (CZ) as
a guide, we determine the Coriolis number (Co), which is the inverse of the
Rossby number, to be of the order of ten or larger at the base of the solar CZ.
Therefore we perform convection calculations in the range Co = 0...10 and
interpret the value of Co realised in the calculation to represent a depth in
the solar CZ. In order to study the dependence on rotation, we compute the
mixing length parameters alpha_T and alpha_u relating the temperature and
velocity fluctuations, respectively, to the mean thermal stratification. We
find that the mixing length parameters for the rapid rotation case,
corresponding to the base of the solar CZ, are 3-5 times smaller than in the
nonrotating case. Introducing such depth-dependent alpha into a solar structure
model employing a non-local mixing length formalism results in overshooting
which is approximately proportional to alpha at the base of the CZ. Although
overshooting is reduced due to the reduced alpha, a discrepancy with
helioseismology remains due to the steep transition to the radiative
temperature gradient. In comparison to the mixing length models the transition
at the base of the CZ is much gentler in the 3D models. It was suggested
recently (Rempel 2004) that this discrepancy is due to the significantly larger
(up to seven orders of magnitude) input energy flux in the 3D models in
comparison to the Sun and solar models, and that the 3D calculations should be
able to approach the mixing length regime if the input energy flux is decreased
by a moderate amount. We present results from local convection calculations
which support this conjecture.Comment: 6 pages, 3 figures, to appear in Convection in Astrophysics, Proc.
IAUS 239, edited by F. Kupka, I.W. Roxburgh, K.L. Cha
Physically motivated heat conduction treatment in simulations of solar-like stars: effects on dynamo transitions
Context. Results from global magnetoconvection simulations of solar-like
stars are at odds with observations in many respects: They show a surplus of
energy in the kinetic power spectrum at large scales, anti-solar differential
rotation profiles, with accelerated poles and a slow equator, for the solar
rotation rate, and a transition from axi- to non-axisymmetric dynamos at a much
lower rotation rate than what is observed. Even though the simulations
reproduce the observed active longitudes in fast rotators, their motion in the
rotational frame (the so-called azimuthal dynamo wave, ADW) is retrograde, in
contrast to the prevalent prograde motion in observations. Aims. We study the
effect of a more realistic treatment of heat conductivity in alleviating the
discrepancies between observations and simulations. Methods. We use
physically-motivated heat conduction, by applying Kramers opacity law, on a
semi-global spherical setup describing convective envelopes of solar-like
stars, instead of a prescribed heat conduction profile from mixing-length
arguments. Results. We find that some aspects of the results now better
correspond to observations: The axi- to non-axisymmetric transition point is
shifted towards higher rotation rates. We also find a change in the propagation
direction of ADWs so that also prograde waves are now found. The transition
from anti-solar to solar-like rotation profile, however, is also shifted
towards higher rotation rates, leaving the models into an even more unrealistic
regime. Conclusions. Although a Kramers-based heat conduction does not help in
reproducing the solar rotation profile, it does help in the faster rotation
regime, where the dynamo solutions now match better with observations.Comment: 10 pages, 6 figures, 1 appendix. Submitted to A&
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
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