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&

Oscillatory large-scale dynamos from Cartesian convection simulations

Peer reviewe

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