J. E. Snellman, P. J. Käpylä, M. J. Mantere, M. Rheinhardt, B. Dintrans
Aims: To compare simple analytical closure models of turbulent Boussinesq convection for stellar applications with direct three-dimensional simulations both in homogeneous and inhomogeneous (bounded) setups. Methods: 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 fit methods using simulation data. Unique determination of the closure parameters is possible only in the non-rotating case and 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. Results: The simulation data for the Reynolds stress and heat fluxes in the homogeneous case broadly agree with previous compressible simulations. The closure works fairly well in the homogeneous case with slow rotation but its quality degrades as the rotation rate is increased. We find that the closure parameters depend not only on $\Tay$ but also on latitude. Furthermore, in the inhomogeneous case the closure is unable to reproduce the vertical profiles of the horizontal components of the Reynolds stress.
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http://arxiv.org/abs/1209.4923
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