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Register a new userOn Dissipation inside Turbulent Convection Zones from 3D Simulations of Solar Convection
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Kaloyan Penev
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The development of 2D and 3D simulations of solar convection has lead to a picture of convection quite unlike the usually assumed Kolmogorov spectrum turbulent flow. We investigate the impact of this changed structure on the dissipation properties of the convection zone, parametrized by an effective viscosity coefficient. We use an expansion treatment developed by Goodman & Oh 1997, applied to a numerical model of solar convection (Robinson et al. 2003) to calculate an effective viscosity as a function of frequency and compare this to currently existing prescriptions based on the assumption of Kolmogorov turbulence (Zahn 1966, Goldreich & Keeley 1977). The results match quite closely a linear scaling with period, even though this same formalism applied to a Kolmogorov spectrum of eddies gives a scaling with power-law index of 5/3.
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We have adapted the anelastic spectral code of Barranco & Marcus (2006) to simulate a turbulent convective layer with the intention of studying the effectiveness of turbulent eddies in dissipating external shear (e.g. tides). We derive the anelastic equations, show the time integration scheme we use to evolve these equations and present the tests we ran to confirm that our code does what we expect. Further we apply a perturbative approach to find an approximate scaling of the effective eddy viscosity with frequency, and find that it is in general agreement with an estimate obtained by applying the same procedure to a realistic simulation of the upper layers of the solar convective zone.
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The impressive development of global numerical simulations of turbulent stellar interiors unveiled a variety of possible differential rotation (solar or anti-solar), meridional circulation (single or multi-cellular), and dynamo states (stable large scale toroidal field or periodically reversing magnetic fields). Various numerical schemes, based on the so-called anelastic set of equations, were used to obtain these results. It appears today mandatory to assess their robustness with respect to the details of the numerics, and in particular to the treatment of turbulent sub-grid scales. We report on an ongoing comparison between two global models, the ASH and EULAG codes. In EULAG the sub-grid scales are treated implicitly by the numerical scheme, while in ASH their effect is generally modelled by using enhanced dissipation coefficients. We characterize the sub-grid scales effect in a turbulent convection simulation with EULAG. We assess their effect at each resolved scale with a detailed energy budget. We derive equivalent eddy-diffusion coefficients and use the derived diffusivities in twin ASH numerical simulations. We find a good agreement between the large-scale flows developing in the two codes in the hydrodynamic regime, which encourages further investigation in the magnetohydrodynamic regime for various dynamo solutions.
Turbulent properties of the quiet Sun represent the basic state of surface conditions, and a background for various processes of solar activity. Therefore understanding of properties and dynamics of this `basic state is important for investigation of more complex phenomena, formation and development of observed phenomena in the photosphere and atmosphere. For characterization of the turbulent properties we compare kinetic energy spectra on granular and sub-granular scales obtained from infrared TiO observations with the New Solar Telescope (Big Bear Solar Observatory) and from 3D radiative MHD numerical simulations (SolarBox code). We find that the numerical simulations require a high spatial resolution with 10 - 25 km grid-step in order to reproduce the inertial (Kolmogorov) turbulence range. The observational data require an averaging procedure to remove noise and potential instrumental artifacts. The resulting kinetic energy spectra show a good agreement between the simulations and observations, opening new perspectives for detailed joint analysis of more complex turbulent phenomena on the Sun, and possibly on other stars. In addition, using the simulations and observations we investigate effects of background magnetic field, which is concentrated in self-organized complicated structures in intergranular lanes, and find an increase of the small-scale turbulence energy and its decrease at larger scales due to magnetic field effects.
The current understanding of the turbulent dissipation in stellar convective zones is based on the assumption that the turbulence follows Kolmogorov scaling. This assumption is valid for some cases in which the time frequency of the external shear is high (e.g., solar p modes). However, for many cases of astrophysical interest (e.g., binary orbits, stellar pulsations, etc.), the timescales of interest lie outside the regime of applicability of Kolmogorov scaling. We present direct calculations of the dissipation efficiency of the turbulent convective flow in this regime, using simulations of anelastic convection with external forcing. We show that the effects of the turbulent flow are well represented by an effective viscosity coefficient, we provide the values of the effective viscosity as a function of the perturbation frequency and compare our results to the perturbative method for finding the effective viscosity of Penev et al. that can be applied to actual simulations of the surface convective zones of stars.
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