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Register a new userHelioseismology challenges models of solar convection
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Convection is the mechanism by which energy is transported through the outermost 30% of the Sun. Solar turbulent convection is notoriously difficult to model across the entire convection zone where the density spans many orders of magnitude. In this issue of PNAS, Hanasoge et al. (2012) employ recent helioseismic observations to derive stringent empirical constraints on the amplitude of large-scale convective velocities in the solar interior. They report an upper limit that is far smaller than predicted by a popular hydrodynamic numerical simulation.
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In this study we investigate the effects of turbulent convection on formation of large-scale inhomogeneous magnetic structures by means of Large-Eddy Simulation (LES) for convection in solar-type stars. The main idea of this study is the implementation of a new subgrid-scale model for the effective Lorentz force in a three-dimensional nonlinear radiative magnetohydrodynamics (MHD) code developed for simulating the upper solar convection zone and lower atmosphere. To this end we derived the energy budget equations, which include the effects of the subgrid-scale turbulence on the Lorentz-force, and implemented the new subgrid-scale turbulence model (TELF-Model) in a three-dimensional nonlinear MHD LES code. Using imposed initial vertical and horizontal uniform magnetic fields in LES with the TELF-Model, we have shown that the magnetic flux tubes formation is started when the initial mean magnetic field is larger than a threshold value (about 100 G). This is in agreement with the theoretical studies by Rogachevskii and Kleeorin (2007). We have determined the vertical profiles of the velocity and magnetic fluctuations, total MHD energy and anisotropy of turbulent magneto-convection, kinetic and current and cross helicities.
Small-scale dynamo action is often held responsible for the generation of quiet-Sun magnetic fields. We aim to determine the excitation conditions and saturation level of small-scale dynamos in non-rotating turbulent convection at low magnetic Prandtl numbers. We use high resolution direct numerical simulations of weakly stratified turbulent convection. We find that the critical magnetic Reynolds number for dynamo excitation increases as the magnetic Prandtl number is decreased, which might suggest that small-scale dynamo action is not automatically evident in bodies with small magnetic Prandtl numbers as the Sun. As a function of the magnetic Reynolds number (${rm Rm}$), the growth rate of the dynamo is consistent with an ${rm Rm}^{1/2}$ scaling. No evidence for a logarithmic increase of the growth rate with ${rm Rm}$ is found.
We study the effects of rotation on the growth and saturation of the double-diffusive fingering (thermohaline) instability at low Prandtl number. Using direct numerical simulations, we estimate the compositional transport rates as a function of the relevant non-dimensional parameters - the Rossby number, inversely proportional to the rotation rate, and the density ratio which measures the relative thermal and compositional stratifications. Within our explored range of parameters, we generally find rotation to have little effect on vertical transport. However, we also present one exceptional case where a cyclonic large scale vortex (LSV) is observed at low density ratio and fairly low Rossby number. The LSV leads to significant enhancement in the fingering transport rates by concentrating compositionally dense downflows at its core. We argue that the formation of such LSVs could be relevant to solving the missing mixing problem in RGB stars.
We present the first 3-dimensional, fully compressible gas-dynamics simulations in $4pi$ geometry of He-shell flash convection with proton-rich fuel entrainment at the upper boundary. This work is motivated by the insufficiently understood observed consequences of the H-ingestion flash in post-AGB stars (Sakurais object) and metal-poor AGB stars. Our investigation is focused on the entrainment process at the top convection boundary and on the subsequent advection of H-rich material into deeper layers, and we therefore ignore the burning of the proton-rich fuel in this study. We find that, for our deep convection zone, coherent convective motions of near global scale appear to dominate the flow. At the top boundary convective shear flows are stable against Kelvin-Helmholtz instabilities. However, such shear instabilities are induced by the boundary-layer separation in large-scale, opposing flows. This links the global nature of thick shell convection with the entrainment process. We establish the quantitative dependence of the entrainment rate on grid resolution. With our numerical technique simulations with $1024^3$ cells or more are required to reach a numerical fidelity appropriate for this problem. However, only the result from the $1536^3$ simulation provides a clear indication that we approach convergence with regard to the entrainment rate. Our results demonstrate that our method, which is described in detail, can provide quantitative results related to entrainment and convective boundary mixing in deep stellar interior environments with veryvstiff convective boundaries. For the representative case we study in detail, we find an entrainment rate of $4.38 pm 1.48 times 10^{-13}M_odot mathrm{/s}$.
(abridged) Context: The ratio of kinematic viscosity to thermal diffusivity, the Prandtl number, is much smaller than unity in stellar convection zones. Aims: To study the statistics of convective flows and energy transport as functions of the Prandtl number. Methods: Three-dimensional numerical simulations convection in Cartesian geometry are used. The convection zone (CZ) is embedded between two stably stratified layers. Statistics and transport properties of up- and downflows are studied separately. Results: The rms velocity increases with decreasing Prandtl number. At the same time the filling factor of downflows decreases and leads to stronger downflows at lower Prandtl numbers, and to a strong dependence of overshooting on the Prandtl number. Velocity power spectra do not show marked changes as a function of Prandtl number. At the highest Reynolds numbers the velocity power spectra are compatible with the Bolgiano-Obukhov $k^{-11/5}$ scaling. The horizontally averaged convected energy flux ($overline{F}_{rm conv}$) is independent of the Prandtl number within the CZ. However, the upflows (downflows) are the dominant contribution to the convected flux at low (high) Prandtl number. These results are similar to those from Rayleigh-Benard convection in the low Prandtl number regime where convection is vigorously turbulent but inefficient at transporting energy. Conclusions: The current results indicate a strong dependence of convective overshooting and energy flux on the Prandtl number. Numerical simulations of astrophysical convection often use Prandtl number of unity. The current results suggest that this can lead to misleading results and that the astrophysically relevant low Prandtl number regime is qualitatively different from the parameters regimes explored in typical simulations.
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