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Register a new userTurbulent transport of radiation in the solar convective zone
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A turbulent transport of radiation in the solar convective zone is investigated. The mean-field equation for the irradiation intensity is derived. It is shown that due to the turbulent effects, the effective penetration length of radiation can be increased in several times in comparison with the mean penetration length of radiation (defined as an inverse mean absorption coefficient). Using the model of the solar convective zone based on the mixing length theory, where the mean penetration length of radiation is usually much smaller than the turbulent correlation length, it is demonstrated that the ratio of the effective penetration length to the mean penetration length of radiation increases in 2.5 times in the vicinity of the solar surface. The main reason are the compressibility effects that become important in the vicinity of the solar surface where temperature and density fluctuations increase towards the solar surface, enhancing fluctuations of the radiation absorption coefficient and increasing the effective penetration length of radiation.
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(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.
The Sun, aside from its eleven year sunspot cycle is additionally subject to long term variation in its activity. In this work we analyse a solar-like convective dynamo simulation, containing approximately 60 magnetic cycles, exhibiting equatorward propagation of the magnetic field, multiple frequencies, and irregular variability, including a missed cycle and complex parity transitions between dipolar and quadrupolar modes. We compute the turbulent transport coefficients, describing the effects of the turbulent velocity field on the mean magnetic field, using the test-field method. The test-field analysis provides a plausible explanation of the missing cycle in terms of the reduction of $alpha_{phiphi}$ in advance of the reduced surface activity, and enhanced downward turbulent pumping during the event to confine some of the magnetic field at the bottom of the convection zone, where local maximum of magnetic energy is observed during the event. At the same time, however, a quenching of the turbulent magnetic diffusivities is observed, albeit differently distributed in depth compared to the other transport coefficients. Therefore, dedicated mean-field modelling is required for verification.
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.
The effect of oscillatory shear flows on turbulent transport of passive scalar fields is studied by numerical computations based on the results provided by E. Kim [emph{Physics of Plasmas}, {bf 13}, 022308, 2006]. Turbulent diffusion is found to depend crucially on the competition between suppression due to shearing and enhancement due to resonances, depending on the characteristic time and length scales of shear flow and turbulence. Enhancements in transport occur for turbulence with finite memory time either due to Doppler and parametric resonances. Scalings of turbulence amplitude and transport are provided in different parameter spaces. The results suggest that oscillatory shear flows are not only less efficient in regulating turbulence, but also can enhance the value of turbulent diffusion, accelerating turbulent transport.
Stars of sufficiently low mass are convective throughout their interiors, and so do not possess an internal boundary layer akin to the solar tachocline. Because that interface figures so prominently in many theories of the solar magnetic dynamo, a widespread expectation had been that fully convective stars would exhibit surface magnetic behavior very different from that realized in more massive stars. Here I describe how recent observations and theoretical models of dynamo action in low-mass stars are partly confirming, and partly confounding, this basic expectation. In particular, I present the results of 3--D MHD simulations of dynamo action by convection in rotating spherical shells that approximate the interiors of 0.3 solar-mass stars at a range of rotation rates. The simulated stars can establish latitudinal differential rotation at their surfaces which is solar-like at ``rapid rotation rates (defined within) and anti-solar at slower rotation rates; the differential rotation is greatly reduced by feedback from strong dynamo-generated magnetic fields in some parameter regimes. I argue that this ``flip in the sense of differential rotation may be observable in the near future. I also briefly describe how the strength and morphology of the magnetic fields varies with the rotation rate of the simulated star, and show that the maximum magnetic energies attained are compatible with simple scaling arguments.
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