No Arabic abstract
We present numerical simulations of hydrodynamic overshooting convection in local Cartesian domains. We find that a substantial fraction of the lower part of the convection zone (CZ) is stably stratified according to the Schwarzschild criterion while the enthalpy flux is outward directed. This occurs when the heat conduction profile at the bottom of the CZ is smoothly varying, based either on a Kramers-like opacity prescription as a function of temperature and density or a static profile of a similar shape. We show that the subadiabatic layer arises due to nonlocal energy transport by buoyantly driven downflows in the upper parts of the CZ. Analysis of the force balance of the upflows and downflows confirms that convection is driven by cooling at the surface. We find that the commonly used prescription for the convective enthalpy flux being proportional to the negative entropy gradient does not hold in the stably stratified layers where the flux is positive. We demonstrate the existence of a non-gradient contribution to the enthalpy flux, which is estimated to be important throughout the convective layer. A quantitative analysis of downflows indicates a transition from a tree-like structure where smaller downdrafts merge into larger ones in the upper parts to a structure in the deeper parts where a height-independent number of strong downdrafts persist. This change of flow topology occurs when a substantial subadiabatic layer is present in the lower part of the CZ.
One of the largest sources of uncertainty in stellar models is caused by the treatment of convection in stellar envelopes. One dimensional stellar models often make use of the mixing length or equivalent approximations to describe convection, all of which depend on various free parameters. There have been attempts to rectify this by using 3D radiative-hydrodynamic simulations of stellar convection, and in trying to extract an equivalent mixing length from the simulations. In this paper we show that the entropy of the deeper, adiabatic layers in these simulations can be expressed as a simple function of og g and log T_{eff} which holds potential for calibrating stellar models in a simple and more general manner.
It has recently been recognized that the convective velocities achieved in the current solar convection simulations might be over-estimated. The newly-revealed effects of the prevailing small-scale magnetic field within the convection zone may offer possible solutions to this problem. The small-scale magnetic fields can reduce the convective amplitude of small-scale motions through the Lorentz-force feedback, which concurrently inhibits the turbulent mixing of entropy between upflows and downflows. As a result, the effective Prandtl number may exceed unity inside the solar convection zone. In this paper, we propose and numerically confirm a possible suppression mechanism of convective velocity in the effectively high-Prandtl number regime. If the effective horizontal thermal diffusivity decreases (the Prandtl number accordingly increases), the subadiabatic layer which is formed near the base of the convection zone by continuous depositions of low entropy transported by adiabatically downflowing plumes is enhanced and extended. The global convective amplitude in the high-Prandtl thermal convection is thus reduced especially in the lower part of the convection zone via the change in the mean entropy profile which becomes more subadiabatic near the base and less superadiabatic in the bulk.
The extent of mixed regions around convective zones is one of the biggest uncertainties in stellar evolution. 1D overshooting descriptions introduce a free parameter ($f_{ov}$) that is in general not well constrained from observations. Especially in small central convective regions the value is highly uncertain due to its tight connection to the pressure scale height. Long-term multi-dimensional hydrodynamic simulations can be used to study the size of the overshooting region and the involved mixing processes. Here we show how one can calibrate an overshooting parameter by performing 2D Maestro simulations of Zero-Age-Main-Sequence stars ranging from $1.3$ to $3.5 M_odot$. The simulations cover the convective cores of the stars and a large fraction of the surrounding radiative envelope. We follow the convective flow for at least 20 convective turnover times, while the longest simulation covers 430 turnover time scales. This allows us to study how the mixing as well as the convective boundary evolve with time, and how the resulting entrainment can be interpreted in terms of overshooting parameters. We find that increasing the overshooting parameter $f_{ov}$ beyond a certain value in the initial model of our simulations, changes the mixing behaviour completely. This result can be used to put limits on the overshooting parameter. We find $0.010 < f_{ov} < 0.017$ to be in good agreement with our simulations of a $3.5 M_odot$ mass star. We also identify a diffusive mixing component due to internal gravity waves (IGW) that is active throughout the convectively stable layer, but likely overestimated in our simulations. Furthermore, applying our calibration method to simulations of less massive stars suggests a need for a mass-dependent overshooting description where the mixing in terms of the pressure scale height is reduced for small convective cores.
In this paper, we calibrate the coefficients for the one-dimensional Reynolds stress model with the data generated from the three-dimensional numerical simulations of upward overshooting in turbulent compressible convection. It has been found that the calibrated convective and isotropic coefficients are almost the same as those calibrated in the pure convection zone. However, the calibrated diffusive coefficients differ significantly from those calibrated in the pure convection zone. We suspect that the diffusive effect induced by the boundary is stronger than by the adjacent stable zone. We have checked the validity of the downgradient approximation. We find that the prediction of the downgradient approximation on the third-order moments is unsatisfactory. However, the prediction on their derivatives is much better. It explains why the performance of the Reynolds stress model is reasonable in application to the real stars. With the calibrated coefficients, we have solved the full set of nonlocal turbulent equations on Reynolds stress model. We find that the Reynolds stress model has successfully produced the thermal adjustment layer and turbulent dissipation layer, which were identified in the three-dimensional numerical simulations. We suggest to use the inflection point of the auto-correlation of temperature perturbation and the Peclet number as the indicators on measuring the extents of the thermal adjustment layer and turbulent dissipation layer, respectively. This result may offer a practical guidance on the application of the Reynolds stress model in 1D stellar structure and evolution models.
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.