Numerical Analysis of Nonlocal Convection --- Comparison with Three-dimensional Numerical Simulations of Efficient Turbulent Convection

Abstract

We compare 1D nonlocal turbulent convection models with 3D hydrodynamic numerical simulations. We study the validity of closure models and turbulent coefficients by varying the Prandtl number, the P$\acute{e}$clet number, and the depth of the convection zone. Four closure models of the fourth-order moments are evaluated with the 3D simulation data. The performance of the closure models varies among different cases and different fourth-order moments. We solve the dynamic equations of moments together with equations of the thermal structure. Unfortunately, we cannot obtain steady-state solutions when these closure models of fourth-order moments are adopted. The numerical solutions of the down-gradient approximations of the third-order moments, on the other hand, are robust. We calibrate the coefficients of the 1D down-gradient model from the 3D simulation data. The calibrated coefficients are more robust in the cases of deep convection zones. Finally we have compared the 1D steady-state solutions with the 3D simulation results. The 1D model has captured many features appearing in the 3D simulations : (1) $\nabla -{\nabla }_a$ has a U-shape with a minimum value at the lower part of the convection zone. (2) There exists a bump for $\nabla -{\nabla }_a$ near the top of the convection zone when the P$\acute{e}$clet number is large. (3) The temperature gradient can be sub-adiabatic due to the nonlocal effect. Apart from these similarities, the prediction on the kinetic energy flux, however, is unsatisfactory.

arXiv comment39 pages, 21 figures, accepted for publication by ApJ

References in corpus (12)

• Scaling in thermal convection: A unifying theory
• 3D convection simulations of the outer layers of the Sun using realistic physics
• The Solar-Stellar Connection
• A-star envelopes: a test of local and non-local models of convection
• Solar overshoot region and small-scale dynamo with realistic energy flux
• A Theory of Non-Local Mixing Length Convection. III. Comparing Theory and Numerical Experiment
• Turbulent convection: comparing the moment equations to numerical simulations
• A k-omega model for stellar turbulent convection
• Empirical Constraints on Convective Core Overshoot
• A model of the entropy flux and Reynolds stress in turbulent convection
• White dwarf envelopes: further results of a non-local model of convection
• 3D stellar atmospheres for stellar structure models and asteroseismology

Cited by in corpus (5)

• Broadband reflection spectroscopy of MAXI J1535-571 using AstroSat: Estimation of black hole mass and spin
• Overshooting in simulations of compressible convection
• Upward Overshooting in Turbulent Compressible Convection. III. Calibrate Parameters for One-dimensional Reynolds Stress Model
• Spontaneous Generated Convective Anticyclones in Low Latitude -- A Model for the Great Red Spot
• Third order correlations and skewness in convection. I. A new approach suitable for three-equation non-local models