Prandtl number dependence of compressible convection: Flow statistics and convective energy transport

Abstract

(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 (${\overline{F}}_{\mathrm{conv}}$) 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-Benárd 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.

arXiv comment15 pages, 20 figures, submitted to Astron. Astrophys

References in corpus (34)

• Magnetic field generation in fully convective rotating spheres
• Structure and Evolution of Giant Cells in Global Models of Solar Convection
• The Pencil Code, a modular MPI code for partial differential equations and particles: multipurpose and multiuser-maintained
• Anomalously Weak Solar Convection
• A simulation of convective dynamo in the solar convective envelope: maintenance of the solar-like differential rotation and emerging flux
• Seismic Sounding of Convection in the Sun
• Computational aspects of astrophysical MHD and turbulence
• Global and local statistics in turbulent convection at low Prandtl numbers
• Confirmation of bistable stellar differential rotation profiles
• The Spectral Amplitude of Stellar Convection and its Scaling in the High-Rayleigh-Number Regime
• Helioseismic Imaging of Fast Convective Flows Throughout the Near-Surface Shear Layer
• Evidences of Bolgiano scaling in 3D Rayleigh-Benard convection
• Stellar mixing length theory with entropy rain
• Calibration of the Mixing-Length Theory for Convective White Dwarf Envelopes
• Extended subadiabatic layer in simulations of overshooting convection
• Efficient small-scale dynamo in solar convection zone
• Velocity Amplitudes in Global Convection Simulations: The Role of the Prandtl Number and Near-Surface Driving
• Solar overshoot region and small-scale dynamo with realistic energy flux
• Rossby and Magnetic Prandtl Number Scaling of Stellar Dynamos
• Supergranulation as the largest buoyantly driven convective scale of the Sun
• Consequences of high effective Prandtl number on solar differential rotation and convective velocity
• Overshooting in simulations of compressible convection
• Star-in-a-box simulations of fully convective stars
• Effects of a subadiabatic layer on convection and dynamos in spherical wedge simulations
• Effect of the radiative background flux in convection
• Convective velocity suppression via the enhancement of subadiabatic layer: Role of the effective Prandtl number
• Driving Solar Giant Cells through the Self-Organization of Near-Surface Plumes
• Near-polytropic simulations with a radiative surface
• Weakly non-Boussinesq convection in a gaseous spherical shell
• Physically motivated heat conduction treatment in simulations of solar-like stars: effects on dynamo transitions
• On global solar dynamo simulations
• Prandtl-Number Effects in High-Rayleigh-Number Spherical Convection
• Power spectrum of turbulent convection in the solar photosphere
• Effects of small-scale dynamo and compressibility on the $\Lambda$ effect

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• Turbulent mesoscale convection in the Boussinesq limit and beyond
• Simulations of entropy rain-driven convection
• Small-scale and large-scale dynamos in global convection simulations of solar-like stars
• Instabilities in visco-thermodiffusive swirling flows
• Scale-resolved turbulent Prandtl number for Rayleigh-Bénard convection at $\mathbf{Pr}=10^{-3}$