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.

15 pages, 20 figures, submitted to Astron. Astrophys

References in corpus (14)

• 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
• A simulation of convective dynamo in the solar convective envelope: maintenance of the solar-like differential rotation and emerging flux
• Global and local statistics in turbulent convection at low Prandtl numbers
• Helioseismic Imaging of Fast Convective Flows Throughout the Near-Surface Shear Layer
• Calibration of the Mixing-Length Theory for Convective White Dwarf Envelopes
• Efficient small-scale dynamo in solar convection zone
• Solar overshoot region and small-scale dynamo with realistic energy flux
• Star-in-a-box simulations of fully convective stars
• Effect of the radiative background flux in convection
• Convective velocity suppression via the enhancement of subadiabatic layer: Role of the effective Prandtl number
• On global solar dynamo simulations
• Power spectrum of turbulent convection in the solar photosphere

Cited by in corpus (9)

• Stellar convective penetration: parameterized theory and dynamical simulations
• Convective mesoscale turbulence at very low Prandtl numbers
• Transition from anti-solar to solar-like differential rotation: Dependence on Prandtl number
• Modelling stellar convective transport with plumes: I. Non-equilibrium turbulence effect in double-averaging formulation
• 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 $\mathbf{Pr}=10^{-3}$