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

(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 statistics convective flows and energy transport as functions number. Methods: Three-dimensional numerical simulations Cartesian geometry are used. zone (CZ) embedded between two stably stratified layers. Statistics properties up- downflows studied separately. Results: rms velocity increases with decreasing At same time filling factor decreases leads stronger at lower numbers, a strong dependence overshooting on Velocity power spectra do not show marked changes function highest Reynolds numbers compatible Bolgiano-Obukhov $k^{-11/5}$ scaling. horizontally averaged convected flux ($\overline{F}_{\rm conv}$) independent number within CZ. However, upflows (downflows) dominant contribution low (high) These results similar those from Rayleigh-Ben\'ard regime where vigorously turbulent but inefficient transporting energy. Conclusions: current indicate Numerical astrophysical often use unity. suggest that this can lead misleading astrophysically relevant qualitatively different parameters regimes explored typical simulations.