  (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 ($\overline{F}_{\rm conv}$) 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-Ben\'ard 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.

Solar and Stellar Astrophysics;Fluid Dynamics