  We simulate numerically Boussinesq convection in non-rotating spherical
shells for a fluid with a unity Prandtl number and Rayleigh numbers up to
$10^9$. In this geometry, curvature and radial variations of the gravitationnal
acceleration yield asymmetric boundary layers. A systematic parameter study for
various radius ratios (from $\eta=r_i/r_o=0.2$ to $\eta=0.95$) and gravity
profiles allows us to explore the dependence of the asymmetry on these
parameters. We find that the average plume spacing is comparable between the
spherical inner and outer bounding surfaces. An estimate of the average plume
separation allows us to accurately predict the boundary layer asymmetry for the
various spherical shell configurations explored here. The mean temperature and
horizontal velocity profiles are in good agreement with classical
Prandtl-Blasius laminar boundary layer profiles, provided the boundary layers
are analysed in a dynamical frame, that fluctuates with the local and
instantaneous boundary layer thicknesses. The scaling properties of the Nusselt
and Reynolds numbers are investigated by separating the bulk and boundary layer
contributions to the thermal and viscous dissipation rates using numerical
models with $\eta=0.6$ and a gravity proportional to $1/r^2$. We show that our
spherical models are consistent with the predictions of Grossmann \& Lohse's
(2000) theory and that $Nu(Ra)$ and $Re(Ra)$ scalings are in good agreement
with plane layer results.
