  We obtain lower limits on the amplitude of convective velocities in the deep
solar convection zone based only on the observed properties of the differential
rotation and meridional circulation together with simple and robust dynamical
balances obtained from the fundamental MHD equations. The linchpin of the
approach is the concept of gyroscopic pumping whereby the meridional
circulation across isosurfaces of specific angular momentum is linked to the
angular momentum transport by the convective Reynolds stress. We find that the
amplitude of the convective velocity must be at least 30 m s$^{-1}$ in the
upper CZ ($r \sim 0.95 R$) and at least 8 m s$^{-1}$ in the lower CZ ($r \sim
0.75 R$) in order to be consistent with the observed mean flows. Using the base
of the near-surface shear layer as a probe of the rotational influence, we are
further able to show that the characteristic length scale of deep convective
motions must be no smaller than 5.5--30 Mm. These results are compatible with
convection models but suggest that the efficiency of the turbulent transport
assumed in advection-dominated flux-transport dynamo models is generally not
consistent with the mean flows they employ.
