Astronomical hydrodynamics is usually almost ideal in the sense that the Reynolds number (Re) is enormous and any effective viscosity must be due to shocks or turbulence. Astronomical magnetohydrodynamics (MHD) is often also nearly ideal, so that magnetic fields and plasma are well coupled. In particular, dissipation of orbital energy in accretion disks around black holes is readily explained by MHD turbulence. On the other hand, the planet-bearing disks around protostars are magnetically far from ideal because of very low fractional ionization. MHD turbulence is at best marginal in these disks, yet accretion is observed. The Reynolds numbers based on orbital-velocity gradients are enormous, so by analogy with high-Re terrestrial flows, one might expect hydrodynamic (i.e., unmagnetized) turbulence. Direct numerical simulations indicate that such turbulence is somehow suppressed by keplerian rotation, though the mechanism is
unclear and the simulations are limited in Re. Recently, a few groups have studied the question via Taylor-Couette experiments at somewhat higher Re, obtaining conflicting results. Complicating and enriching this debate is the recent discovery that turbulence tends to have a finite lifetime in shear flows that admit a formally linearly stable laminar solution: this includes flow in smooth pipes and probably also unmagnetized keplerian disks. Some suggestions will be offered as to how these open questions might be resolved.