  The direct numerical simulation (DNS) of the Taylor--Couette flow in the
fully turbulent regime is described. The numerical method extends the work by
Quadrio & Luchini (Eur. J. Mech. B / Fluids, v.21, pp.413--427, 2002), and is
based on a parallel computer code which uses mixed spatial discretization
(spectral schemes in the homogeneous directions, and fourth-order, compact
explicit finite-difference schemes in the radial direction). A DNS is carried
out to simulate for the first time the turbulent Taylor--Couette flow in the
turbulent regime. Statistical quantities are computed to complement the
existing experimental information, with a view to compare it to planar,
pressure-driven turbulent flow at the same value of the Reynolds number. The
main source for differences in flow statistics between plane and curved-wall
flows is attributed to the presence of large-scale rotating structures
generated by curvature effects.
