Direct Numerical Simulation of turbulent Taylor–Couette flow

The Direct Numerical Simulation (DNS) of the Couette–Taylor flow in the fully turbulent regime is described. Following Quadrio & Luchini (Eur. J. Mech. B / Fluids, 21, 413–427, 2002), the in-compressible Navier–Stokes equations in cylindrical coordinates are transformed into two scalar equations for the radial component of velocity and vorticity vectors, with the divergence-free condition accounted for implicitely. The spatial discretization is mixed, with spectral schemes in the homogeneous directions, and finite differences in the radial direction. Main improvements are the use of fourth-order, compact explicit finite-differences schemes, and an innovative parallel strategy designed to obtain high parallel performance on a distributed/shared memory machine made by personal computers. A computationally demanding DNS is then carried out to sim-ulate for the first time the Taylor–Couette flow in the turbulent regime. Statistical quantities are computed to complement the existing experimental information available for the turbulent Taylor–Couette flow, 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 be-tween plane and curved-wall flows is attributed to the presence of large-scale vortical structures generated by curvature effects. 1