  Turbulent flows exhibit wide ranges of time and length scales. Their
small-scale dynamics is well understood, but less is known about the mechanisms
governing the dynamics of large-scale coherent motions in the flow field. We
perform direct numerical simulations of axisymmetric Taylor--Couette flow and
show that beyond a critical domain size, the largest structures (turbulent
Taylor rolls) undergo erratic drifts evolving on a viscous time scale. We
estimate a diffusion coefficient for the drift and compare the dynamics to
analogous motions in Rayleigh--B\'enard convection and Poiseuille flow. We
argue that viscous processes govern the lateral displacement of large coherent
structures in wall-bounded turbulent flows.
