A double Hopf bifurcation has been found of the flow in a cylinder
driven by the rotation of an endwall. A detailed analysis of the
multiple solutions in a large region of parameter space, computed with
an efficient and accurate three-dimensional Navier-Stokes solver, is
presented. At the double Hopf points, an axisymmetric limit cycle and
a rotating wave bifurcate simultaneously. The corresponding mode
interaction generates an unstable two-torus modulate rotating wave
solutions and gives a wedge-shaped region in parameter space where the
two periodic solutions are both stable. By exploring in detail the
three-dimensional structure of the flow, we have identified the two
mechanisms that compete in the neighborhood of the double Hopf. Both
are associated with the jet that is formed when the Ekman layer on the
rotating endwall is turned by the stationary sidewall.