Chaos and unstable periodic orbits in subcritical Taylor-Couette flow*

Although spectral approximation of turbulence typically requires a large number of modes, for relatively low Reynolds numbers the turbulent attractor lies on a low-dimensional manifold in phase space. The most extreme case is when the main features of the chaotic attractor can be quantified by a one-dimensional map on Poincaré section. We find this can indeed happen in subcritical Taylor-Couette flow, which should offer an important test case for connecting turbulence and periodic orbit analysis.