The purpose of present work was to observe isolated mixing regions (IMRS) under laminar flow conditions in a Taylor-vortex-flow reactor with the aspect ratio Gamma=2. In the range less than Re=200, the IMRs took clearly the form of two toroidal vortices, one each in the upper and lower circulating flows. A simple core torus was observed in the case of a rotating inner cylinder with smooth surface, while a set of thin tori spirally wrapping around the core of the IMR was observed in the case of an inner cylimder with surface protrusions. Different numbers of tori were obtained for different numbers of protrusions, even at nearly the same Reynolds number. Hence, it can be considered that these structures of IMR depend on periodical perturbations caused by the rotating inner cylinder with protrusions. Numerical investigation using a Lagragian procedure determined the number of perturbations, n(e), during one revolution of a marker particle around the IMR. It was found that n(e) corresponded to the number of thin tori. This indicates that the Poincare-Birkhoff theorem is applicable to the geometrical structures of the IMRs.