Proper orthogonal decomposition and recurrence map for the identification of spatial–temporal patterns in a low-Re wake downstream of two cylinders

Flow decomposition methods provide systematic ways to extract the flow modes, which can be regarded as the spatial distribution of a coherent structure. They have been successfully used in the study of wake, boundary layer, and mixing. However, real flow structures also possess complex temporal patterns that can hardly be captured using the spatial modes obtained in the decomposition. In order to analyze the temporal variation of coherent structures in a complex flow field, this paper studies the recurrence in phase space to identify the pattern and classify the evolution of the flow modes. The recurrence pattern depends on the time delay and initial condition. In some cases, the flow system will revisit a previous state regardless of the initial state, and in other cases, the system’s recurrence will depend on the initial state. These patterns are determined by the arrangement and interactions of coherent structures in the flow. The temporal order of the repetition pattern reflects the possible ways of flow evolution.