Classification of spatial-temporal flow patterns in a low Re wake based on the recurrent trajectory clustering

Abstract

Coherent structures are ubiquitous in unsteady flows. They can be regarded as certain kinds of spatial-temporal patterns that interact with the neighboring field. Although they play a key role in convection and mixing, there is no consensus on how to define them, and their dynamics are complicated. In the past decades, many methods are developed to identify coherent structures based on instantaneous velocity fields (e.g., vortex identification) or long-time statistics (e.g., proper orthogonal decomposition), but the evolution process of individual structures is not well considered in the identification. In this paper, we propose a new method to classify coherent motions according to their evolution dynamics. Specifically, the evolutions are represented by trajectories in the phase space. We define a distance between two trajectories and use it to construct a network that characterizes all evolution patterns. Using spectrum clustering, we categorize these patterns into various groups. This method is applied to a low Reynolds number wake flow downstream of two cylinders-in-tandem, where one of the cylinders oscillates in the transverse direction. The flow is quasi-periodic, and four types of recurrent spatial-temporal patterns can be identified. It is a useful tool to investigate low Reynolds number unsteady flows.