Abstract

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.

Highlights

  • Flow fields of jets and wakes usually contain coherent structures that possess various spatial and temporal scales

  • The DMD is widely used to extract flow structures,11,12 and the usefulness of proper orthogonal decomposition (POD) and DMD is sometimes compared in analyzing the same flow

  • We examine the POD modes and the recurrence of flow dynamics in the phase space to analyze the temporal features of coherent structures

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Summary

Introduction

Flow fields of jets and wakes usually contain coherent structures that possess various spatial and temporal scales. Vortices can be captured using the Q-criterion, swirling strength, or λ2 method.1,2 These methods are widely used to study turbulence and engineering flows. To extract general flow structures from a complex flow without relying on any conditional criterion, the proper orthogonal decomposition (POD) is used in fluid dynamics.. The POD extracts flow modes based on spatial correlation. These modes are the orthogonal basis of a vector space. They can be regarded as the spatial distribution of coherent structures. The DMD is widely used to extract flow structures, and the usefulness of POD and DMD is sometimes compared in analyzing the same flow.

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