Mode-clustering dynamic mode decomposition method for spatial-temporal multi-scale instantaneous flow fields

Xiaojian Li

doi:10.1007/s10409-026-25945-x

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Mode-clustering dynamic mode decomposition method for spatial-temporal multi-scale instantaneous flow fields

2026-09-10

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DOI：10.1007/s10409-026-25945-x

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Abstract

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Dynamic mode decomposition (DMD) is one of powerful tools for flow field data analysis. For spatial-temporal multi-scale instantaneous flow fields, the DMD modes possess broadband spectral characteristics, and they always carry similar spatial and temporal features with closed physical meanings. However, it is commonly time-consuming and low-precise to manually identify and distinguish these similar modes. To solve the problem, this study innovatively proposes a DMD variant named as mode-clustering dynamic mode decomposition (MC-DMD). Firstly, a mode similarity criterion is defined based on mode spatial-temporal similarity to identify flow structures with the same physical meaning. Secondly, a mode feature identification method is proposed, and the K-means++ algorithm is introduced to obtain mode clusters containing similar modes. Thirdly, the energy of a mode cluster is defined, and a new ranking criterion of mode clusters is proposed to achieve efficient identification of flow field structures. Finally, the effectiveness of MC-DMD method in mode feature extraction, similarity mode classification, and flow field structure identification is verified through three typical cases.

Keywords:

Dynamic mode decomposition

Spatial-temporal similar mode

Mode feature identification

Mode clustering analysis

Mode clustering ranking