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The modal analysis techniques face difficulties in handling nonstationaryphenomena. This paper presents a variational mode decomposition-basednonstationary coherent structure (VMD-NCS) analysis that enables the extractionand analysis of coherent structures in case of nonstationary phenomena fromhigh-dimensional spatiotemporal data. The VMD-NCS analysis decomposes the inputspatiotemporal data into intrinsic coherent structures (ICSs) that representnonstationary spatiotemporal patterns and exhibit coherence in both the spatialand temporal directions. Furthermore, unlike many conventional modal analysistechniques, the proposed method accounts for the temporal changes in thespatial distribution with time. The performance of the VMD-NCS analysis wasvalidated based on the transient growth phenomena in the flow around acylinder. It was confirmed that the temporal changes in the spatialdistribution, depicting the transient growth of vortex shedding wherefluctuations arising in the far-wake region gradually approach the near-wakeregion, were represented as a single ICS. Further, in the analysis of thequasi-periodic flow field around a pitching airfoil, the temporal changes inthe spatial distribution and the amplitude of vortex shedding behind theairfoil, influenced by the pitching motion of the airfoil, were captured as asingle ICS. Additionally, the impact of two parameters, adjusting the number ofICSs ($K$) and the penalty factor related to the temporal coherence ($\alpha$),was investigated. The results revealed that $K$ has a significant impact on theVMD-NCS analysis results. In the case of a relatively high $K$, the VMD-NCSanalysis tends to extract more periodic spatiotemporal patterns resembling theresults of dynamic mode decomposition, whereas in the case of a small $K$, theanalysis tends to extract more nonstationary spatiotemporal patterns.

Variational Mode Decomposition-Based Nonstationary Coherent Structure Analysis for Spatiotemporal Data