  The conventional modal analysis techniques face difficulties in handling
nonstationary phenomena, such as transient, nonperiodic, or intermittent
phenomena. This paper presents a variational mode decomposition--based
nonstationary coherent structure (VMD-NCS) analysis that enables the extraction
and analysis of coherent structures in the case of nonstationary phenomena from
high-dimensional spatiotemporal data. The VMD-NCS analysis decomposes the input
spatiotemporal data into intrinsic coherent structures (ICSs) that represent
nonstationary spatiotemporal patterns and exhibit coherence in both spatial and
temporal directions. Unlike many conventional modal analysis techniques, the
proposed method accounts for the temporal changes in the spatial distribution
with time. Tthe VMD-NCS analysis was validated based on the transient growth
phenomena in the flow around a cylinder. It was confirmed that the temporal
changes in the spatial distribution, depicting the transient growth of vortex
shedding where fluctuations arising in the far-wake region gradually approach
the near-wake region, were represented as a single ICS. Furthermore, in the
analysis of the quasi-periodic flow field around a pitching airfoil, the
temporal changes in the spatial distribution and the amplitude of vortex
shedding behind the airfoil, influenced by the pitching motion of the airfoil,
were captured as a single ICS. The impact of two parameters that control the
number of ICSs ($K$) and the penalty factor related to the temporal coherence
($\alpha$), was investigated. The results revealed that $K$ has a significant
impact on the VMD-NCS analysis results. In the case of a relatively high $K$,
the VMD-NCS analysis tends to extract more periodic spatiotemporal patterns
resembling the results of dynamic mode decomposition. In the case of a small
$K$, it tends to extract more nonstationary spatiotemporal patterns.
