  A novel data-driven method of modal analysis for complex flow dynamics,
termed as reduced-order variational mode decomposition (RVMD), has been
proposed, combining the idea of the separation of variables and a
state-of-the-art nonstationary signal-processing technique -- variational mode
decomposition. It enables a low-redundant adaptive extraction of coherent
structures in statistically nonstationary flows, with its modes computed by
solving an elaborate optimization problem using the block coordinate descent
algorithm. Discussion on the intrinsic relations between RVMD and some classic
modal decomposition methods demonstrates that RVMD can be reduced into proper
orthogonal decomposition (POD) or discrete Fourier transform (DFT) at
particular parameter settings. The significant advantages of RVMD for
performing time-frequency analysis are highlighted by a signal-processing
analogous categorization of the widely-used modal decomposition techniques. It
is also confirmed that the combination of RVMD and the Hilbert spectral
analysis provides a physically intuitive way to explore the
space-time-frequency characteristics of transient dynamics. Finally, all the
appealing features of RVMD mentioned above are well verified via two canonical
flow problems: the transient cylinder wake and the rectangular turbulent
supersonic screeching jet.

Fluid Dynamics