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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.

Turbulent boundary layer control via a streamwise travelling wave is investigated based on direct numerical simulation of an incompressible turbulent channel Sow. The streamwise travelling wave is induced on one side wall of the channel by a spanwise external force, e.g., Lorenz force, which is confined in the viscous sublayer. As the control strategy used in this study has never been examined, we pay our attention to its efficiency of drag control. It is revealed that the propagating direction of the travelling wave, i.e., the downstream or upstream propagating direction with respect to the streamwise Bow, has an important role on the drag control, leading to a significant drag reduction or enhancement for the parameters considered. The coherent structures of turbulent boundary layer are altered and the underlying mechanisms are analysed. The results obtained provide physical insight into the understanding of turbulent boundary layer control.

A fully developed compressible turbulent flow in a channel with a lower wavy wall and a upper plane wall is studied using large eddy simulation. We mainly attempt to deal with the curvature effect on compressible turbulent flow over the wavy wall. Some typical quantities including the mean turbulence statistics, dilatation and baroclinic terms in the enstrophy equation, turbulent kinetic energy budgets and the near-wall turbulent structures are analysed. The results obtained in this study provide physical insight into the understanding of the effects of curvature and compressibility on wall-bounded compressible turbulent flow.