A Time–frequency Modal Decomposition for the Analysis of Non-stationary Separated Flow

Fluid motion, especially at relatively high Reynolds numbers, often presents non-stationary dynamics characterized by the evolution of the statistical description of the flow and its fluctuations over time, which may arise from external changes in the flow configuration or from the presence of intermittent or transient physical processes. Variational mode decomposition (VMD) is a time–frequency analysis framework that separates a scalar signal into independent amplitude- and frequency-modulated components, each characterized by a finite frequency bandwidth. This paper extends the VMD with two refinements, found to be necessary to ensure the robustness of the technique when applied to fluid flows: (i) the incorporation of orthogonality-promoting objectives into the determination of the modes and (ii) the determination of each mode's frequency bandwidth based on the data. The proposed method, multivariate orthogonalized variational mode decomposition (OVMD), is applied to different cases, including the transient development of a cylinder wake and separated flow over a wall-mounted bump under a harmonic change of the inlet bulk velocity. Each case corresponds to a different scenario of non-stationary flow dynamics. The results illustrate the potential of OVMD in analyzing and modeling flows involving non-stationary dynamical processes.