Fourier mode decomposition of PIV data

The modal decomposition technique is one of the most effective methods for studying the flow dynamics in a complex flow. By rejuvenating the discrete Fourier transform (DFT), this paper proposes a Fourier mode decomposition (FMD) method for the time series of particle image velocimetry (PIV) data from the fluid field. An experimental case concerning the control of the flow around a circular cylinder by a synthetic jet positioned at the rear stagnation point is used to demonstrate the use of the FMD method. In the three different regimes where the natural shedding frequency and actuation frequency dominate respectively or simultaneously, it is found that the FMD method is capable of extracting the dynamic mode along with its amplitude and phase according to the selected characteristic frequency based on the global power spectrum. For the quasiperiodic flow phenomena presented in this particular case, the FMD method can reconstruct the original flow field using the zero-th mode and the selected mode corresponding to the characteristic frequency. Similarities and differences between the FMD method and the dynamical mode decomposition (DMD) and proper orthogonal decomposition (POD) methods are also discussed.