A modified proper orthogonal decomposition method for flow dynamic analysis

•A single-frequency Proper Orthogonal Decomposition (F-POD) method is proposed;•F-POD is based on Discrete Fourier Transform and corresponding inverse operation;•The method is validated by analytical cases and a cylinder wake case;•The dynamic structures with single-frequency and growth rate are obtained;•F-POD is better than Dynamic Mode Decomposition for the transient flow field. The numerical analysis method of Proper Orthogonal Decomposition (POD) is usually used to decompose the correlated nonlinear flow field and extract the structures with maximum energy contents (also called POD modes). However, it tends to mix the temporal frequencies in most modes, which confuses the physical interpretation and makes the flow dynamic characteristics unclear. For the transient flow field with discrete frequencies, to obtain the coherent structures with single-frequency dynamic characteristics, a new single-frequency POD method (F-POD) is proposed by utilizing Discrete Fourier Transform (DFT) and the corresponding inverse operation. In this way, the POD modes can be re-decomposed from the perspective of frequency. Particularly, for the spectra with a band of adjacent frequencies around some isolated peaks, the selection criterion of the frequency range in the inverse operation process is discussed to obtain the growth rate information of the modes. To illustrate the feasibility of F-POD, several multi-frequencies analytical cases with various growth patterns and a transitional cylinder wake case are investigated. In addition, the results are quantitatively compared with dynamic mode decomposition (DMD). It shows that the single-frequency POD modes with temporal evolutions can be well distinguished. Therefore, for the transitional flow scenarios with discrete frequencies, the F-POD could be an alternative method to extract the dynamic coherent structure with single-frequency and growth rate. We also found that the F-POD has challenges to deal with broadband turbulence, since it is hard to find main frequency.