Kernel Mode Decomposition for Time-Frequency Localization of Transient Flow

Kernel mode decomposition (KMD) is a powerful method to identify modes with varying amplitude and frequency. This work aims to extend this technique to study different fluid problems with transient responses to reveal and evolve the relevant spatial structures. The results are compared to other modal decomposition methods and show good agreement in the spatial modes, while the proposed KMD method is capable of isolating the important scales inherently. The KMD works with any signal by comparing the input to very fine modes then combine the fine modes based on the extent of alignment to recover the dominant components. The many benefits of KMD include that it does not involve any learning process, it is modular and interpretable with each step being mathematically derived, and it is easy to modify for different scenarios such as using different base waveforms as the fine modes.