Wavelet-based resolvent analysis of temporally-varying turbulent flows

In this work, we reformulate resolvent analysis and adapt it to the study of transient flows with a time-varying mean state. In our formulation, the resolvent operator links input and output states that have been wavelet-transformed rather than Fourier-transformed in time, which preserves both temporal and frequency information in the system. We validate this methodology for traditional turbulent channel flow and show that the wavelet-based and Fourier-based resolvent analyses are equivalent for statistically-stationary flows. We then apply wavelet-based resolvent analysis to temporally-evolving parallel shear flows such as an oscillating boundary layer and three-dimensional channel flow.