Time-localized analytic resolvent analysis

This talk will develop an analytic framework for studying time-localized linear energy amplification mechanisms in wall-bounded turbulent flows. In this approach, the standard Fourier temporal expansion used in the resolvent framework is modified to instead consider localized temporal wavepackets, taking the form of Gabor wavelets. We show that temporal wavepackets with this structure (corresponding to Fourier modes modulated by Gaussian envelopes) naturally emerge when the singular value decomposition used in resolvent analysis is modified to promote sparse-in-time modes. We will demonstrate that an analytic formulation of resolvent analysis can be extended to consider such time-localized wavepackets, and will compare analytic predictions to numerical findings concerning the dependence of mode structure and amplification on the extent of time-localization. We will discuss connections to empirical and theoretical findings concerning the existence of spatial wavepackets with similar structure, and will also comment on the potential application of this method to non-statistically-stationary flows.