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This work introduces a variant of resolvent analysis that identifies forcingand response modes that are sparse in both space and time. This is achievedthrough the use of a sparse principal component analysis (PCA) algorithm, whichformulates the associated optimization problem as a nonlinear eigenproblem thatcan be solved with an inverse power method. We apply this method to parallelshear flows, both in the case where we assume Fourier modes in time (as instandard resolvent analysis) and obtain spatial localization, and where weallow for temporally-sparse modes through the use of a linearized Navier-Stokesoperator discretized in both space and time. Appropriate choice of desired modesparsity allows for the identification of structures corresponding to highamplification that are localized in both space and time. We report on thesimilarities and differences between these structures and those from standardmethods of analysis. After validating this space-time resolvent analysis onstatistically-stationary channel flow, we next implement the methodology on atime-periodic Stokes boundary layer, demonstrating the applicability of theapproach to non-statistically-stationary systems.

A sparsity-promoting resolvent analysis for the identification of spatiotemporally-localized amplification mechanisms