Characterizing and categorizing linear amplification mechanisms in non-canonical turbulent flows using sparsity-promoting optimization

Despite their highly nonlinear nature, linear mechanisms are a key component of the dynamics of many highly turbulent flow configurations. While the flow physics associated with coherent structures and mechanisms are generally well understood in canonical flow configurations, the physical origins of coherent structures in more complex flows are comparatively less well understood. In this work, we apply a methodology that determines the terms with governing equations primarily responsible for linear energy amplification at specified spatiotemporal scales. The approach is based on a convex optimization problem, which identifies a minimal set of terms within the governing equations required to reproduce the dominant mechanism exhibited by the full system. We show that the dimensionality of this optimization problem can be greatly reduced by a projection step utilizing the leading resolvent forcing and response modes, making the methodology feasible for flows with at least two dimensions of spatial or spatiotemporal inhomogeneity. For an example case of flow through ducts with rectangular cross sections, we uncover linear amplification mechanisms not present in canonical channel and boundary layer flows.