Resolvent-based modeling of coherent wave packets in a turbulent jet

Abstract

Coherent turbulent wave-packet structures in a jet at Reynolds number 460000\nand Mach number 0.4 are extracted from experimental measurements and are\nmodeled as linear fluctuations around the mean flow. The linear model is based\non harmonic optimal forcing structures and their associated flow response at\nindividual Strouhal numbers, obtained from analysis of the global linear\nresolvent operator. These forcing-response wave packets ("resolvent modes") are\nfirst discussed with regard to relevant physical mechanisms that provide energy\ngain of flow perturbations in the jet. Modal shear instability and the nonmodal\nOrr mechanism are identified as dominant elements, cleanly separated between\nthe optimal and suboptimal forcing-response pairs. A theoretical development in\nthe framework of spectral covariance dynamics then explicates the link between\nlinear harmonic forcing-response structures and the cross-spectral density\n(CSD) of stochastic turbulent fluctuations. A low-rank model of the CSD at\ngiven Strouhal number is formulated from a truncated set of linear resolvent\nmodes. Corresponding experimental CSD matrices are constructed from extensive\ntwo-point velocity measurements. Their eigenmodes (spectral proper orthogonal\nor SPOD modes) represent coherent wave-packet structures, and these are\ncompared to their counterparts obtained from the linear model. Close agreement\nis demonstrated in the range of "preferred mode" Strouhal numbers, around a\nvalue of 0.4, between the leading coherent wave-packet structures as educed\nfrom the experiment and from the linear resolvent-based model.\n