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

Lutz Lesshafft1, Onofrio Semeraro1,2, Vincent Jaunet3, André V. G. Cavalieri4, and Peter Jordan3

  • 1Laboratoire d'Hydrodynamique, CNRS/École polytechnique, 91120 Palaiseau, France
  • 2LIMSI, CNRS/Université Paris-Saclay, 91400 Orsay, France
  • 3Institut Pprime, CNRS/Université de Poitiers/ENSMA, 86962 Futuroscope Chasseneuil, France
  • 4Divisão de Engenharia Aeronáutica, Instituto Tecnológico de Aeronáutica, São José dos Campos, 12228-900 São Paulo, Brazil

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Phys. Rev. Fluids 4, 063901 – Published 6 June, 2019

DOI: https://doi.org/10.1103/PhysRevFluids.4.063901

Abstract

Coherent turbulent wave-packet structures in a jet at Reynolds number 460000 and Mach number 0.4 are extracted from experimental measurements and are modeled as linear fluctuations around the mean flow. The linear model is based on harmonic optimal forcing structures and their associated flow response at individual Strouhal numbers, obtained from analysis of the global linear resolvent operator. These forcing-response wave packets (“resolvent modes”) are first discussed with regard to relevant physical mechanisms that provide energy gain of flow perturbations in the jet. Modal shear instability and the nonmodal Orr mechanism are identified as dominant elements, cleanly separated between the optimal and suboptimal forcing-response pairs. A theoretical development in the framework of spectral covariance dynamics then explicates the link between linear harmonic forcing-response structures and the cross-spectral density (CSD) of stochastic turbulent fluctuations. A low-rank model of the CSD at given Strouhal number is formulated from a truncated set of linear resolvent modes. Corresponding experimental CSD matrices are constructed from extensive two-point velocity measurements. Their eigenmodes (spectral proper orthogonal or SPOD modes) represent coherent wave-packet structures, and these are compared to their counterparts obtained from the linear model. Close agreement is demonstrated in the range of “preferred mode” Strouhal numbers, around a value of 0.4, between the leading coherent wave-packet structures as educed from the experiment and from the linear resolvent-based model.

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Phys. Rev. Fluids 4, 063901– Published 6 June, 2019
  • Received 23 October 2018
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