Ambiguity in mean-flow-based linear analysis

@article{Karban2020AmbiguityIM,
  title={Ambiguity in mean-flow-based linear analysis},
  author={U. Karban and B. Bugeat and Eduardo Martini and Aaron Towne and Andr{\'e} V. G. Cavalieri and Lutz Lesshafft and Akshat Agarwal and Peter Jordan and Tim Colonius},
  journal={Journal of Fluid Mechanics},
  year={2020},
  volume={900}
}
Abstract Linearisation of the Navier–Stokes equations about the mean of a turbulent flow forms the foundation of popular models for energy amplification and coherent structures, including resolvent analysis. While the Navier–Stokes equations can be equivalently written using many different sets of dependent variables, we show that the properties of the linear operator obtained via linearisation about the mean depend on the variables in which the equations are written prior to linearisation, and… 

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