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Reduced-order Galerkin models of plane Couette flow

André V. G. Cavalieri1,* and Petrônio A. S. Nogueira2,†

  • 1Divisão de Engenharia Aeroespacial, Instituto Tecnológico de Aeronáutica, São José dos Campos, SP 12228-900, Brazil
  • 2Department of Mechanical and Aerospace Engineering, Laboratory for Turbulence Research in Aerospace and Combustion, Monash University, Clayton VIC 3800, Australia

  • *andre@ita.br
  • †petronio.nogueira@monash.edu
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Phys. Rev. Fluids 7, L102601 – Published 21 October, 2022

DOI: https://doi.org/10.1103/PhysRevFluids.7.L102601

Abstract

Reduced-order models were derived for plane Couette flow using Galerkin projection, with orthonormal basis functions taken as the leading controllability modes of the linearized Navier-Stokes system for a few low wave numbers. Resulting Galerkin systems comprise ordinary differential equations, with a number of degrees of freedom ranging from 144 to 600, which may be integrated to large times without any indication of numerical instability. The reduced-order models so obtained are also found to match statistics of direct numerical simulations at Reynolds number 500 and 1200 with reasonable accuracy, despite a truncation of orders of magnitude in the degrees of freedom of the system. The present models offer thus an interesting compromise between simplicity and accuracy in a canonical wall-bounded flow, with relatively few modes representing coherent structures in the flow and their dominant dynamics.

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Phys. Rev. Fluids 7, L102601– Published 21 October, 2022
  • Received 20 May 2022
  • Accepted 3 October 2022
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