Modal-based generalised quasilinear approximations for turbulent plane Couette flow
Theoretical and Computational Fluid Dynamics(2024)
Abstract
We study generalised quasilinear (GQL) approximations applied to turbulent plane Couette flow. The GQL framework is explored in conjunction with a Galerkin reduced-order model (ROM) recently developed by Cavalieri and Nogueira (Phys Rev Fluids 7:102601, 2022), which considers controllability modes of the linearised Navier–Stokes system as basis functions, representing coherent structures in the flow. The velocity field is decomposed into two groups: one composed by high-controllability modes and the other by low-controllability modes. The former group is solved with the full nonlinear equations, whereas the equations for the latter are linearised. We also consider a new GQL framework wherein the linearised equations for the low-controllability modes are driven by nonlinear interactions of modes in the first group, which are characterised by large-scale coherent structures. It is shown that GQL-ROMs successfully recover the statistics of the full model with relatively high controllability thresholds and sparser nonlinear operators. Driven GQL-ROMs were found to converge more rapidly than standard GQL approximations, providing accurate description of the statistics with a larger number of linearised modes. This indicates that the forcing of linearised flow structures by large-scale coherent structures is an important feature of turbulence dynamics that should be considered in GQL models. The results presented here reveal that further model reductions are attainable with GQL-ROMs, which can be valuable to extend these models to larger Reynolds numbers.
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Key words
Wall-bounded turbulence,Reduced-order models,Generalised quasilinear approximations,Coherent structures
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