2023/11/24 by Igor A. Maia, Maia, Igor A., André V. G. Cavalieri +1 · 1 citation
Engineering · Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Fluid Dynamics and Turbulent Flows #Fluid Dynamics and Vibration Analysis #Model Reduction and Neural Networks
paper · pdf · doi:10.48550/arxiv.2311.14585
openalex publication_date 2023/11/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 & Nogueira (Phys. Rev. Fluids 7, L102601, 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 lowcontrollability 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 lowcontrollability 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.