The role of basis functions in reduced-order modelling for plane Couette flow

This study examines the effect of basis functions on reduced order models (ROMs) on capturing the flow physics of parallel shear flows, focusing on plane Couette flow at Re=500 within a minimal flow unit domain. Four different sets of POD-mode-based basis functions are computed from 1) DNS (POD-DNS); 2) stochastic response of the linearised Navier-Stokes (LNS) operator about the laminar base flow (POD-LB); 3) stochastic response of the LNS operator about turbulent mean flow (POD-TM); 4) stochastic response of an eddy-viscosity-enhanced LNS operator about turbulent mean flow (POD-ETM). The ROMs are subsequently constructed using Galerkin projections, and they all show converged flow statistics at sufficiently large degrees of freedom (DoF). When truncated moderately, both POD-DNS and POD-ETM show better performance than the other two cases especially for replicating turbulence statistics and dynamics. However, they do not retain the linear stability of the laminar state especially when truncated severely, in sharp contrast to POD-LB case, where the laminar state is found to be stable even with very low degrees of freedom. In the final presentation, a more detailed discussion will be provided for this comparison. An extra section will also be added to address the ROM constructed using a basis of balanced modes.