Reynolds stress anisotropy and secondary flow prediction in turbulent channel flow over riblets: A comparison of large-eddy simulation with linear and nonlinear Reynolds-averaged Navier–Stokes closures

Abstract

Near-wall Reynolds stress anisotropy and secondary flows play a dominant role in drag reduction over riblets. In this study, a systematic evaluation of the wall-adapting local eddy-viscosity model, the shear-stress transport (SST) k–ω model, and the Wallin–Johansson explicit algebraic Reynolds stress model (WJ-BSL-EARSM) is conducted for turbulent channel flow over riblets under s+=20 and s+=40 regimes, focusing on macroscopic drag variation, secondary flows, and near-wall statistical characteristics. Results demonstrate that large eddy simulation (LES) reproduces pairs of counter-rotating secondary vortices, the lifting and pinning effects on quasi-streamwise vortices, and shear-layer instabilities, with the resolved turbulent kinetic energy ratio exceeding 98.61%, satisfying the Pope criterion threshold (M=kresolved/ktotal≥80%). The standard SST k–ω model fails due to the breakdown of its isotropic assumption, rendering it incapable of responding to the Reynolds normal-stress difference ⟨v′2⟩−⟨w′2⟩, which leads to a failure in predicting drag increase (12.42% lower than direct numerical simulation). In contrast, the non-linear WJ-BSL-EARSM model captures stress anisotropy by virtue of high-order tensor cross-terms, reconstructing Prandtl's second-kind secondary flows and capturing the key physical trend of drag reversing from negative to positive (4.92%). This study reveals how Reynolds stress anisotropy affects drag in riblet flows, clarifies the predictive performance gaps and physical limitations between Reynolds-averaged Navier–Stokes models and LES, and provides theoretical foundation for turbulent flows over riblet walls.