Restricted nonlinear simulations of flow over riblets: Characterizing drag reduction and its breakdown

Abstract

The restricted nonlinear (RNL) model is employed as low-order representation of turbulent flow over riblets at $R{e}_{\tau }\approx 395$. Comparisons with direct numerical simulations (DNS) verify the ability of the model to accurately capture low-order statistics, as well as trends in drag-alteration and secondary motion as a function of riblet geometry and spacing. We demonstrate the ability of the RNL model to reproduce additional flow features by decomposing the roughness function to isolate contributions from the total stress and comparing its predictions to DNS data. An analysis of the spectra of Reynolds shear stress shows that the RNL model captures Kelvin-Helmholtz-like rollers linked to riblet drag reduction breakdown but slightly over predicts the total stresses. The reproduction of the overall trends in stresses and flow features linked to the breakdown of riblet induced drag-reduction suggests that the nonlinearity and scale interactions retained in the RNL system are adequate to capture the key mechanisms underlying turbulent flow over a range of riblet geometries. These results also indicate that examining the limitations of the model may provide insight into the critical nonlinear interactions underlying drag alteration due to riblets.