Influence of freestream turbulence on the flow over a wall roughness

Abstract

The effect of freestream turbulence on the dynamics of an incompressible flow past a cylindrical roughness element in subcritical conditions (i.e., for Reynolds numbers below the onset of linear instability) has been investigated by the joint application of direct numerical simulations, linear modal and nonmodal stability analyses, and dynamic mode decomposition. At first, the influence of the Reynolds number and the ratio of the boundary layer’s thickness to roughness height on the three-dimensional spatiotemporal (global) stability of the flow has been investigated. Depending on the operating conditions, the leading instability can either be varicose (symmetric) or sinuous (antisymmetric). In both cases, when the flow is excited by broadband frequency forcing, dynamic mode decomposition extracts only varicose coherent structures even though optimal response analysis predicts a strong amplification of sinuous disturbances having frequency close to that of the marginally stable sinuous eigenmode. This apparent discrepancy is attributed to the fact that the sinuous instability is sensitive to a very limited range of frequencies barely excited by freestream turbulence while varicose disturbances are associated with high amplification in a much wider frequency range. Hence, in this case the flow behaves as an amplifier of varicose perturbations rather than a resonator. Consequences on the subsequent transition to turbulence have been studied, highlighting that varicose perturbations extract energy from the near-wake region, get continuously amplified due to the excitation provided by freestream turbulence, and eventually give rise to a shedding of hairpin vortices.