Spatial and Temporal Growth of Perturbations in Open-Channel Viscous Transverse Shear Flow

Abstract

AbstractThe comparison between spatial and temporal growth of perturbations in a shear layer is revisited for the case of a viscous open-channel flow with velocity inflection. Turbulence is characterized by two distinct scales: a subdepth turbulence associated with the bed shear stress and a large-scale turbulence associated with the large horizontal eddies that develop in the shear layer. Temporal and spatial linear stability analyses are performed. The base flow is assumed to be affected only by the subdepth scale turbulence. Therefore, the base flow represents not the average flow but the flow completely free of the effect of the instability of the shear layer. Temporal and spatial approaches present less discrepancy in the viscous than in the previously analyzed in-viscous case. In particular, the phase velocity was found to be strongly correlated to the frequency in both the temporal and spatial approaches.