Localized turbulent flows on scouring granular beds

Hydrodynamic Structure with Scour Hole Downstream of Bed Sills

Experimental turbulence measurements of scour hole downstream of bed sills in alluvial channels with non-cohesive sediments are investigated. Using an Acoustic Doppler Velocimeter (ADV), the flow velocity-field within the equilibrium scour hole was comprehensively measured. In this study, we especially focus on the flow hydrodynamic structure in the scour hole at equilibrium. In addition to the flow velocity distribution in the equilibrium scour hole, the turbulence intensities, the Reynolds shear stresses, the turbulent kinetic energy, and the turbulent length scales are analyzed. Since the prediction of equilibrium scour features is always very uncertain, in this study and based on laboratory turbulence measurements, we apply the phenomenological theory of turbulence to predict the maximum equilibrium scour depth. With this approach, we obtain a new scaling of the maximum scour depth at equilibrium, which is validated using experimental data, satisfying the validity of a spectral exponent equal to −5/3. The proposed scaling shows a quite reasonable accuracy in predicting the equilibrium scour depth in different hydraulic structures.

Spectral theory of the turbulent mean-velocity profile

It has long been surmised that the mean-velocity profile (MVP) of pipe flows is closely related to the spectrum of turbulent energy. Here we perform a spectral analysis to identify the eddies that dominate the production of shear stress via momentum transfer. This analysis allows us to express the MVP as a functional of the spectrum. Each part of the MVP relates to a specific spectral range: the buffer layer to the dissipative range, the log layer to the inertial range, and the wake to the energetic range. The parameters of the spectrum set the thickness of the viscous layer, the amplitude of the buffer layer, and the amplitude of the wake.