Near-bed eddy scales and clear-water local scouring around vertical cylinders

In the last five decades much research has been devoted to the development of predictive formulae to quantify the maximum local-scour depth developing around hydraulic structures (e.g bridge piers). Owing to the complexity of the problem, most of the proposed formulae were developed on empirical grounds, which made them susceptible to scale issues. Recently, a new theoretical approach was proposed to develop a better understanding of the physics of local scouring around piers. The analysis rested on two stringent hypotheses whereby the momentum-transport rate at the sediment–water interface was dominated by eddies belonging to the inertial range and the sediment critical bed shear stress was independent from roughness Reynolds number and relative roughness effects. The present paper builds upon that previous work and explores the scaling of the equilibrium scour depth when these two hypotheses are relaxed. Results from theoretical considerations and empirical evidence are then combined to derive a new formula for maximum local-scour depth prediction.