Physically based formula for the maximum scour depth induced by a propeller jet

Abstract

In the last two decades, many studies have been dedicated to the employment of predictive formulas able to assess the maximum scour depth produced by propeller jets. Owing to the complexity of the phenomenon, most of the literature formulas were built on empirical arguments, making them susceptible to scale issues and not fully coherent with the physics underpinning the scouring problem. Recent studies exploited the phenomenological theory of turbulence and the paradigms of sediment incipient-motion theory to derive a predictive formula of the maximum equilibrium scour depth in different cases: scour produced by jet, scour at bridge piers, and scour downstream of hydrokinetic turbines. In the present study, using the same considerations of the aforementioned works, we propose a new model that allows the derivation of a predictive physically based formula that includes all the relevant parameters controlling the scouring process induced by the propeller rotation. The theory is validated at the laboratory scale with experimental published data: a good agreement between theoretical predictions and literature data is shown. The proposed design formula clearly indicates that, when tested against experimental data, it leads to lower scattering levels than those obtained with empirical literature formulas.