A general theoretical framework for equilibrium scour due to inclined jets based on the Phenomenological Theory of Turbulence

We present the derivation and validation of a novel, complete theoretical framework for jet-induced scour, illuminated by the Phenomenological Theory of Turbulence. The framework is designed to account for all flow conditions and a wide range of bed-particle sizes, with the potential to extend it to the entire range. The theory naturally subsumes previous results obtained by the first author for coarser materials under the assumption of the Reynolds number tending to infinity. By invoking the different stages of the power spectrum of the turbulent energy and the incipient conditions for sediment motion, the developed framework allows for a unique, physically based description of the changing habits of jet scour, as a function of the particle size and power of the jet at the equilibrium state. After specifying the details of the general theory, we focus on finer materials and uncover a novel expression as a special case. We test the model using experimental data involving an extremely wide range of particle sizes. The model appears to very well predict the experiments for non-cohesive sediment. The comparison with cohesive sediment provides noteworthy insights, highlighting the need for further research to incorporate cohesive-sediment parameters into the developed framework. We determine important constants from previous developments and re-interpret the flow resistance phenomenon at the bottom of the scour hole. Finally, we discuss a bi-modal perspective for the analysis of the problem of scour.