Temporal evolution of jet induced scour depth in cohesionless granular beds and the phenomenological theory of turbulence

Abstract

In this work, we investigate the temporal evolution of the jet-driven scour depth in a pothole lying on a cohesionless granular bed, by using diverse approaches. First, we present new experiments which encompass cases with jet angles ranging from 45 to 90° from the horizontal, several initial water depths, and different particle sizes, supplementing experiments developed recently by the last two authors. In particular, we address relatively-large angles, mostly absent in previous analyses. Our results first confirm the existence of two very different stages in the scour process, essentially overlooked in datasets used to obtain the traditional formulas-developing and developed phases; they then provide unprecedented evidence of the very distinct behavior at 90°, characterized by a step-wise behavior. Second, after revisiting the rationale of a theory our new, and other datasets. Finally, we provide interesting interpretations of the scour process by using the results of the theory.

Effect of Pressure Fluctuations and Flow Confinement on Shear Stress in Jet-Driven Scour Processes

“…We show that other authors' approaches significantly underestimate the maximum shear stress for the jet-driven scour process and propose a new value of the shear stress coefficient C s for the analyzed configuration. Finally, this study also furnishes another unprecedented result, i.e., it corroborates the approach based on the phenomenological theory of turbulence recently developed by [23], showing that it can be successfully applied to estimate maximum shear stress.…”

“…In fact, the average shear stress is a result derived from the application of the angular momentum conservation law, which takes into account the torque contributions given by the shear stress distribution and the momentum flux of the impinging jet. The approach proposed by [30] is fully consistent with that based on the phenomenological theory of turbulence developed by [23], which is valid regardless of the gradation of the granular material and scale. However, further investigations are needed to validate its applicability in the generality of the cases.…”

“…where h Gi,i+1 and x Gi,i+1 are the vertical and longitudinal coordinates of the center of mass G i,i+1 of each segment i−i+1 (Figure 3a), and the origin O of the reference system is located at the intersection of the vertical plane containing the maximum scour depth with the water surface. It is worth mentioning that Equation (5) also reflects the findings of [4,12,16,23,25,[27][28][29], who showed that shear stress reduces with the water depth and longitudinal distance from the jet impact zone. Furthermore, [30] showed that T i,i+1 and, consequently, the corresponding shear stress τ i,i+1 acting on the scour profile segment i−i+1 can be computed as follows:…”

“…This aspect is crucial to understand and explain the mentioned difference. In addition, [7] showed that the maximum scour depth (or, equivalently, ∆ + D, D being constant) decreases with the amount of rotating material in the scour hole, and [23] demonstrated that the shear stress scales with 1/(∆ + D). Therefore, apart from flow confinement effect, the presence of rotating material within the scour hole provides a further explanation of the deviation between τ m values calculated using Equations (26) and (28) and τ av values measured by [30] Based on these observations, in the following, we furnish an estimation of both C s and τ m for tests conducted by [30], assuming the longitudinal shear stress distribution proposed by [25].…”

“…Nevertheless, their analysis has been only recently validated with experimental and field data. Following the approach proposed by [18,19], the authors of [23] analyzed the temporal evolution of the scour depth for both 2D and 3D cases. In so doing, they were able to determine the value of the constant K for both equilibrium configurations.…”