The geometric scaling of a developing scour hole

Abstract

A novel scanning technique using a rotating-head sonar profiler attached to a slider mechanism is presented as a means to directly measure the complex erosion and deposition features of local scour holes developing in clear-water conditions around vertical cylinders mimicking bridge piers. Extensive validation shows that the method produces high-density elevation surfaces to within ≅±1% accuracy (relative to the flow depth) in a quasi-non-invasive manner. Experimental data from eleven trials, conditioned to vary the flow regime (and therefore the effect of viscosity relative to inertial forces) within the scour hole over a wide range, indicate that monitoring of the whole scour hole in time (instead of only the maximum depth as is commonly isolated in laboratory experiments) can reveal important information about local scour evolution. In particular, results show that the development of the scour hole volume (ν_OL), within vicinity of the horseshoe vortex, scales with respect to the maximum scour depth (y_s) cubed (i.e. ν_OL∼y_s³) through three linear regimes. Whilst the first and second regimes are attributable to the initial generation and steady growth of the horseshoe vortex respectively, transition to a third regime after significant scour development was found to represent a step change in the scour evolution process. Following the recent theoretical framework proposed by Manes and Brocchini (2015), this change, termed the crossover point, was interpreted as the physical point in time beyond which the production of turbulent kinetic energy plateaus which corresponds to a stabilisation in the erosive power of the horseshoe vortex. Scour development beyond the crossover point is characterised by a significant reduction in the rate of volumetric scour, relative to the steadily-increasing maximum scour depth. This overall reduction in volume development is attributed to a balance between erosion and deposition characteristics from in-front and around the sides of the pier which was observed using topography analysis. Intriguingly, the sediment erosion and deposition trade-off in the third regime was found to be influenced by the flow regime within the scour hole. While the sediment trade-off for the fully-rough regime was characterised by erosion in front of and deposition around the sides of the pier, the viscosity-dominated hydraulically-smooth regime showed erosion and deposition patterns that are completely the opposite. As such, the presence of a crossover point is physically underwritten by sediment redistribution which varies as a function of the flow regime inside the scour hole. Under the assumption that at the crossover point the shear stress acting on the scour hole surface (τ) approaches the critical shear stress of the sediment (i.e. τ ≈ τ_c ), the crossover depth was modelled using a theoretical approach by Manes and Brocchini (2015) which provided an excellent fitting to the fully-rough crossover data. This model was extended to account for
viscosity effects within the scour hole (owing to a change in flow regime) by considering the dependency of τ and τ_c on the flow regime in turn, following the work by Brownlie (1981) and Batchelor (e.g. Lohse and Muller-Groeling, 1994). The crossover depth was used as a scaling parameter for quantifying other geometric properties of the scour hole at the point of crossover using empirical data-fitting. The final formulae presented are very promising for engineering applications. The existence of a well-defined crossover point presents itself as an excellent candidate for defining characteristic length and time scales that may effectively describe local scour dynamics and evolution in time, which may be used for modelling purposes. This is extremely relevant because, especially in clear-water conditions, the definition of such scales is still elusive as the equilibrium scour depth and time are well known to be arbitrarily defined. For completeness, the similarity analysis was extended to defining the evolution of the scour hole boundaries, which were found to develop in proportion with the maximum scour depth and independent of time. The scaling relationships presented within the text for the scour boundaries are suitable for engineering applications as a good estimation of the scour major axes and footprint for a given scour depth.

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ORCID for Gustavo De Almeida: orcid.org/0000-0002-3291-3985

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