Suspended sand concentration models under breaking waves: Evaluation of new and existing formulations

A total of 7 reference concentration (C₀) models (6 existing and 1 newly proposed) were validated against 119 test cases from 4 recently published datasets collected under the LIP, CROSSTEX, SandT-Pro and SINBAD experimental studies. These models were evaluated for performance in different cross-shore regions: the shoaling zone, breaking (outer surf) zone and inner surf zone, under regular and irregular breaking wave conditions. In almost all existing C₀ models, substantial under-prediction was found particularly around the wave plunging point (point at which breaking wave plunges and surface generated turbulent kinetic energy, TKE, is injected into the water column) where strong localised increases in C₀ were observed. This strong increase in concentration was attributed to the large-scale breaking-generated turbulent vortices invading the wave bottom boundary layer (WBBL) and entraining dense clouds of sediment near the plunging point. Models that were directly or indirectly driven by local wave climate such as the local wave height (H), breaker height (H_b) or local water depth (d), were found to perform quite poorly in the breaking region under regular and irregular plunging breaker waves. Formulations that related C₀ to the sand pickup rate (i.e. depending on exerted bed shear exceeding critical bed shear for entrainment) were adept in regions unaffected by external breaking-induced TKE (e.g. the shoaling zone) but could not account for the high levels of concentration observed at the plunging point. This is because these formulations were based on the implicit assumption that sediment entrainment is only induced by the local TKE generated by bed shear; not taking surface-generated breaking-induced TKE into account. This assumption was addressed in more recent studies, by including breaking-induced TKE into sediment pickup rate or reference concentration formulations. Though latest studies have shown promising relationships between near-bed TKE (k_b) and reference concentration/sediment pickup, such formulations also face inherent limitations. These formulations are highly dependent on the accuracy of measured or modelled k_b and are also sensitive to the magnitude of k_b. For example, the magnitude of measured k_b was found to vary by a factor of 1.1–1.3 between regular and irregular wave conditions, with k_b being smaller under irregular wave conditions. This resulted in varied performance between datasets in k_b-driven reference concentration formulations. The Froude-scaled TKE produced smaller deviations in magnitude of TKE between datasets, suggesting that it may be a more suitable driving parameter for reference concentration models than k_b. A new reference concentration model, L19, was empirically derived from an inverse relationship observed between d and C₀, and from the roller energy dissipation rate. The newly proposed L19 model shows good agreement with measured C₀ (with RMSE ranging between 0.36 and 1.79 kg/m³ over the different datasets) in regular and irregular wave conditions, even at the plunging point where concentration is highest. The modified concentration profile [C(z)] equation also performs well, generally capturing the vertical concentration profile accurately throughout the whole water column.