Limitations of empirical sediment transport formulas for shallow water and their consequences for swash zone modelling

Abstract

Volumetric sediment concentrations computed by phase-resolving swash morphodynamic models are shown to exceed unity minus porosity (i.e., the maximally physically possible concentration value) by up to factor 10 5 when using standard expressions to compute the sediment transport rate. An ad hoc limit of sediment concentration is introduced as a means to evaluate consequences of exceeding physically realistic concentration by standard expressions. We find that implementation of this ad hoc limit strongly changes the quantitative and qualitative predictions of phase-resolving swash morphodynamic models, suggesting that existing swash predictions are unreliable. This is because standard expressions inappropriately consider or ignore the fact that the shallow swash water depth limits the storage capacity of transported sediment.

Numerical modelling of the flow and bed evolution of a single bore-driven swash event on a coarse sand beach

“…When θ inf is used the MPM formula reads: In the MPM formula the onset of the sediment transport is determined by the Shields parameter reaching a threshold value, the quantitative impact of this threshold, is also investigate by testing θ cr = 0. Finally, the recent approach by Li et al (2017) is also tested as an alternative to the MPM. This approach limits the estimate of q b provided by the Grass formula to an upper limit that corresponds to the maximum possible concentration of sediment in the water column.…”

“…Eq. (20) does not take into account the role of h. Li et al (2017) propose the relationship:…”

“…( 20)) because the dependence on U 3 is explicit. Following this, the Li et al (2017) relationship is modified as:…”

“…Neither of the two approaches explicitly accounts for the water depth. Li et al (2017) proposed to limit the local value of sediment transport based on the idea that the sediment can reach a maximum possible concentration in the water column that corresponds to water filled with sediments. The sediment discharge is therefore computed as the minimum value between this upper limit and that provided by a sediment transport formula.…”

“…The sediment discharge is therefore computed as the minimum value between this upper limit and that provided by a sediment transport formula. The Li et al (2017) approach is tested for semi-analytical test cases and for a specific value of the bed mobility parameter in the Grass formula. The MPM sediment transport formula is very commonly used in numerical models.…”