promotie ir. C.M. Dohmen-Janssen

Grain size influence on sediment transport in oscillatory sheet flow: phase lags and mobile-bed effects

promotoren: prof.ir. J.A. Battjes (TUD) en prof.ir. K. d'Angremond (TUD)

The study presented in this thesis focuses on cross-shore sand transport in combined wave-current flow in the sheet flow regime. Sheet flow conditions mainly occur during storms when large wave heights cause large near-bed velocities, such that ripples are washed out and the sand is transported in a thin layer (in the order of a few cm) close to the bed. Accurate predictions of cross-shore transport rates are still very difficult: Van Rijn et al. (1995) showed that predictions of yearly-averaged cross-shore transport rates at the 8 m water depth contour along the Dutch coast varied from -10 to +10 m 3/m/year. Apparently, even the direction of the net transport rate is uncertain. Therefore the main aim of the present study is to increase insight in cross-shore transport processes in sheet flow conditions and to improve model predictions. Attention is focused on the influence of grain size, the importance of phase-lags between near-bed flow velocities and sediment concentrations and the mobile-bed effects due to the presence of a sheet flow layer with high concentrations and large concentration gradients.

Experimental research
Experiments were performed in the Large Oscillating Water Tunnel (LOWT) Of WL- Delft Hydraulics, in which the orbital motion underneath a wave can be simulated at full scale. In addition, a net current can be generated. Three series of experiments were carried out with mobile sand beds consisting of relatively uniform sand with different median grain size: D50 = 0.13 mm, D50 = 0.21 mm and D50 = 0.32 mm. Net (wave-averaged) sand transport rates were measured using a mass conservation technique. At different heights above the bed time-dependent flow velocities and sediment concentrations were measured, using various instruments. In addition, one series of fixed-bed experiments was carried out in order to study the difference in flow velocity above a fixed bed and above a mobile sand bed.

Sand transport models
Experimental results are compared with predictions of different existing sand transport models: two quasi-steady models (Bailard, 1981; Ribberink, 1998), a semi-unsteady model (Dibajnia and Watanabe, 1992) and an unsteady model (Ribberink and Al-Salem, 1995). In quasi-steady models it is assumed that the instantaneous sand transport rate is directly related to the instantaneous flow velocity or bed shear stress. This assumption has often been applied in sheet flow conditions, since the majority of the sand is transported close to the bed and a quick sediment response is expected. Grain size influence on sediment transport in oscillatory sheet flow Semi-unsteady models take into account the effect of phase-lags between flow velocity and sand transport rate, without modelling the time-dependent behaviour of flow velocity and sediment concentration, as in unsteady models. The unsteady model of Ribberink and Al-Salem is based on a IDV-momentum equation to describe the flow velocity and a 1 DV advection-diffusion equation to describe the sediment concentration. Sediment concentrations are assumed to be so low that they do not affect the flow velocity. In the present study a new semi-unsteady model has been developed, in which phase-lags are taken into account by multiplying the net transport rates predicted by the quasi-steady model of Ribberink with a phase-lag correction factor r. This phase-lag correction factor is defined as the ratio between the net transport rate with and without phase-lag effects, both of which are calculated from an analytical unsteady sand transport model. The unsteady model of Ribberink and Al-Salem is extended by taking into account mobile-bed effects in two ways: 1) simulating sediment-flow interaction and turbulence damping by increasing the imposed roughness height and reducing the eddy viscosity. 2) including sediment-flow interaction by modelling an intergranular component of the shear stress.

Phase-lag effects
The present study shows that even in sheet flow conditions phase-lags between velocity and sediment concentration can significantly reduce the net transport rate. These phase-lags are caused by the fact that particles need time to move upward into the flow and time to settle back to the bed. They are characterised by a phase-lag parameter that represents the ratio of the fall time of a sediment particle to the wave period. lt is assumed that particles are entrained up to a height, which is equal to the sheet flow layer thickness. If the fall time of a particle is comparable to the wave period, part of the sediment is transported backward during the succeeding half wave cycle resulting in reduced net transport rates. Although unsteady models take into account these phenomena, phase-lags in sediment concentration are underpredicted by the unsteady model. Best agreement with the measured net transport rates is found with the new semi-unsteady model.

Limited pick-up of sand
The present study indicates that the sediment-load entrained into the flow and therefore the net transport rates may be limited by the available time to erode the sandy bed. This is the case if the required pick-up time is comparable to the wave period. The hypothesis is confirmed by measurements of erosion depth, sheet flow layer thickness, and sediment concentration. In contrast with existing theory these all increase for increasing wave period. The phenomenon of a limited pick-up of sand is not included in any of the models, but should be included to improve predictions of net transport rate and transport processes.

Mobile-bed effects
Experimental results in comparison with predictions of unsteady models above the sheet flow layer indicate that the presence of a sheet flow layer leads to an increased flow resistance due to sediment-flow interaction in the sheet flow layer and to damping of turbulence. The latter can be explained by the negative density gradient in the sheet flow layer. Results indicate that the roughness height is in the order of the sheet flow layer thickness and that turbulence damping is stronger if the sheet flow layer thickness is larger. Due to these mobile-bed effects velocities and concentrations and thus net transport rates are reduced. Although some agreement can be found between measurements and predictions in the suspension layer, large differences are observed in the sheet flow layer. This shows that different transport processes are important here. In order to improve predictions of transport processes in the sheet flow layer more advanced models should be used, like two-phase flow models.

Sheet-flow layer thickness
It is found that the sheet flow layer thickness is a very important parameter for the occurrence of phase-lag effects and mobile-bed effects. According to existing expressions, the sheet flow layer thickness is almost the same for different sands and is increasing for decreasing wave periods. These assumptions are contradicted by the present study, which shows that for fine sand (D50 = 0.13 mm) the sheet flow layer thickness is larger than for coarser sand (D50 > 0.21 mm). Moreover, for fine sand the sheet flow layer thickness decreases for decreasing wave periods. Therefore it is recommended to study systematically the behavior of this sheet flow layer thickness.

Voor meer informatie: a.m.klijnstra@utwente.nl