Phase lags in oscillatory sheet flow: experiments and bed load modelling

Abstract

Sheet flow corresponds to the high velocity regime when small bed ripples are washed out and sand is transported in a thin layer close to the bed. Therefore, it is often assumed that sand transport in oscillatory sheet flow behaves quasi-steady: time-dependent transport rates are assumed to be instantaneously related to the near-bed orbital velocity. However, new experimental results show that even in sheet flow, phase lags between sediment concentration and near-bed velocity can become so large that they lead to a reduction of the net (wave-averaged) transport rate. A phase lag parameter is defined, which shows that phase lags become important for fine sand, high velocities and short wave periods. A semi-unsteady model is developed that includes the effects of phase lags on the net transport rate. New experiments were carried out in a large oscillating water tunnel with three different sands ( D 50=0.13, 0.21 and 0.32 mm) for a range of prototype, combined wave–current flow conditions. Measured net transport rates were compared with predictions of a quasi-steady model and the new semi-unsteady model. This comparison indicates that net transport rates are reduced if phase lags become important: the quasi-steady model overestimates the net transport rates and the semi-unsteady model gives better agreement with the data. Time-dependent measurements of velocities and concentrations show that the reduced net transport rates can indeed be explained by phase lag effects, because for tests with smaller net transport rates than predicted by the quasi-steady model, considerable phase lags between velocities and concentrations were observed, even inside the sheet flow layer. Verification of the semi-unsteady model against a larger data set confirms the occurrence of phase lag effects in oscillatory sheet flow. Also for the larger data set the semi-unsteady model yields better agreement with the data than the quasi-steady model.