Bed-load transport for steady flows and unsteady oscillatory flows

The validity of a bed-load transport formula, based on the bed-shear concept of Meyer-Peter and Mueller, was investigated for steady unidirectional flows, oscillatory flows and oscillatory flows with superimposed net currents. The aim of the study was to develop a general bed-load transport concept for a wide range of flow and sediment conditions, as occurring in the marine coastal environment. The results of more than 150 laboratory experiments, including more than 75 recent bed-load transport measurements in oscillating water tunnels, were used for the study. For oscillatory flows, the time-dependent bed-load transport was treated in a ‘quasi-steady' way and an equivalent Shields parameter θeq′ was defined in order to enable a comparison between ‘steady fow' and ‘unsteady oscillatory flow' measurements. A good correlation was found between the non-dimensional transport parameter Φb and the non-dimensional excess bed-shear θeq′−θc for different sets of oscillatory bed-load transport measurements. However, especially in the lower Shields regime, the oscillatory flow data show a clear deviation from an extensive set of steady flow bed-load data. A good agreement between the (oscillatory flow and the steady flow) data sets could then be obtained by reducing the lower limit of the roughness height ks for oscillatory flows from the (steady flow) value 3D90 to D50. Based on the obtained concept a generalized bed-load formula was derived for both flow types, including oscillatory flows and superimposed currents under an arbitrary angle. A verification, carried out with a set of (co-linear) oscillatory+superimposed current measurements, showed a good agreement between calculated and measured bed-load transport rates. Finally, the validity and limitations of the obtained bed-load model are discussed.