Bed-load transport for steady flows and unsteady oscillatory flows

Abstract

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 θ eq′ 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 Φ b and the non-dimensional excess bed-shear θ eq′− θ c 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 k s for oscillatory flows from the (steady flow) value 3 D 90 to D 50. 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.