Incipient motion of coarse particles under regular shoaling waves

Abstract

Incipient motion of coarse particles under regular shoaling waves is examined. Experiments are performed to investigate the effects of bed fluid acceleration on coarse particle stability. By varying wave height, wave period and water depth, combinations of similar peak orbital velocities and weak to strong intra-wave accelerations were created. The particles used in these experiments have two different sizes both of a centimeter order-of-magnitude. The data confirm that acceleration is important for the initiation of motion, since combinations of similar orbital velocity and varying acceleration magnitude resulted in no motion, some motion and motion as acceleration increased. Qualitatively we found that initiation of motion occurs at or is very close to the maximum shear stress due to the combined effects of drag / lift and acceleration as introduced by Nielsen and Callaghan [Nielsen, P. and Callaghan, D.P. (2003), Shear stress and sediment transport calculations for swash zone modelling. Coastal Engineering, 47, pp. 347–354]. However, quantitatively their formulation does not lead to convincing discrimination between motion and no-motion. We expect this to be due to the assumption that the coefficients for drag / lift and acceleration in their formulation are taken equal and constant. From literature and from plotting our data against the Keulegan–Carpenter number we expect that these coefficients strongly vary due to flow separation effects. To arrive at a more convincing discrimination between motion and no-motion we introduce a new fluid acceleration descriptor for nonlinear shoaling waves. The combination of this descriptor with a Reynolds number Re g more clearly delineates the regions with particle motion and without particle motion and has the potential to serve as a descriptor of the incipient motion of coarse particles under nonlinear and skewed, regular waves.