Sediment Threshold under Oscillatory Waves

As the velocity of the water motion near the bottom under oscillatory waves is increased, there comes a stage when the water exerts a stress on the particles sufficient to cause them to move. This study reviews data on threshold of sediment motion under wave action and compares the results with the established curves for threshold under a unidirectional current. For grain diameters less than about 0.05 cm (medium sands and finer) the threshold is best related by the equation $$\frac{\text{ρ}{\text{u}}_{\text{m}}^2}{{\text{(ρ}}_{\text{s}}-\text{ρ)}\text{g}\text{D}}=0.21{({\text{d}}_0/\text{D})}^{1/2}$$ where u_m and d₀ are the near-bottom velocity and orbital diameter of the wave motion, ρ is the density of water, and ρ_s and D are respectively the density and diameter of the sediment grains. For grain diameters greater than 0.05 cm (coarse sands and coarser) the equation $$\frac{\text{ρ}{\text{u}}_{\text{m}}^2}{{\text{(ρ}}_{\text{s}}-\text{ρ)}\text{g}\text{D}}=0.46\pi {({\text{d}}_0/\text{D})}^{1/4}$$ gives the best prediction of threshold. Evaluating the drag coefficient with the graph of Jonsson for wave motions, the data on threshold under waves is found to show good agreement with the curves of Shields and Bagnold for the threshold under a unidirectional current.