Modeling sediment transport beneath skewed asymmetric waves above a plane bed

Abstract

A one‐dimensional model solving the Reynolds‐averaged Navier‐Stokes and advection‐diffusion equations in conjunction with a k − ε model for turbulence closure is used to systematically explore net sediment transport rates beneath skewed asymmetric waves under sheet flow conditions. The model, which reproduces net rates obtained in U tube experiments under purely skewed and asymmetric oscillatory flow well, is forced with an analytical expression of free stream oscillatory flow in which we varied the degree of skewness versus asymmetry, the magnitude of the total wave nonlinearity, the oscillatory flow amplitude, and the wave period. We find that for a wide range of conditions sediment entrained into the flow during a particular wave half‐cycle has not completely settled before flow reversal and tends to be transported during the next half‐cycle. Consistent with earlier work, these phase‐lag effects reduce transport rates under oscillatory flow dominated by velocity skewness, while they enhance net transport rates under oscillatory flow dominated by velocity asymmetry. Phase‐lag effects are particularly important in fine‐medium sands (<≈250 μm). For a given grain size phase‐lag effects become more pronounced with an increase in wave nonlinearity and in velocity amplitude, and with a decrease (increase) in wave period under skewed (asymmetric) oscillatory flow. When phase‐lag effects are negligible, transport rates are largest under skewed oscillatory flow containing some asymmetry; otherwise, they are largest under asymmetric flow. Our work implies that nearshore sediment transport equations based on the instantaneous bed shear stress may be restricted in applicability to situations when the grain size exceeds ≈250 μm.