Combined wave and current interaction with a rough bottom

TLDR

The model’s implications for sediment transport and shelf circulation are examined. The study develops an analytical theory to describe combined wave–current motion near a rough bottom and its boundary shear stress. Using a combined wave–current friction factor and a linearly increasing eddy‑viscosity closure, the authors solve linearized equations for wave and current kinematics inside and outside the boundary layer and introduce an apparent bottom roughness that depends on physical roughness, wave characteristics, and flow direction. The theory predicts that waves increase the resistance felt by the current, with the wave–current friction factor and apparent roughness varying with relative velocity, roughness, and angle; predictions agree with laboratory and field data.

Abstract

An analytical theory is presented to describe the combined motion of waves and currents in the vicinity of a rough bottom and the associated boundary shear stress. Characteristic shear velocities are defined for the respective wave and current boundary layer regions by using a combined wave‐current friction factor, and turbulent closure is accomplished by employing a time invariant turbulent eddy viscosity model which increases linearly with height above the seabed. The resulting linearized governing equations are solved for the wave and current kinematics both inside and outside the wave boundary layer region. For the current velocity profile above the wave boundary layer, the concept of an apparent bottom roughness is introduced, which depends on the physical bottom roughness as well as the wave characteristics. The net result is that the current above the wave boundary layer feels a larger resistance due to the presence of the wave. The wave‐current friction factor and the apparent roughness are found as a function of the velocity of the current relative to the wave orbital velocity, the relative bottom roughness, and the angle between the currents and the waves. In the limiting case of a pure wave motion the predictions of the velocity profile and wave friction factor from the theory have been shown to give good agreement with experimental results. The reasonable nature of the concept of the apparent bottom roughness is demonstrated by comparison with field observations of very large bottom roughnesses by previous investigators. The implications of the behavior predicted by the model on sediment transport and shelf circulation models are discussed.