Effect of currents on nonlinear waves in shallow water

Abstract

Effect of various forms of currents on regular nonlinear waves in shallow water is investigated by use of a computational fluid dynamics approach. A range of wave conditions with different wave heights and wave periods are considered. Effect of three types of currents on these waves is investigated, namely (i) uniform current over the water depth, (ii) shear current from the seafloor to the still-water level, and (iii) a custom current profile that changes over the water depth. The current profiles are considered in both following and opposing directions of the incoming wave, forming in total 18 wave–current configurations. The Navier–Stokes equations for a laminar flow are solved computationally in two dimensions. A numerical wave–current maker is created to generate combined nonlinear waves and currents in shallow water. The effect of the currents on the change of the wave field, including quantitative change of the surface elevation, wave height, wavelength, horizontal particle velocity, and the velocity and pressure fields is presented and discussed. It is found that presence of the current can alter the wave field significantly, and the current profile and direction play a significant role in the change of the wave field. A following current in shallow water increases the peak of surface elevation, horizontal particle velocity and pressure, along with an increase in wavelength and wave height, while an opposing current reduces these. The change of wave height with current direction appears to be opposite to that observed in deep water in the literature. It is also concluded that a linear superposition of the undisturbed wave and current velocities can describe the horizontal particle velocity of the wave–current field for following currents (particularly under the wave trough) reasonably well, but larger differences are observed for opposing currents.