An analytical model investigating the impact of current shear and topographic fluctuations on surface waves

Abstract. There are interactions between surface waves and currents, the latter includes wind-driven current and tidal current. Currents influence surface waves though advection transport and shear instability generation processes. While the horizontal gradient of current is commonly considered to calculate wave-current interaction source term in most wave models, the vertical gradient of current (current shear) has been simplified. In coastal waters, strong background currents with topographic fluctuations at the scale of surface waves have a resonance effect on surface waves. However, this resonance process is currently ignored in existing wave models. To evaluate the effects of current shear and topographic fluctuations on surface waves more accurately, an analytical model is proposed to describe the modification of the amplitude of orbital velocities for surface waves. The amplitude of orbital velocities exhibits significant variations when considering both current shear and topographic fluctuation effects. Wave particle trajectory equations that incorporate current shear and topographic fluctuations are derived based on this analytical model. In deep waters, current shear can increase or decrease the horizontal radius of wave particle trajectory by approximately 0.3 m, while the modification of horizontal amplitude of orbital velocities is about 0.3 m/s. In shallow waters, with both topographic fluctuations and background current present, both horizontal and vertical radii of wave particle trajectory change by approximately ±0.1 m respectively, and the modification of both horizontal and vertical amplitudes of orbital velocities is about 0.2–0.3 m/s. Moreover, in some cases, there are reversals in the direction of wave particle trajectories.