Influence of ocean currents and surface tension on class II Bragg resonance using multi-scale analysis.

This article presents a theoretical investigation of class II Bragg resonance—resonant reflection of surface waves by composite sinusoidal seabed topographies—in the presence of uniform ocean currents and surface tension, using a multi-scale analytical approach. The study derives coupled evolution equations for incident and reflected wave amplitudes, obtaining analytical expressions for reflection and transmission coefficients that extend previous models by incorporating current and surface tension effects. Numerical results reveal that the reflection coefficient and Bragg resonance peak exhibit distinct behaviors across three current velocity ranges, linked to transitions in group velocity from positive to negative, with surface tension influencing the resonance amplitude, phase shift, and bandwidth differently depending on current strength. The number of seabed ripples required for full reflection depends on current speed, with larger ripple counts needed near critical current values where resonance bandwidth narrows sharply. These findings enhance understanding of wave-current-bottom interactions relevant to coastal engineering, sediment dynamics, and coastal protection strategies.