A laboratory study of class III Bragg resonance of gravity surface waves by periodic beds

When moderately steep waves travel over a periodic rippled bed, class III Bragg resonance may occur due to the third-order quartet wave-bottom interaction among one bottom and three surface wave components. The theory, however, has not been experimentally confirmed. To verify the existence of class III Bragg resonance, we consider the simplest possible case involving a single incident wave and conduct a series of physical experiments. The experiments show that as the theory predicts, class III Bragg resonance could generate not only the reflected waves (from subharmonic resonance) but also the transmitted waves (from superharmonic resonance), and the reflection and transmission coefficients vary linearly along the rippled bottom patch. Furthermore, the experimental data of the reflected and transmitted waves (due to class III resonance) agree quantitatively well with the prediction by high-order spectral (HOS) method computations. To further understand the characteristics of class III resonance, we apply HOS simulations to study the more general cases including the presence of two incident waves of different frequencies as well as the presence of an incident wave group with Gaussian envelope. The results show that in addition to class I and class II Bragg resonances, class III Bragg resonance can significantly influence the evolution of surface wave fields passing over a rippled bottom, especially in the case of shallow water.