We theoretically and experimentally investigate the mechanism underlying the generation of upstream-propagating waves induced by a steady current over a horizontal bottom with a patch of sinusoidal ripples. By considering the triad resonant wave–ripple interactions involving two unsteady wave components (which have the same frequency but different wavenumbers) and one bottom ripple component in the presence of a steady uniform current, we derive the general condition under which unsteady upstream- and/or downstream-propagating waves can be induced. The frequency and wavenumbers of the induced propagating waves are given by the triad resonance condition in terms of current speed, water depth and bottom ripple wavenumber. By means of a multiple-scale perturbation analysis, we obtain the nonlinear amplitude evolution equations governing the spatio-temporal evolution of resonance-generated waves. Based on these equations, we find that the amplitude of the generated upstream-propagating waves is dramatically amplified when the associated triad resonance occurs in the neighbourhood of the critical current speed/frequency (corresponding to zero group velocity of unsteady waves in the presence of a current). A series of laboratory experiments in a long wave flume with wide ranges of current speeds and water depths are conducted to verify the theory. The experiments confirm the observation of the phenomenon of upstream-propagating wave generation in a steady flow over a rippled bottom. In particular, the experimental measurements of the kinematics of upstream-propagating waves as well as the critical flow condition for the observation of such wave generation compare well with the theoretical prediction.
Submerged breakwaters based on Bragg resonance could be one of the measures used for mitigating marine disasters and coastal erosion in nearshore areas. Here, flume experiments were conducted to investigate the Bragg resonant reflection of waves propagating over porous submerged breakwaters. Furthermore, the influence of permeability, relative width, relative height, and section shapes of submerged breakwaters on Bragg resonant reflection were considered. This revealed that the Bragg resonant reflection coefficient increased with the decrease in permeability and increase in the relative height of submerged breakwaters. However, a slowing trend occurred when the Bragg resonant reflection coefficient peak decreased with the increase in permeability and increased with the increase in relative height. Moreover, the primary peak Bragg resonance increased with the increase in the relative width of submerged breakwaters in the range of 0.1–0.3. This was consistent with the numerical results of Ni and Teng (2021), to a certain extent, as the reflection coefficient first increased and then decreased with the relative bar width. In addition, rectangular submerged breakwaters demonstrated a better reflection effect than the trapezoidal submerged breakwaters, and the triangular submerged breakwaters demonstrated a poor reflection effect.
Oscillating buoy device, also known as point absorber, is an important wave energy converter (WEC) for wave energy development and utilization. The previous work primarily focused on the optimization of mechanical design, buoy’s array configuration and the site selection with larger wave energy density in order to improve the wave energy generation performance. In this work, enlightened by the potential availability of Bragg reflection induced by multiple submerged breakwaters in nearshore areas, we investigate the energy conversion behavior of oscillating buoy devices under different wave types (traveling waves, partial and fully standing waves) by flume experiments. The localized partial standing wave field is generated by the Bragg resonance at the incident side of rippled bottoms. Furthermore, the fully standing wave field is generated by the wave reflection of vertical baffle installed in flume. Then the wave power generation performance is discussed under the conditions with the same wave height but different wave types. The experimental measurements show that the energy conversion performance of the oscillating buoy WEC could be improved under the condition of standing waves when compared with traveling waves. This work provides the experimental comparison evidence of wave energy conversion response of oscillating buoy devices between travelling waves and standing (fully or partial) wave conditions.