The studies of the evolution of surface gravity waves near shoals are very important for the management and control of coastal environments. The processes may include beach erosion, sediment transport, and pollutant dispersion, which are critical for the design of coastal structures to minimize the environmental impact. The dynamics may include the transmission, reflection, absorption and dissipation of the wave energy when interacting with the bottom/beach. Theoretical investigations of the problem of wave-bottom interactions were largely based on a mild slope approximation where the change in water depth (or bottom) in the horizontal direction is assumed to be very small. Approximated solutions for the wave field can be obtained analytically only if the bottom slope is constant, while...[ Read more ]

The studies of the evolution of surface gravity waves near shoals are very important for the management and control of coastal environments. The processes may include beach erosion, sediment transport, and pollutant dispersion, which are critical for the design of coastal structures to minimize the environmental impact. The dynamics may include the transmission, reflection, absorption and dissipation of the wave energy when interacting with the bottom/beach. Theoretical investigations of the problem of wave-bottom interactions were largely based on a mild slope approximation where the change in water depth (or bottom) in the horizontal direction is assumed to be very small. Approximated solutions for the wave field can be obtained analytically only if the bottom slope is constant, while for general variable slopes the solutions are obtained through numerical simulation. Only few laboratory experiments were performed to address the problem with specific coastal geometry.

In this study, the propagation of surface gravity waves from deep water to shallow water through a continuous ramp was investigated experimentally in a wave tank to explore the interaction of the waves with the bottom. The experiments were carried out in a water tank of 6.5m long and 0.4m wide with a maximal water depth of 0.3m. A flap-type wave-maker is installed at the upstream end of the tank and a wave absorbing beach at the downstream end. A continuous ramp (breakwater) varying from the tank bottom to a height of 0.2m is installed at the middle of the tank. The ramp was continued with a horizontal solid platform to maintain the same height until reaching the beach end. The setup forms a deep water region of 0.3m depth in the upstream and creates a shallow water region of 0.1m depth at the downstream of the ramp. Hence, when the water depth in the upstream varies from 0.3m to 0.275m and 0.250m, the water depth in the shallow water region drops from 10cm to 7.5cm and 5.0cm to reach the condition of shallow water waves has been reached. In this experiment, two types of the same ramp shape but of different materials were used: one is permeable and the other is impermeable. The permeable ramp was constructed by filling the ramp volume with porous foam materials and using a wire screen to define the shape of the ramp. The impermeable ramp is a solid construction. Monochromatic surface gravity water waves with frequency at 1.4 Hz was generated by the wave-maker. The waves will become established in the deep water region, propagate over the ramp, attenuate in the shallow water region and then dissipate at the beach.

A capacitance wave height gauge was utilized to measure the surface displacement of the waves along the tank to characterize the evolution of wave field. Fast Fourier Transform (FFT) was employed to analyze the time-sequence data to determine the energy (amplitude) and phase angle of the waves. The variations of wave energy with space are then further analyzed by implementing Hilbert Huang Transform (HHT). With these transforms, it is possible to separate the contributions due to incident and reflected waves respectively. The wave reflection coefficients, the decay of incident wave, as well as the variations of wave number along the propagation direction of incident waves are then determined experimentally. The experimental results of wave number are compared with those obtained from the theoretical dispersion relation, and they are in good agreement. The effects of water depths, as well as of a ramp filled with porous materials, on the wave evolution were also investigated.