||This thesis discusses the plunging or spilling wave breaking profiles for the progressive water waves propagating on gentle sloping bottoms. Due to the shoaling effect, the wave height will increase and the wave length will shorten as well as the asymmetry of wave profile will appear. As the wave continues to move to the shore, the wave velocity will decrease and the wave profile will be pushed to steep in the vertical direction. As the slope of wave profile approaches to large, the horizontal velocity of the water particle at the wave crest will larger than wave phase velocity and the wave breaking will occur and move forward in the free-body projectile motion.The theoretical solution derived by Chen at al. (2005) for the progressive waves propagating on sloping bottoms, the wave breaking criteria and the equation of the particle projectile motion after the wave breaking are included to discuss the continuous variations of wave profile for the plunging or spilling breaking waves.|
A laboratory experiment is conducted in order to validate the theoretical wave breaking profile on sloping bottoms with measures. Wave breaking profiles can be verified obtained by the theoretical solution and experimental measurements. The experimental measurements were carried out in a glass-walled wave tank, 21m×0.7m×0.5m, in Tainan Hydraulics Laboratory , National Cheng Kung University. A High-Speed camera was set up in front of the glass-wall at the different breaking point locations depending on the initial wave conditions. This method allows to successively capturing the wave breaking profiles. Images were captured by a High-Speed camera (MS55k2, Canadian Photonic Labs Inc.), which has a 1280*1080 pixel resolution and maximum framing rate 1020 frames per second (fps). A transparent acrylic-plastic sheet (0.9 m×0.625m) was calibrated at 1-mm intervals in 5 mm×5 mm grids. Its function is a virtual grid in the picture. The experiments were conducted at two different bottom slope ( ,1/20) and two different water depth (d=37.6m, 40.0cm) and various wave periods from =0.8sec~3.0sec). The range of incident wave heights were from 4 cm~8cm.
According to the comparison results between the theoretical solution and experimental data, the wave profile evolution of plunging or spilling breaking wave on sloping bottoms can be described. Meanwhile, it is also proved that the instantaneous wave profiles after the breaking wave is good agreement. The duration of the overturning wave is less known by the analytical solution. The present theory can well describe the wave shoaling, as well as the occurrence of breaking wave and wave overturning, similar to the plunging jet in the breaking water waves over sloping bottom. Comparing the sequence of computed wave breaking profiles with snapshots of breaking wave behavior over a sloping bottom captured by the high-speed camera shows a good agreement of the theoretical wave breaking profile with laboratory measurements. The breaker jet creating a forward moving jet is well observed in the present theoretical results. This indicates that the theoretical solution is accurate for modeling such post-breaking waves.