Analytical Study of Obliquely Incident Wave Transformation on Gentle Slope

• Main Authors: Bin-Da Yang, 楊炳達
• Other Authors: Shan-Hwei Ou
• Format: Others
• Language: zh-TW
• Published: 2004
• Online Access: http://ndltd.ncl.edu.tw/handle/qazhvz

博士 === 國立成功大學 === 水利及海洋工程學系碩博士班 === 92 === 　　Although numerous analytical models have been developed to investigate the obliquely incident wave transformation on gentle slope, very few researchers have considered the effect of bottom slope, and the tangential relationship between the direction of a water-particle velocity and the curved surface of a wave ray. In the present study, various aspects of the wave field, including wave deformation, refraction and shoaling has been investigated. Unlike in the previous studies, the effect of bottom slope on the wave propagation has been considered here, and the geometric characteristic of wave refraction is investigated. 　　The present study is based on linearized free surface boundary conditions in absence of wave breaking. In order to describe the effect of bottom slope, the physical quantities related to wave motion are cast in a perturbed series with the bottom slope as the parameter. With the wave-ray coordinate system, the water-particle velocity can be tangential to the curved surface of a wave ray. Accordingly, an explicit expression for the velocity potential is derived as a function of the bottom slope, perturbed to the second order in the Eulerian system. Afterwards, the parametric functions for the water-particle motion are obtained by using a linear transformation between the Eulerian system and the Lagrangian system. By using the parametric functions, the process of successive deformation of a wave profile, the breaking index, the fluid-particle trajectory, the spatial and temporal asymmetry of wave profile, and the variation of wave height have been obtained before the wave breaking occurs. 　　For the Lagrangian system, the wave characteristics, as discussed in the thesis, are derived as explicit solutions, and illustrated with a series of figures under different conditions of the wave steepness in deep water, such as, the water depth, the incident angle and the bottom slope. In order to correspond with the physical characteristic of wave refraction, all the wave characteristics are specially analyzed along the direction of wave rays. However, the bottom slope is observed to affect the wavenumber, the breaking index, the temporal asymmetry of the wave profile and the variation of wave height, which are therefore presented in second-order in terms of the perturbed expansion. The foregoing could not be accurately described using the first-order analytic models. 　　Since the phenomenon of wave breaking is not considered in this study, the present results are applicable for the wave field before the breaking takes place. In the non-breaking region, the theoretical restrictions can be conditionally satisfied for the present analytical model under bottom slope < 1/2. For a steeper bottom slope, the effect of the bottom slope terms can be reinforced, however, it becomes inadequate to expect the full effect of the bottom slope because of the weak nature of convergence of the perturbation series.