On the Improvement of Boundary Conditions and Applications of Boussinesq Equations

• Main Authors: I-Fan Tseng, 曾以帆
• Other Authors: Tai-Wen Hsu
• Format: Others
• Language: zh-TW
• Published: 2005
• Online Access: http://ndltd.ncl.edu.tw/handle/40738647075016694891

博士 === 國立成功大學 === 水利及海洋工程學系碩博士班 === 93 === 　To improve the weak nonlinearity and weak dispersion of the classical Boussinesq equation, a 2nd-order fully nonlinear Boussinesq model based on Wei and Kirby (1995)’s scheme is established in this study. This model also uses the eddy viscosity technique to model breaking, and a “slotted beach” to simulate run-up phenomena. The damping coefficients of the sponge layer boundary in this model are derived theoretically. The present result differs from former researches in which the free parameters in the damping coefficients are suggested by numerical tests to control the effect of the sponge layer. Numerical experiments show that the proposed damping coefficients work efficiently on reducing the energy of reflected waves from the sponge layer. The numerical tests are performed to verify the applicability and validity of the present model. 　The present model is performed to simulate the deformation of waves propagating over the varying topography, including shoaling, breaking, recovery, runup and setup, etc. With different wave conditions and beach slopes, numerical analysis of the surf similarity parameter, runup elevation and reflection coefficient result in extended range of the empirical formulas. 　This study is also applied to simulate the Bragg reflection of monochromatic and random waves due to artificial sand ripples. The numerical results are compared with the theoretical solutions of Miles (1981), and with the corresponding results using the evolution equation for mild slope equation of Hsu et al. (2003) and the experimental data. For the monochromatic wave, the present model can predict the reflection coefficients of the primary and second-harmonic resonance well. For the random waves, the reflection coefficients of the primary resonance are smaller and the reflection bandwidth is wider than the monochromatic wave, so the Bragg reflection of random waves is different from that of the monochromatic wave. In addition, present model is applied to study the affecting factors of the Bragg reflection, including the number, the height and the spacing of artificial sand ripples.