Numerical Modeling of Tidal Waves in Coastal Waters

• Main Authors: Guo, Si Yin, 郭思吟
• Other Authors: Cai, Ding Gui
• Format: Others
• Language: zh-TW
• Published: 1995
• Online Access: http://ndltd.ncl.edu.tw/handle/75043235339716087885

碩士 === 國立臺灣大學 === 土木工程學研究所 === 83 === This research is to study the change of wave amplitude and phase for wave reflection, diffraction and refraction around a structure or an island when the effects of the earth''s rotation are considered. The purpose is to extend the existing model to be adequate for computations of very long period wavesb such as tidal waves. For waves propagating over a very long distance, or when wave period becomes very long, or both, the effects of the earth''s rotation (or Coriolis effects) may not be negligible. Following a procedure Tsay(1991) used, an equation which is an extension of the mild-slope equation is derived. For waves with longer periods, this equation shows the effects of the earth''s rotation. For waves with shorter periods, it becomes the mild- slope equation. Analytical solutions of tidal waves propagating in two cases: a constant water depth and a paraboloidal water depth are obtained to calibrate the finite element numerical model. To find out the analytical solutions, an equation by the definition of no flux boundary condition is derived. When f.neq. 0, the equation contains .prtl..eta./.prtl..theta., which is the influence of f on the no flux boundary. This correct boundary condition not only take out mistakes from the boundary condition derived by Tsay(1991) but also can be used to obtain the analytical solutions of two special cases. From the results of numerical calculation, the effects of Coriolis factor are evident in both cases. When f is getting large, the equal amplitude lines and the equal phase lines are getting twisty, which means the symmetry of the contour is getting spoiled. In the case of constant water depth, when wave period is 46800sec and f=0.000143, the waves will be trapped and the trapped waves will circulate clockwise around the circular island, which is the same as what Longuet Higgins proved in 1969.