AbstractThis thesis is motivated by recent field observations of tsunamis which point out that use of solitary waves as model tsunami is not theoretically justified. In order to generate very long waves in laboratory, a bottom-tilting wave maker is designed and used at the University of Dundee. This new type of wave maker can produce waves longer than the effective length of solitary waves, which provides better long wave model. The main idea of the bottom-tilting wave maker is that moving the entire bottom can lead to the wave as long as the given wave tank. Meanwhile, some analytical solutions and numerical models are developed in this research for theoretical investigation. Wave behaviour in the tank without beach and the wave run-up on a plane beach are of main interest. The unique contributions for the two scenarios are that wave profile or run-up height of very
long waves with a variety of bottom motions and surface problems have been investigated, respectively.
A series of experiments are conducted in the new wave tank by inputting the prescribed bottom motions to the electrical motor with varying water depth, bottom motion displacement and speed. The free surface elevation time-histories are measured by acoustic wave gauges while the maximum run-up heights of varying waves are observed by a video camera.
Nonlinear and dispersive numerical models are developed in this thesis for modelling the wave tank. A shock-capturing finite volume scheme with high-order reconstruction method is used to solve the governing equations, coupling with a computational domain mapping technique to estimate the moving shoreline. By comparing to the experimental measurements, the numerical models are verified and able to approximate the resulting waves in the wave tank. Surface waves studied in Boussinesq scaling with time dependent bottom bathymetry gives a better performance in approximating the wave generation in the tank without a beach, while nonlinear shallow water system is good at approximating the wave run-up on a plane beach. The computational domain is as long as the wave tank and bounded by two fully-reflective vertical walls at the two ends. The analytical solutions of the time-history of free surface elevation are derived by the linear wave theory in an infinite domain. To further extend the study, the numerical model based on the Boussinesq equations in a semi-infinite wave tank is developed, in order to estimate the wave period which can not be easily determined from the experiments and to explore the wave profile in a tank with long propagation distance.
For wave generation in the tank without a beach, it can be verified that the new wave maker can provide new long wave model better than solitary waves by the theoretical results from the linear wave theory and the numerical model based on the Boussinesq equations. All the waves within the measured range are longer than the effective wavelength of the solitary waves with same wave amplitude, which can reach seven times longer at most. Using both the theoretical and experimental results, the relations between the bottom motions and the resulting waves have been investigated in terms of the wave amplitude, wave peak time and wave period. Note that only for estimating the wave period is assumed that the wave tank has semi-infinite domain by using the Boussinesq equations. In particular, wave amplitudes can be expressed by power function. For wave run-up on a plane beach, the parametric studies based on the nonlinear shallow water equations reveal how the run-up height relates to the bottom motion and the leading wave profile in a wave tank with adjustable beach slope. Monotonous dependence of the maximum run-up height on the wave height or wave-front steepness is discovered. Furthermore, the influence of the bottom friction and wave breaking are addressed.
|Date of Award
|Korea Institute of Ocean Science & Technology
|Yong Sung Park (Supervisor)