| Summary: | 碩士 === 國立中山大學 === 海洋環境及工程學系研究所 === 94 === The good of this thesis is to apply a numerical model for studying waveform of an internal solitary wave (ISW) on variable seabed topography. The numerical model developed by Lynett and Liu (2002) is adopted for this work but with modification to improve its accuracy, both mathematically and in programming codes. Numerical experiments using the modified model are then performed and the results compared with laboratory experiments of Kuo (2005), in order to validate its accuracy.
The mathematical model derived in the present study is based on the assumption that an internal wave is weakly nonlinear and weakly dispersive in an inviscid fluid. The governing equations based on the continuity equation and Euler equations are solved for ISW propagation over variable topography. The input conditions for the numerical experiments include physical parameters related to water depth and geometry of submarine obstacle, such as depth ratio between upper and lower layers (H1/H2), height (hs) and type (triangular ridge and trapezoidal shelf) of obstacles, in addition to the amplitude (ai) of an incident ISW. From the results of numerical experiments, wave amplitude, phase speed, and wave energy of a transmitted ISW are obtained and compared with that of laboratory experiments. (Kuo, 2005)
ISW propagation over a single obstacle is affected by a dimensionless parameter called “blockage parameter", ζ= (a1+h1)/(h1+h2-hs). Three types of interaction may be classified (weak interaction, moderate interaction, and wave breaking) depending on the value ofζ . For an ISW propagating over two consecutive obstacles, the interval between them is significant in reducing its amplitude and energy, as the interval reduces. Moreover, the effect of relative height between two obstacles may also be classified into two types: (i) within the range of weak interaction, energy dissipation is less for a high obstacle first than for it as the second; (ii) within the range of moderate interaction, the energy dissipation is higher for a high obstacle first than for it as the second.
Further comparisons have shown that the modified numerical model is in better agreement with the results of laboratory experiments (Kuo, 2005) than the original model of Lynett and Liu (2002). The results obtained from the present numerical experiments for ISW evolution on variable topography is encouraging which could benefit other who may be interested in internal wave propagation for practical applications in oceanography.
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