Numerical Study On The Evolution Process Of Internal Solitary Waves In Two-layer Fluids

Under the theory of classic KdV equation and the multi-factor KdV equation, the evolution process of internal solitary waves is numerically simulated over the flat terrain and the slope-shelf topography. The particle feature of the KdV-type equation is tested during the solitons' interaction, and the physical variables are investigated in this process. All of the above work can provide a basic reference for the future numerical model. The two-dimensional, depth integrated model of internal wave propagation is carefully studied, which is proposed by Lynett & Liu. Some errors in the detailed derivation are corrected. Compared with the experimental data, the modified model can better predict the wave profile than the original model. The same simulation test as the KdV-type equation over flat terrain and the slope-shelf topography is done in horizontal one dimension, and some comparisons between them are made. On the horizontal two-dimensional level, the process of the internal solitary wave traveling into and out of the tank with different shape of outlet is modeled. Some factors, which may affect this process, are qualitatively proposed through the comparison of the vertical wave profile and the horizontal two-dimensional wave motion in three different cases. The numerical experiment concerning the interaction of two solitons with different wave direction is carried out. The case of no evident change on the wave direction is analytically analyzed, and some suggestions are made for this area. The study of internal solitary wave propagation over the real topography of the South China Sea is carried on, and the process of solitons traveling from the neighboring area of Luzon Island to the shelf of the South China Sea is simulated. The result proves the opinion on the change of wave direction in the vicinity of the DongSha Island. The weak nonlinear L-L type model can't correctly forecast the propagation process of internal wave with large amplitude and full nonlinearity. So based on the fully nonlinear internal wave theory proposed by Choi & Camassa, we extend their unidirectional model to horizontal two-dimension, substitute the free surface condition for the original rigid top wall, and derive the fully nonlinear internal wave theory in two-fluid system. The theory still should be checked, and it's one part work of the next numerical simulation.