Nonlinear Numerical Wave Tanks And Their Applications

The nonlinear numerical wave tanks that based on the boundary element methods and the high-order Boussinseq-type equations respectively are utilized to study the breaking criteria, the fractional energy losses due to wave breaking, and the generation mechanics of some special waves. The orginal model that based on the boundary element method with the linear element is denoted as DAS here. Its first improved model, which modifies the analytical integral formula in the DAS, is referred to as MDAS, while the second improved model, which changes the linear element into the cubic element on the free surface, is referred to as MDAS2.Considering that DAS was used by Song and Banner (2002, 2004) to propose a breaking thresholdδth that based on an averaged growth rate of the dimensionless local maximum energy density, in the present study, firstly,δth are proved to be still valid for MDAS and MDAS2. Secondly, the influences of the seafloor slopes on theδth are studied, and the results support thatδth are still valid for the slopes gentler than 1:100 in the intermediate-depth water. Thirdly,δth are tested for the focusing waves with constant amplitude spectrums, constant steepness spectrums and PM spectrums, the results show thatδth are valid for the focusing waves with these spectrums.MDAS is used to study the dependence of the frational energy loss on the maximum energy grow rateδmax for the constant amplitude spectrum. This fractional energy loss is found to have near-linear dependence on theδmax. The experimental data from Banner and Pierson (2007) are further used, and the results show that the dependences of the fractional energy losses onδmax for the different spectrums are consistent. In contrast, the dependences of the fractional energy losses on the initial steepnesses (ak)0 have significant discrepancies for the different spectrums. In addition, the fractional energy loss due to wave breaking for the wave passing over a submerged bar is studied by a high-order Boussinesq-type model. The investigations reveal that the nonlinearity and the dispersion of the incident wave as well as the dimensionless bar height (normalized by the water depth) have more significant effects on the fractional energy loss than the slope and the horizontal length of the submerged bar.MDAS are also used to simulate the wave generations caused by the bottom elevations, the bottom collapses and the falling rocks in the wave tanks. For the wave genetions by the bottom elevations, the nonlinear effects are siginificant for the generated wave elevations. For the waves generated by the bottom collapses and the falling rocks, the numerical simulations are compared with the corresponding experimental data, and good agreements between them support that MDAS are capable to simulate these wave generations.