A fully nonlinear and weakly dispersive water wave model for simulating the propagation,interaction,and transformation of solitary waves

This paper presents the development of a theoretical model of fully nonlinear and weakly dispersive(FNWD)waves and numerical techniques for simulating the propagation,interaction,and transformation of solitary waves.Using the standard expansion method and without the limit of small nonlinear parameter defined as the ratio of the wave height versus water depth,a set of model equations describing the FNWD waves in a domain of moderately varying bottom topography are formulated.Exact solitary wave solutions satisfying the FNWD equations are also derived.Numerically,a time-accurate and stabilized finite-element code to solve the governing equations is developed for wave simulations.The solitary wave solutions of FNWD,weakly nonlinear and weakly dispersive(WNWD),and Laplace equations based models in terms of wave profile and phase speed are compared to examine their related features and differences.Investigations on the overtaking collision of two unidirectional solitary waves of different amplitudes,i.e.,ax and a2 where a1>a2,are carried out using both the FNWD and WNWD water wave models.Selected cases by running the FNWD and WNWD models are performed to identify the critical values of a1/a2 for forming a flattened merging wave peak,which is the condition used to determine if the stronger wave is to pass through the weaker one or both waves are to remain separated during the encountering process.It is interesting to note the critical values of a1/a2 obtained from the FNWD and WNWD models are found to be different and greater than the value of 3 proposed by Wu through the theoretical analysis of the Korteweg-de Vries(KdV)equations.Finally,the phenomena of wave splitting and nonlinear focusing of a solitary wave propagating over a three-dimensional semicircular shoal are simulated.The results obtained from both the FNWD and WNWD models showing the fission process of separating a main solitary wave into multiple waves of decreasing amplitudes are presented,compared,and discussed.

Transient curvilinear-coordinate based fully nonlinear model for wave propagation and interactions with curved boundaries

This paper presents a newly developed 3-D fully nonlinear wave model in a transient curvilinear coordinate system to simulate propagation of nonlinear waves and their interactions with curved boundaries and cylindrical structures. A mixed explicit and implicit finite difference scheme was utilized to solve the transformed governing equation and boundary conditions in grid systems fitting closely to the irregular boundaries and the time varying free surface. The model＇s performance was firstly tested by simulating a solitary wave propagating in a curved channel. This three-dimensional solver, after comparing the results with those obtained from the generalized Boussinesq（g B） model, is demonstrated to be able to produce stable and reliable predictions on the variations of nonlinear waves propagating in a channel with irregular boundary. The results for modeling a solitary wave encountering a vertical cylinder are also presented. It is found the computed wave elevations and hydrodynamic forces agree reasonably well with the experimental measurements and other numerical results.