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

作     者：Zhengyong Zhong Keh-Han Wang 

作者机构：INTECSEA Inc.HoustonTXUSA Department of Civil and Environmental EngineeringUniversity of HoustonHoustonTXUSA 

出 版 物：《Journal of Hydrodynamics》 (水动力学研究与进展B辑（英文版）)

年 卷 期：2019年第31卷第6期

页      面：1099-1114页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：It is a pleasure to write this paper in honor of Prof. Theodore Yao-tsu Wu’s 95th birthday and his tremendous scholarly contributions to many scientific areas  including wave hydrodynamics. The corresponding author is grateful to have had the opportunity to work as a Postdoctoral Research Fellow under Prof. Wu’s supervision from 1985 to 1988. He wishes to express his utmost gratitude to Prof. Wu’s insightful guidance and inspiring discussion on his research advancement and personal growth. Happy Birthday  Prof. Wu 

主　　题：Fully nonlinear and weakly dispersive waves overtaking collision Boussinesq models solitary waves finite-element method wave shoaling 

摘      要：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 *** 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 *** solitary wave solutions satisfying the FNWD equations are also ***,a time-accurate and stabilized finite-element code to solve the governing equations is developed for wave *** 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 *** on the overtaking collision of two unidirectional solitary waves of different amplitudes,i.e.,ax and a2 where a1a2,are carried out using both the FNWD and WNWD water wave *** 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 *** 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)***,the phenomena of wave splitting and nonlinear focusing of a solitary wave propagating over a three-dimensional semicircular shoal are *** 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 dis