Head-on collision between capillary–gravity solitary waves

被引：0
作者：
Marin Marin
M. M. Bhatti
机构：
[1] Transilvania University of Brasov,Department of Mathematics and Computer Science
[2] Shandong University of Science and Technology,College of Mathematics and Systems Science
来源：
Boundary Value Problems | / 2020卷
关键词：
Head-on collision; Solitary waves; Nwogu’s Boussinesq model; Surface tension; Perturbation method;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The present study deals with the head-on collision process between capillary–gravity solitary waves in a finite channel. The present mathematical modeling is based on Nwogu’s Boussinesq model. This model is suitable for both shallow and deep water waves. We have considered the surface tension effects. To examine the asymptotic behavior, we employed the Poincaré–Lighthill–Kuo method. The resulting series solutions are given up to third-order approximation. The physical features are discussed for wave speed, head-on collision profile, maximum run-up, distortion profile, the velocity at the bottom, and phase shift profile, etc. A comparison is also given as a particular case in our study. According to the results, it is noticed that the free parameter and the surface tension tend to decline the solitary-wave profile significantly. However, the maximum run-up amplitude was affected in great measure due to the surface tension and the free parameter.
引用
收藏
相关论文
共 63 条
[1]  
Korteweg D.J.(1895)On the change of form of long waves advancing in a rectangular canal, and on a new type of long stationary waves Philos. Mag. 39 422-443
[2]  
De Vries G.(1967)Method for solving the Korteweg-de Vries equation Phys. Rev. Lett. 19 1095-1097
[3]  
Gardner C.S.(1980)On head-on collisions between two solitary waves J. Fluid Mech. 98 509-525
[4]  
Greene J.M.(1984)The interaction of two pairs of solitary waves in a two-fluid system Sci. Sin., Ser. A 27 507-520
[5]  
Kruskal M.D.(1986)Internal solitary waves and their head-on collision. II Phys. Fluids 29 31-37
[6]  
Miura R.M.(1984)Internal solitary waves and their head-on collision. Part 1 J. Fluid Mech. 147 213-231
[7]  
Su C.H.(1991)On head-on collison between two gKdV solitary waves in a stratified fluid Acta Mech. Sin. 7 300-308
[8]  
Mirie R.M.(1992)Head-on collision between two mKdV solitary waves in a two-layer fluid system Appl. Math. Mech. 13 407-417
[9]  
Dai S.Q.(2018)Head-on collision between two hydroelastic solitary waves in shallow water Qual. Theory Dyn. Syst. 17 103-122
[10]  
Mirie R.M.(2019)Analytical study of the head-on collision process between hydroelastic solitary waves in the presence of a uniform current Symmetry 11 6135-6148
1234567