Abstract
Abstract. The head-on collision of two equal and two unequal steep solitary waves is investigated numerically. The former case is equivalent to the reflection of one solitary wave by a vertical wall when viscosity is neglected. We have performed a series of numerical simulations based on a Boundary Integral Equation Method (BIEM) on finite depth to investigate during the collision the maximum runup, phase shift, wall residence time and acceleration field for arbitrary values of the non-linearity parameter a/h, where a is the amplitude of initial solitary waves and h the constant water depth. The initial solitary waves are calculated numerically from the fully nonlinear equations. The present work extends previous results on the runup and wall residence time calculation to the collision of very steep counter propagating solitary waves. Furthermore, a new phenomenon corresponding to the occurrence of a residual jet is found for wave amplitudes larger than a threshold value.
Highlights
In this paper we investigate the head-on collision of two equal and two unequal solitary waves which are computed by using the algorithm developed by Tanaka (1986)
None of them discussed about a new phenomenon peculiar to head-on collision of very steep solitary waves: the formation of a residual thin jet. This jet is observed for the first time during the collision of the two counter propagating solitary waves In Sect. 2 we present the mathematical statement of the water wave problem, and we describe briefly the numerical method
The horizontal length of the domain, L, is assumed to be large enough to avoid any perturbation generated from the vertical walls during the computational time of the simulations on the solitary wave collision occurring in the middle of the tank
Summary
In this paper we investigate the head-on collision of two equal and two unequal solitary waves which are computed by using the algorithm developed by Tanaka (1986). A lot of works considered analytically, numerically and experimentally this problem, calculating namely the maximum run-up amplitude, phase shift due to the collision and wall residence time. In a numerical study based on the approximate equations derived by Su and Gardner (1969), Mirie and Su (1982) checked the phase shifts and maximum amplitude of a collision with a corresponding perturbation calculation and compared with experiments They found a wave train trailing behind each of emerging solitary waves from the head-on collision. Fenton and Rienecker (1982) developed a numerical method based on a Fourier decomposition for solving nonlinear water wave problems, namely solitary wave interactions They investigated the maximum run-up at the wall and the phase shift during the interaction. During the formation of the residual jet, the curvature becomes important and surface tension effect may be taken into account
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