Phase Shifts in the Counter-Interaction of Shallow Water Waves

Abstract

Purpose. The work is aimed at numerical studying and describing the wave effects arising from the counter-interaction of different polarity single pulses within the framework of the Boussinesq type equation system with regard to dispersion in a constant depth basin. Methods and Results. To simulate the scenarios of the long wave pulse interaction, the CLAWPACK software package was used. It included the hybrid method for numerical solving the equation system which, in its turn, comprised the method of finite volumes and finite differences. The results were compared to the numerical solutions obtained earlier by using a non-dispersive nonlinear system of shallow water equations. Conclusions. The fundamental wave phase shift is studied in its interaction with the counter-propagating pulses of different polarity. It is shown that the phase shift increases with the initial pulse amplitude growth. The dispersion influence is manifested in a single wave transformation into an undular bore. The study novelty consists in detecting and demonstrating such nonlinear effects as the phase shifts in the long wave counter-interaction within the framework of the nonlinear shallow water numerical model including the dispersion terms.

Keywords

• long waves
• numerical experiment
• boussinesq equations
• wave interaction