Internal solitary waves and their head-on collision. Part 1

Abstract

Head-on collision of two (KdV) solitary waves at the interface of an inviscid two-fluid system of rigid upper and lower boundaries is investigated by a perturbation method. We obtain the third-order solution and find a dispersive wavetrain trailing behind each emerging solitary wave. The wavetrain is of the same polarity (depression/elevation) as the main wave. Furthermore, the energy and amplitude of the wave-train are decreasing in time as long as it is still attached to the main wave. This implies an increase in energy of the main wave. Up to the third order of accuracy the solitary wave emerging from a head-on collision retains its initial profile save for a phase shift. This phase shift is found to be amplitude dependent to the second order. The transfer of energy from the wavetrain to the main wave explains the slow recovery of the incident profiles in existing numerical results on the head-on collision of two solitary waves at the surface of an infinite channel.