Laboratory experiments on counter-propagating collisions of solitary waves. Part 1. Wave interactions

This is the publisher’s final pdf. The published article is copyrighted by Cambridge University Press and can be found at: http://journals.cambridge.org/action/displayJournal?jid=FLM.Collisions of counter-propagating solitary waves are investigated experimentally.\ud Precision measurements of water-surface profiles are made with the use of the laser\ud induced fluorescence (LIF) technique. During the collision, the maximum wave\ud amplitude exceeds that calculated by the superposition of the incident solitary waves,\ud and agrees well with both the asymptotic prediction of Su & Mirie (J. Fluid Mech.,\ud vol. 98, 1980, pp. 509–525) and the numerical simulation of Craig et al. (Phys.\ud Fluids, vol. 18, 2006, 057106). The collision causes attenuation in wave amplitude:\ud the larger the wave, the greater the relative reduction in amplitude. The collision also\ud leaves imprints on the interacting waves with phase shifts and small dispersive trailing\ud waves. Maxworthy’s (J. Fluid Mech., vol. 76, 1976, pp. 177–185) experimental results\ud show that the phase shift is independent of incident wave amplitude. On the contrary,\ud our laboratory results exhibit the dependence of wave amplitude that is in support\ud of Su & Mirie’s theory. Though the dispersive trailing waves are very small and\ud transient, the measured amplitude and wavelength are in good agreement with Su\ud & Mirie’s theory. Furthermore, we investigate the symmetric head-on collision of\ud the highest waves possible in our laboratory. Our laboratory results show that the\ud runup and rundown of the collision are not simple reversible processes. The rundown\ud motion causes penetration of the water surface below the still-water level. This\ud penetration causes the post-collision waveform to be asymmetric, with each departing\ud wave tilting slightly backward with respect to the direction of its propagation; the\ud penetration is also the origin of the secondary dispersive trailing wavetrain. The\ud present work extends the studies of head-on collisions to oblique collisions. The\ud theory of Su & Mirie, which was developed only for head-on collisions, predicts well\ud in oblique collision cases, which suggests that the obliqueness of the collision may\ud not be important for this ‘weak’ interaction process