- Collisions of counter-propagating solitary waves are investigated experimentally.
Precision measurements of water-surface profiles are made with the use of the laser
induced fluorescence (LIF) technique. During the collision, the maximum wave
amplitude exceeds that calculated by the superposition of the incident solitary waves,
and agrees well with both the asymptotic prediction of Su & Mirie (J. Fluid Mech.,
vol. 98, 1980, pp. 509–525) and the numerical simulation of Craig et al. (Phys.
Fluids, vol. 18, 2006, 057106). The collision causes attenuation in wave amplitude:
the larger the wave, the greater the relative reduction in amplitude. The collision also
leaves imprints on the interacting waves with phase shifts and small dispersive trailing
waves. Maxworthy’s (J. Fluid Mech., vol. 76, 1976, pp. 177–185) experimental results
show that the phase shift is independent of incident wave amplitude. On the contrary,
our laboratory results exhibit the dependence of wave amplitude that is in support
of Su & Mirie’s theory. Though the dispersive trailing waves are very small and
transient, the measured amplitude and wavelength are in good agreement with Su
& Mirie’s theory. Furthermore, we investigate the symmetric head-on collision of
the highest waves possible in our laboratory. Our laboratory results show that the
runup and rundown of the collision are not simple reversible processes. The rundown
motion causes penetration of the water surface below the still-water level. This
penetration causes the post-collision waveform to be asymmetric, with each departing
wave tilting slightly backward with respect to the direction of its propagation; the
penetration is also the origin of the secondary dispersive trailing wavetrain. The
present work extends the studies of head-on collisions to oblique collisions. The
theory of Su & Mirie, which was developed only for head-on collisions, predicts well
in oblique collision cases, which suggests that the obliqueness of the collision may
not be important for this ‘weak’ interaction process.
- Chen, Y., & Yeh, H. (2014). Laboratory experiments on counter-propagating collisions of solitary waves. Part 1. Wave interactions. Journal of Fluid Mechanics, 749, 577-596. doi:10.1017/jfm.2014.231
|Funding Statement (additional comments about funding)
- This work
was supported by Oregon Sea Grant Program (NA06OAR4170010-NB154L and
NA10OAR4170059-NA223L), and the Oregon State University Edwards Endowment.
Y.C. is partially supported by the China Scholarship Council.