Keywords
Head-on Collision
PIV
Run-up
Phase shifts
How to Cite
Abstract
The behavior of two unequal solitary waves during head-on collision was experimentally studied by optical and particle-tracer methods. Spatial surface profiles were measured using the particle mask correlation method and the image thresholding method, which detects the air-water boundary as a set of locally extreme luminance values. The measured surface displacement of the colliding wave was compared with the corresponding shape of a third-order perturbation approximation. In addition, to estimate the phase shift from the crest at an arbitrary point, the instantaneous surface variations were measured by two wave gauges. The kinetic features of the target and the oncoming and colliding waves were measured by a particle image velocimetry method. To solve the phase shift, we acquired the velocity fields of the colliding waves in a series of experiments and could show our technological advantage over others.References
Boussinesq, M.J. 1871. Théorie des ondes et des remous qui se propagent le long d'un canal réctangulaire horizontal, en communiquant au liquide contenu dans ce canal des vitesses sensiblement pareilles de la surface au fond, J. Math. Pures Appl., 17, 55-108.
Byatt-Smith, J.G.B. 1971. An integral equation for unsteady surface waves and a comment on the Boussinesq equation, J. Fluid Mech., 49, 625-633.
Byatt-Smith, J.G.B. 1988. The reflection of a solitary wave by a vertical wall, J. Fluid Mech., 197, 503-521.
Byatt-Smith, J.G.B. 1989. The head-on interaction of two solitary waves of unequal amplitude, J. Fluid Mech., 205, 573-579.
Chambarel, J., C. Kharif, and J. Touboul. 2009. Head-on collision of two solitary waves and residual falling jet formation, Nonlinear Process. Geophys. 16, 111-122.
Chen, Y. and H. Yeh. 2014. Laboratory experiments on counter-propagating collisions of solitary waves. Part 1. Wave interactions, J. Fluid Mech., 749, 577-596.
Constantin, A. 2011. Nonlinear water waves with applications to wave-current interactions and tsunamis, CBMS-NSF Regional Conference Series in Applied Mathematics, 81, 317p.
Drazin, P.G. and R.S. Johnson. 1989. Solitons: an Introduction, Cambridge, 226p.
Etoh, K. 1999. A study on particle identification in PIV - particle mask correlation method, Journal of Visualization, 1, 313-323.
Fermi, E., J. Pasta, and S.M. Ulam. 1955. Studies in nonlinear problems, Tech. Rep., LA-1940, Los Alamos Sci. Lab.
Gardner, C. S., J. M., Green, M. D., Kruskal, and R. M., Miura. 1967. Method for Solving the Korteweg-de Vries Equation, Phys. Rev. Lett. 19, 1095-1097.
Goring, D.G. 1979. Tsunamis -The propagation of long waves onto a shelf, Ph.D. thesis, Caltech, 337p.
Hammack, J., D. Henderson, P. Guyenne and Y. Ming. 2004. Solitary-wave collisions, A Symp. to honor Theodore Yao-Tsu Wu, OMAE 2004, ASME, 1-12.
Johnson, R.S. 1997. A modern introduction to the mathematical theory of water waves, Cambridge, 445p.
Korteweg, D.J. and G. deVries. 1895. On the change of form of long waves advancing in a rectangular canal and on a new type of long stationary waves, Phil. Mag., 39, 422-443.
Maxworthy, T. 1976. Experiments on collisions between solitary waves, J. Fluid Mech., 76, 177-185.
Miles, J. W. 1977. Resonantly interacting solitary waves, J. Fluid Mech., 79, 171-179.
Mirie, R.M. and C.H. Su. 1982. Collisions between two solitary waves. Part 2. A numerical study, J. Fluid Mech., 115, 475-492.
Rayleigh, Lord. 1876. On waves, Phil. Mag. (5), 1, 257-279.
Renouard, D., F. Santos and A. Temperville. 1985. Experimental study of the generation, damping, and reflexion of a solitary wave, Dyn. Atmos. Oceans, 9, 341-358.
Russell, J.S. 1844. Report on waves, Rep. Meet. Brit. Assoc. Adv. Sci., 14, 311-390.
Russell, J.S. and J. Robison. 1837. Report on waves, Rep., Brit. Assoc. Adv. Sci., 417-496.
Su, C.H. and R.M. Mirie. 1980. On head-on collisions between two solitary wave, J. Fluid Mech., 98, 509-525.
Takehara, K., Adrian, R. J., Etoh, T., and Christensen, K. T. (2000). "A Kalman tracker for super-resolution PIV.† Exp. Fluids, 29(Supp. 1), S034-S41.
Umeyama, M. 2008. PIV techniques for velocity fields of internal waves over a slowly varying bottom topography, J. Water., Port, Coast. & Oc. Eng., ASCE, 134(5), 286-298.
Umeyama, M. 2011. Coupled PIV and PTV measurements of particle velocities and trajectories for surface waves following a steady current, J. Water., Port, Coast. & Oc. Eng., ASCE, 137(2), 85-94.
Umeyama, M. 2012. Eulerian/Lagrangian analysis for particle velocities and trajectories in a pure wave motion using particle image velocimetry, In a Theme Issue 'Nonlinear Water Waves' edited by Adrian Constantin, Phil. Trans. Roy. Soc. A, Roy. Soc. Pub., 370(1964), 1687-1702.
Umeyama, M. 2013. Investigation of single and multiple solitary waves using superresolution PIV, J. Water., Port, Coast. & Oc. Eng., ASCE, 139(4), 303-313.
Umeyama, M., N. Ishikawa and R. Kobayashi. 2014. High-resolution PIV measurements for rear-end and head-on collisions of two solitary waves, Proc., ICCE, ASCE, 34,Waves.40.
Umeyama, M., T. Shintani and S. Watanabe. 2010. Measurements of particle velocities and trajectories in a wave-current motion using PIV and PTV, Proc., ICCE, ASCE, 32, Waves.2.
Zabusky, N.J. and M.D. Kruskal. 1965. Interaction of solitons in a collisionless plasma and the recurrence of initial states, Phys. Rev. Lett., 15, 240-3.