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Evolution of a quasi-steady breaking wave

Published online by Cambridge University Press:  26 April 2006

J. C. Lin  and
D. Rockwell
J. C. Lin
Affiliation:
Department of Mechanical Engineering and Mechanics, Room 354, 19 Memorial Drive West, Lehigh University, Bethlehem, PA 18015, USA
D. Rockwell
Affiliation:
Department of Mechanical Engineering and Mechanics, Room 354, 19 Memorial Drive West, Lehigh University, Bethlehem, PA 18015, USA
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Abstract

The stages of evolution of a quast-steady breaker from the onest of a capillary pattern to a fully evolved breaking wave are cgaracterized using high-image-density particle image velocimetry, which provides instrantaneous representations of the free surface and the patterns of vorticity beneath it. The initial stage, which sets in at a low value of Froude number, involves a capillary pattern along each trough-crest surface of a quasi-stationary wave. The successive crests of the capillary pattern exhihit increasing scale and culminate in a single largest-scale crest of the free surface. Immediately upstream of the large-scale crest, the capillary pattern shows counterclockwise concentrations of vorticity at its troughs and regions of clockwise vorticity beneath its crests. The onset of the final, largest-scale crest exhihits two forms: one involving no flow sparation; and the other exhibiting a small-scale separaed mixing layer. At an intermediate value of Froude number, a breaker occurs and the acpillary pattern is replaced by large-scale distortions of the free surface. The onset of separation, which involves flow deceleration along a region of the free surface having a large radius of curvature, leads to formation of a long mixing layeer, which has substantial levels of vorticity. Downstream of this breaker, the long-wavelength wave pattern is suppressed. At the largest value of Froude number, the onset of flow sparation rapidly occurs in conjunction with an abrupt change in slope of the surface, giving rise to vorticity concentrationa in the mixing layer.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 302 , 10 November 1995 , pp. 29 - 44
Copyright
© 1995 Cambridge University Press

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References

Banner, M. L. 1988 Surging characteristics of spilling zones of quasi-steady beaking water waves. Proc. IUTAM Symp. on Nonlinear Waterwaves, 1987, Takyo, Japan (ed. K. Horikawa & H. Maruo). Springer.
Banner, M. L. 1990 The influence of wave breaking on the surface pressure distribution in wind-wave interactions. J. Fluid Mech 211, 463–495.Google Scholar
Banner, M. L. & Peregrine, D. H. 1993 Wave breaking in deep water. Ann. Rev. Fluid Mech. 25, 373–397.Google Scholar
Battjes, J. A. & Sakai, T. 1981 Velocity field in a stead breaker. J. Fluid Mech. 111, 421–438.Google Scholar
Battjes, L. P. & Kwon, J. T. 1989 Velocity ring dynamics at a free surface. Phys. Fluids A1, 1–61.Google Scholar
Cointe, R. 1987 A theory of breakers and breaking waves. PhD dissertation, University of California, Santa Barbara (University Microfilms Order No. 8811824).
Cointe, R. & Tulin, M. P. 1994 A theory of steady breakers. J. Fluid Mech. 276, 1–20.Google Scholar
Crapper, G. D. 1957 An exact solution for progressive capillary waves of arbitrary amplitude. J. Fluid Mech. 2, 532–540.Google Scholar
Dimas, A. A. & Triantafyllou, G. S. 1994 Nonlinear interaction of shear flow with a free surface’. J. Fluid Mech 260, 211–246.Google Scholar
Dommermuth, D. C. & Yue, D. K. P. 1991 A numerical study of three-dimensional viscous interactions of vor tices with a free surface. InEighteenth Symp. on Naval Hytdrodynamics, University of Michigon. Ann Arbor. pp. 727–788.
Duncan, J. H. 1981 An experimental investigation of breacking waves produced by a towed Hydrofoil. Proc. R. Soc. Lond. A 377, 331–348.
Duncan, J. H., Philomin, V., Behres, M. & Kimmel, J. 1994 The formation of spitling breaking water waves. Phs. Fluids 6, 2558–2560.Google Scholar
Hoyt, J. W. & Selling, R. H. T. 1989 The hydraulic jump as a mixing layer. J. Hydroul. Div. ASCE 115, 1607–1614.Google Scholar
Lin, J.-C. & Rockwell, D. 1994 Instantaneous structure of a breaking wave. Phys. Fluids 6, 2877–2879.Google Scholar
Longuet-Higgins, M. S. 1973 A model of flow separation at a free surface. J. Fluid Mech. 57, 129–148.Google Scholar
Longust-Higgins, M. S. 1990 Flow separation near the crests of short gravity waves. J. Phys. Oceanogr. 20, 595–599.Google Scholar
Longust-Higgins, M. S. 1992 Capillary rollers and bores. J. Fluid Mech. 240, 659–679.Google Scholar
Longust-Higgins, M. S. 1994 Shear instability in spilling breakers. Proc. R. Soc. Lond. A. 446, 399–409.Google Scholar
Longust-Higgins, M. S. & Turner, J. S. 1974 As ‘entraining plume’ model of a spilling breaker. J. Fluid Mech. 236, 461–476.Google Scholar
Meinhart, C. D., Prasad, A. K. & Adrian, R. J. 1992 Parallel digital proessor system for particle image velocimetry, Sixth Intl Symp. on Applications of Laser Techniques to Fluid Mechanics, Lisbon, Portugal, July 20-30 pp. 30.1.1. to 30.1.5.
Ohring, S. & Lugt, H. J. 1989 Two counter-rotating vortices approaching a free surface in a viscous fluid, David Taylor Research Center Rep. DTRC-89/013.Google Scholar
Ohring, S. & Lugt, H. J. 1991 Interaction of a viscous vortex pair with a free surface. J. Fluid Mech. 227, 47–70.Google Scholar
Peregrine, D. H. 1992 Mechanisms of wave breaking. InProc. IUTAM Symp. on Breaking Waves (ed. M. l. Banner & R. H. J. Grimshaw). Springer.
Peregrine, D. H. & Svendsen, I. A. 1978 Spilling breakers, bores and bydraulic jumps. Proc. Sixteenth Conf. on Coastal Engineering pp. 540–550. ASCE.
Rockwell, D., Magness, C., Towfighi, J. Akin, O. & Corcoran, T. 1993 High-image-density particle image velocimetry using laser scanning techniques. Exps. Fluids 14, 181–192.Google Scholar
Sarpkaya. T. & Henderson, D. O. 1984 Surface disturbances due to trailing vortices. Naval Postgraduate School, Monterey, California, Rep. NPS-69-84-004.
Stern, M. E. & Adam, Y. A. 1973 Capillary waves generated by a shear current in water. Mam. Soc. R. Sci. Liège 6, 179–185.Google Scholar
Triantafyllou, G. S. & Dimas, A. A. 1989 Interaction of two-dimensional separated flows with a free surface at low Froude numbers. Phys. Fluids A. 1, 1813–1821.Google Scholar
Tryggvason, G. 1988 Deformation of a free surface as a result of vortical of vortical flows. Phys. fluids 31, 955–957.Google Scholar
Willmarth, W. w., Tryggvason, G. Hirsa, A. & Yu, D. 1989 Vortex pair generation and interaction with surface. Phys. Fluids A. 1, 170–172.Google Scholar
Yu, D. & Tryggvason, G. 1990 The free-surface signature of unsteady, two-dimensional vortex flows. J. Fluid Mech. 218, 547–572.Google Scholar