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An experimental investigation of incipient spilling breakers

Published online by Cambridge University Press:  25 August 2009

J. D. DIORIO ,
X. LIU  and
J. H. DUNCAN
J. D. DIORIO
Affiliation:
Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA
X. LIU
Affiliation:
Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA
J. H. DUNCAN*
Affiliation:
Department of Mechanical Engineering, University of Maryland, College Park, MD 20742, USA
*
†Email address for correspondence: duncan@umd.edu
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Abstract

In the present paper, the profiles of incipient spilling breaking waves with wavelengths ranging from 10 to 120cm were studied experimentally in clean water. Short-wavelength breakers were generated by wind, while longer-wavelength breakers were generated by a mechanical wavemaker, using either a dispersive focusing or a sideband instability mechanism. The crest profiles of these waves were measured with a high-speed cinematic laser-induced fluorescence technique. For all the wave conditions reported herein, wave breaking was initiated with a capillary-ripple pattern as described in Duncan et al. (J. Fluid Mech., vol. 379, 1999, pp. 191–222). In the present paper, it is shown that at incipient breaking the crest shape is self-similar with two geometrical parameters that depend only on the slope of a particular point on the front face of the gravity wave. The scaling relationships appear to be universal for the range of wavelengths studied herein and hold for waves generated by mechanical wavemakers and by wind. The slope measure is found to be dependent on the wave phase speed and the rate of growth of the crest height prior to incipient breaking.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 633 , 25 August 2009 , pp. 271 - 283
Copyright
Copyright © Cambridge University Press 2009

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References

REFERENCES

Banner, M. L. & Peirson, W. L. 2007 Wave breaking onset and strength for two-dimensional deep-water wave groups. J. Fluid Mech. 585, 93–115.CrossRefGoogle Scholar
Banner, M. L. & Peregrine, D. H. 1993 Wave breaking in deep-water. Annu. Rev. Fluid Mech. 25, 373–397.CrossRefGoogle Scholar
Banner, M. L. & Phillips, O. M. 1974 Incipient breaking of small-scale waves. J. Fluid Mech. 65, 647.CrossRefGoogle Scholar
Banner, M. L. & Song, J. B. 2002 On determining the onset and strength of breaking for deep water waves. Part 2. Influence of wind forcing and surface shear. J. Phys. Oceanogr. 32 (9), 2559–2570.CrossRefGoogle Scholar
Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wave trains on deep water. Part 1. Theory J. Fluid Mech. 27, 417–430.CrossRefGoogle Scholar
Crapper, G. D. 1957 An exact solution for progressive capillary waves of arbitrary amplitude. J. Fluid Mech. 6, 532–540.CrossRefGoogle Scholar
Duncan, J. H. 1983 The breaking and nonbreaking wave resistance of a two-dimensional hydrofoil. J. Fluid Mech. 126, 507–520.CrossRefGoogle Scholar
Duncan, J. H. 2001 Spilling breakers. Annu. Rev. Fluid Mech. 33, 519–547.CrossRefGoogle Scholar
Duncan, J. H., Qiao, H., Philomin, V. & Wenz, A. 1999 Gentle spilling breakers: crest profile evolution. J. Fluid Mech. 379, 191–222.CrossRefGoogle Scholar
Fedorov, A. V. & Melville, W. K. 1998 Nonlinear gravity–capillary waves with forcing and dissipation. J. Fluid Mech. 354, 1–42.CrossRefGoogle Scholar
Fedorov, A. V., Melville, W. K. & Rozenberg, A. 1998 An experimental and numerical study of parasitic capillary waves. Phys. Fluids 10 (6), 1315–1323.CrossRefGoogle Scholar
Lake, B. M., Yuen, H. C., Rungaldier, H. & Ferguson, W. E. 1977 Nonlinear deep-water waves: theory and experiment. Part 2. Evolution of a continuous wavetrain. J. Fluid Mech. 83, 49–74.CrossRefGoogle Scholar
Liu, X. & Duncan, J. H. 2006 An experimental study of surfactant effects on spilling breakers. J. Fluid Mech. 567, 433–455.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1974 Breaking waves in deep or shallow water. In Tenth Symposium on Naval Hydrodynamics, Cambridge, MA.Google Scholar
Longuet-Higgins, M. S. 1978 Instabilities of gravity-waves of finite-amplitude in deep-water. Part 2. Subharmonics. Proc. R. Soc. Lond. A 360, 489–505.Google Scholar
Longuet-Higgins, M. S. 1992 Capillary rollers and bores. J. Fluid Mech. 240, 659–679.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1996 Capillary jumps on deep water. J. Phys. Oceanogr. 96, 1957–1965.2.0.CO;2>CrossRefGoogle Scholar
Longuet-Higgins, M. S. & Dommermuth, D. G. 1997 Crest instabilities of gravity waves. Part 3. Nonlinear development and breaking. J. Fluid Mech. 336, 33–50.CrossRefGoogle Scholar
Melville, W. K. 1982 The instability and breaking of deep-water waves. J. Fluid Mech. 115, 165–185.CrossRefGoogle Scholar
Melville, W. K. 1996 The role of surface-wave breaking in air-sea interaction. Annu. Rev. Fluid Mech. 28, 279–321.CrossRefGoogle Scholar
Miller, M., Nennstiel, T., Duncan, J. H., Dimas, A. & Prostler, S. 1999 Incipient breaking of steady waves in the presence of surface wakes J. Fluid Mech. 383, 285–305.CrossRefGoogle Scholar
Mui, R. C. Y. & Dommermuth, D. G. 1995 The vortical structure of parasitic capillary waves. J. Fluids Engng 117, 355–361.CrossRefGoogle Scholar
Qiao, H. & Duncan, J. H. 2001 Gentle spiling breakers: crest flow-field evolution. J. Fluid Mech. 439, 57–85.CrossRefGoogle Scholar
Rapp, R. & Melville, W. K. 1990 Laboratory measurements of deep water breaking waves. Phil. Trans. R. Soc. Lond. A 331, 735.Google Scholar
Song, J. B. & Banner, M. L. 2002 On determining the onset and strength of breaking for deep water waves. Part 1. Unforced irrotational wave groups. J. Phys. Oceanogr. 32 (9), 2541–2558.CrossRefGoogle Scholar
Stokes, G. G. 1847 On the theory of oscillatory waves. Trans. Camb. Phil. Soc. 8, 441–455. Reprinted in. 1, 314–326.Google Scholar
Thorpe, S. A. 1995 Dynamical processes of transfer at the sea surface. Prog. Oceanogr. 35, 315–352.CrossRefGoogle Scholar
Tulin, M. P. 1996 Breaking of ocean waves and downshifting. In Waves and Nonlinear Processes in Hydrodynamics (ed. Grue, J., Gjevik, B. & Weber, J. E.), pp. 177–190. Kluwer Academic.CrossRefGoogle Scholar
Tulin, M. P. & Landrini, M. 2001 Wave breaking in the ocean and around ships. In 23rd Symposium on Naval Hydrodyanamics, Val de Reuil, France.Google Scholar