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Wave breaking onset and strength for two-dimensional deep-water wave groups

Published online by Cambridge University Press:  07 August 2007

MICHAEL L. BANNER  and
WILLIAM L. PEIRSON
MICHAEL L. BANNER
Affiliation:
School of Mathematics and Statistics, The University of New South Wales, Sydney 2052, Australia
WILLIAM L. PEIRSON
Affiliation:
Water Research Laboratory, School of Civil and Environmental Engineering, The University of New South Wales, Sydney 2052, Australia
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Abstract

The numerical study of J. Song & M. L. Banner (J. Phys. Oceanogr. vol. 32, 2002, p. 254) proposed a generic threshold parameter for predicting the onset of breaking within two-dimensional groups of deep-water gravity waves. Their parameter provides a non-dimensional measure of the wave energy convergence rate and geometrical steepening at the maximum of an evolving nonlinear wave group. They also suggested that this parameter might control the strength of breaking events. The present paper presents the results of a detailed laboratory observational study aimed at validating their proposals.

For the breaking onset phase of this study, wave potential energy was measured at successive local envelope maxima of nonlinear deep-water wave groups propagating along a laboratory wave tank. These local maxima correspond alternately to wave group geometries with the group maximum occurring at an extreme carrier wave crest elevation, followed by an extreme carrier wave trough depression. As the nonlinearity increases, these crest and trough maxima can have markedly different local energy densities owing to the strong crest–trough asymmetry. The local total energy density was reconstituted from the potential energy measurements, and made dimensionless using the square of the local (carrier wave) wavenumber. A mean non-dimensional growth rate reflecting the rate of focusing of wave energy at the envelope maximum was obtained by smoothing the local fluctuations.

For the cases of idealized nonlinear wave groups investigated, the observations confirmed the evolutionary trends of the modelling results of Song & Banner (2002) with regard to predicting breaking onset. The measurements confirmed the proposed common breaking threshold growth rate of 0.0014±0.0001, as well as the predicted key evolution times: the time taken to reach the energy maximum for recurrence cases; and the time to reach the breaking threshold and then breaking onset, for breaking cases.

After the initiation and subsequent cessation of breaking, the measured wave packet mean energy losses and loss rates associated with breaking produced an unexpected finding: the post-breaking mean wave energy did not decrease to the mean energy level corresponding to maximum recurrence, but remained significantly higher. Therefore, pre-breaking absolute wave energy or mean steepness do not appear to be the most fundamental determinants of post-breaking wave packet energy density.

However, the dependence of the fractional breaking energy loss of wave packets on the parametric growth rate just before breaking onset proposed by Song & Banner (2002) was found to provide a plausible collapse to our laboratory data sets, within the experimental uncertainties. Further, when the results for the energy loss rate per unit width of breaking front were expressed in terms of a breaker strength parameter b multiplying the fifth power of the wave speed, it is found that b was also strongly correlated with the parametric growth rate just before breaking. Measured values of b obtained in this investigation ranged systematically from 8 × 10−5 to 1.2 × 10−3. These are comparable with open ocean estimates reported in recent field studies.

Type
Papers
Information
Journal of Fluid Mechanics , Volume 585 , 25 August 2007 , pp. 93 - 115
Copyright
Copyright © Cambridge University Press 2007

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References

REFERENCES

Alves, J. H. & Banner, M. L. 2003 Performance of a saturation-based dissipation source term for wind wave spectral modelling. J. Phys. Oceanogr. 33, 1274–1298.2.0.CO;2>CrossRefGoogle Scholar
Badulin, S. I., Pushkarev, A. N., Resio, D. & Zakharov, V. E. 2005 Self-similarity of wind driven seas. Nonlinear Proc. Geophys. 12, 891–945.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. & Song, J. 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, 2559–2570.CrossRefGoogle Scholar
Banner, M. L. & Tian, X. 1998 On the determination of the onset of breaking for modulating surface gravity water waves. J. Fluid Mech. 367, 107–137.CrossRefGoogle Scholar
Banner, M. L., Gemmrich, J. R. & Farmer, D. M. 2002 Multiscale measurements of ocean wave breaking probability. J. Phys. Oceanogr. 32, 3364–3375.2.0.CO;2>CrossRefGoogle Scholar
Dias, F. & Kharif, C. 1999 Nonlinear gravity and capillary-gravity waves. Annu. Rev. Fluid Mech. 31, 301–346.CrossRefGoogle Scholar
Dold, J. W. & Peregrine, D. H. 1986 Water–wave modulation. Proc. 20th Intl Conf. Coastal Engng Taipei, ASCE vol. 1, pp. 163–175.Google Scholar
Donelan, M. A. 1999 Wind-induced growth and attenuation of laboratory waves. In Wind over Wave Couplings (ed. Sajjadi, S. G., Thomas, N. H. & Hunt, J. C. R., Clarendon), pp. 183–194.CrossRefGoogle Scholar
Donelan, M. A., Longuet-Higgins, M. S. & Turner, J. S. 1972 Whitecaps. Nature 239, 449–451.CrossRefGoogle Scholar
Duncan, J. H. 1981 An experimental investigation of breaking waves produced by towed hydrofoil. Proc. R. Soc. Lond. A 377, 331–348.Google Scholar
Duncan, J. H. 1983 The breaking and non-breaking resistance of a two-dimensional hydrofoil. J. Fluid Mech. 126, 507–520.CrossRefGoogle Scholar
Dysthe, K. B. 1979 Note on a modification to the nonlinear SchrÖdinger equation for application to deep water waves. Proc. R. Soc. Lond. A 369, 105–114.Google Scholar
Gemmrich, J. 2005 On the occurrence of wave breaking. Proc. Hawaiian Winter Workshop on Rogue Waves (ed. Muller, P. & Henderson, D.), pp. 123–130. University of Hawaii SOEST.Google Scholar
Gemmrich, J. R. & Farmer, D. M. 2004 Observations of the scale and occurrence of breaking surface waves. J. Phys. Oceanogr. 34, 1067–1086.2.0.CO;2>CrossRefGoogle Scholar
Holthuijsen, L. H. & Herbers, T. H. C. 1986 Statistics of breaking waves observed as whitecaps in the open sea. J. Phys. Oceanogr 16, 290–297.2.0.CO;2>CrossRefGoogle Scholar
Jessup, A. T. & Phadnis, K. R. 2005 Measurement of the geometric and kinematic properties of microsacle breaking waves from infrared imagery using a PIV algorithm. Meas. Sci. Technol. 16, 1961–1969.CrossRefGoogle Scholar
Kway, J. H. L., Loh, Y.-S. & Chan, E.-S. 1998 Laboratory study of deep-water breaking waves. Ocean Engng 25, 657–676.CrossRefGoogle Scholar
Loewen, M. R. & Melville, W. K. 1991 Microwave backscatter and acoustic radiation from breaking waves. J. Fluid Mech. 224, 601–623.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1984 Statistical properties of wave groups in a random sea state. Phil. Trans. R. Soc. Lond. A 312, 219–250.Google Scholar
Melville, W. K. 1982 The instability and breaking of deep-water waves. J. Fluid Mech. 115, 165–185.CrossRefGoogle Scholar
Melville, W. K. 1983 Wave modulation and breakdown. J. Fluid Mech. 128, 489–506.CrossRefGoogle Scholar
Melville, W. K. 1994 Energy dissipation by breaking waves. J. Phys. Oceanogr. 24, 2041–2049.2.0.CO;2>CrossRefGoogle Scholar
Melville, W. K. 1996 The role of surface-wave breaking in air-sea interaction. Annu. Rev. Fluid Mech. 26, 279–321.CrossRefGoogle Scholar
Melville, W. K. & Matusov, P. 2002 Distribution of breaking waves at the ocean surface. Nature 417, 58–63.CrossRefGoogle ScholarPubMed
Nepf, H. M., Wu, C. H. & Chan, E. S. 1998 A comparison of two-and three-dimensional wave breaking. J. Phys Oceanogr. 28, 1496–1510.2.0.CO;2>CrossRefGoogle Scholar
Osborne, A. R., Onorato, M. & Serio, M. 2000 The nonlinear dynamics of rogue waves and holes in deep water gravity wave trains. Phys. Lett. A 275, 386–393.CrossRefGoogle Scholar
Papadimitrakis, Y. A., Huang, N. E., Bliven, L. F. & Long, S. R. 1988 An estimate of wave breaking probability for deep water waves. In Sea Surface Sound – Natural Mechanisms of Surface-Generated Noise in the Ocean (ed. Kerman, B. R.), pp. 71–83. Kluwer.Google Scholar
Peirson, W. L. & Banner, M. L. 2000 On the strength of breaking of deep water waves. In Coastal Engineering 2000, ASCE, Sydney (ed. Cox, R.), pp. 369–381.Google Scholar
Phillips, O. M. 1985 Spectral and statistical properties of the equilibrium range in wind-generated gravity waves. J. Fluid Mech. 156, 505–531.CrossRefGoogle Scholar
Phillips, O. M., Gu, D. & Donelan, M. A. 1993 Expected structure of extreme waves in a Gaussian Sea, Part 1. Theory and SWADE buoy measurements. J. Phys. Oceanogr. 23, 992–1000.2.0.CO;2>CrossRefGoogle Scholar
Phillips, O. M., Posner, F. L. & Hansen, J. P. 2001 High range resolution radar measurements of the speed distribution of breaking events in wind-generated ocean waves: surface impulse and wave energy dissipation rates. J. Phys. Oceanogr. 31, 450–460.2.0.CO;2>CrossRefGoogle Scholar
Rapp, R. J. & Melville, W. K. 1990 Laboratory measurements of deep water breaking waves. Phil. Trans. Roy. Soc. Lond. A 331, 735–800.Google Scholar
Skyner, D. 1996 A comparison of numerical predictions and experimental measurements of the internal kinematics in a deep-water plunging wave. J. Fluid Mech. 315, 51–64.CrossRefGoogle Scholar
Song, J. & 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, 2541–2558.CrossRefGoogle Scholar
Stansell, P. A. & MacFarlane, C. 2002 Experimental investigation of wave breaking criteria based on wave phase speeds. J. Phys. Oceanogr. 32, 1269–1283.2.0.CO;2>CrossRefGoogle Scholar
Terray, E. A., Donelan, M. A., Agrawal, Y. C., Drennan, W. M., Kahma, K. K., Williams, A. J. III, Hwang, P. A. & Kitaigorodskii, S. A. 1996 Estimates of kinetic energy dissipation under breaking waves. J. Phys. Oceanogr. 26, 792–807.2.0.CO;2>CrossRefGoogle Scholar
Thorpe, S. A. 1993 Energy loss by breaking waves. J. Phys. Oceanogr. 23, 2498–2502.2.0.CO;2>CrossRefGoogle Scholar
Tulin, M. P. & Li, J. J. 1992 On the breaking of energetic waves. Intl J. Offshore Polar Engng 2, 46–53.Google Scholar
Tulin, M. P. & Waseda, T. 1999 Laboratory observations of wave group evolution, including breaking effects. J. Fluid Mech. 378, 197–232.CrossRefGoogle Scholar