Abstract
An improvement was proposed for the statistical theory of breaking entrainment depth and surface whitecap coverage of real sea waves in this study. The ratio of the kinetic and potential energy was estimated on a theoretical level, and optimal constants were determined to improve the statistical theory model for wave breaking. We also performed a sensitivity test to the model constants. A comparison between the model and in situ observations indicated that the level of agreement was better than has been achieved in previous studies.
Similar content being viewed by others
References
Anguelova M D. 2002. Whitecaps, Sea-Salt Aerosols, and Climate. Doctoral Dissertation. Delaware: University of Delaware.
Anguelova M D, Webster F. 2006. Whitecap coverage from satellite measurements: A first step toward modeling the variability of oceanic whitecaps. J Geophys Res, 111: C03017
Guan C L, Sun J. 2004. Similarities of some wind input and dissipation source terms (in Chinese). China Ocean Eng, 18: 629–642
Guan C, Hu W, Sun J, Li R. 2007. The whitecap coverage model from breaking dissipation parametrizations of wind waves. J Geophys Res, 112: C05031
Hasselmann K. 1974. On the spectral dissipation of ocean waves due to white capping. Bound-Layer Meteorol, 6: 107–127
He H, Song J. 2014. Determining the onset and strength of unforced wave breaking in a numerical wave tank. China Ocean Eng, 28: 501–509
Kalvoda P M, Xu L L, Wu J. 2003. Macrobubble clouds produced by breaking wind waves: A laboratory study. J Geophys Res, 108: 3207
Kinsman B. 1965. Wind Waves. Upper Saddle River: Prentice-Hall. 676
Komen G J, Hasselmann K, Hasselmann K. 1984. On the existence of a fully developed wind-sea spectrum. J Phys Oceanogr, 14: 1271–1285
Kraan G, Oost W A, Janssen P A E M. 1996. Wave energy dissipation by whitecaps. J Atmos Ocean Technol, 13: 262–267
Lamarre E, Melville W K. 1991. Air entrainment and dissipation in breaking waves. Nature, 351: 469–472
Leckler F, Ardhuin F, Filipot J F, Mironov A. 2013. Dissipation source terms and whitecap statistics. Ocean Modell, 70: 62–74
Longuet-Higgins M S. 1969. On wave breaking and the equilibrium spectrum of wind-generated waves. Proc R Soc A-Math Phys Eng Sci, 310: 151–159
Melville W K. 1996. The role of surface-wave breaking in air-sea interaction. Annu Rev Fluid Mech, 28: 279–321
Melville W K, Loewen M R, Lammarre E. 1992. Sound production and air entrainment by breaking waves: A review of recent laboratory experiments. In: Banner M L, Grimshaw R H J, eds. Breaking Waves-IUTAM Symposium. Berlin: Springer-Verlag. 139–146
Monahan E C. 1971. Oceanic whitecaps. J Phys Oceanogr, 1: 139–144
Monahan E C, O’Muircheartaigh I G. 1986. Whitecaps and the passive remote sensing of the ocean surface. Int J Remote Sens, 7: 627–642
Monahan E C. 1988. Whitecap coverage as a remotely monitorable indication of the rate of bobbie injection into the oceanic mixed layer. In: Kerman B R, ed. Sea Surface Sound. Berlin: Springer Netherlands. 85–96
Monahan E C. 2002. Oceanic whitecaps: Sea surface features detectable via satellite that are indicators of the magnitude of the air-sea gas transfer coefficient. J Earth Syst Sci, 111: 315–319
Neuman G, Pierson W J. 1957. A detailed comparison of theoretical wave spectra and wave forecasting methods. Deut Hydrograph Z, 10: 134–146
Reul N, Chapron B. 2003. A model of sea-foam thickness distribution for passive microwave remote sensing applications. J Geophys Res, 108: 3321
Rosenkranz P W, Staelin D H. 1972. Microwave emissivity of ocean foam and its effect on nadiral radiometric measurements. J Geophys Res, 77: 6528–6538
Ross D B, Cardone V. 1974. Observations of oceanic whitecaps and their relation to remote measurements of surface wind Speed. J Geophys Res, 79: 444–452
Stogryn A. 1972. The emissivity of sea foam at microwave frequencies. J Geophys Res, 77: 1658–1666
Sun B N, Yang Y Z, Teng Y, Sun M, Lian Z. 2014. Study on wave characteristic parameters in the coastal area of Rushan Bay. Adv Mar Sci, 32: 459–466
Group T W. 1988. The WAM Model—A Third generation ocean wave prediction model. J Phys Oceanogr, 18: 1775–1810
Xu D L, Yu Y D, Lu H M. 1998. A whitecap coverage model based on the surface slope for criterion of wave breaking. China Ocean Eng, 12: 73–85
Yuan Y L, Tung C C, Huang N E. 1986. Statistical characteristics of breaking waves. In: Phillips O M, Hasselmann K, eds. Wave Dynamics and Radio Probing of the Ocean Surface. New York: Plenum Press. 265–272
Yuan Y, Han L, Hua F, Zhang S, Qiao F, Yang Y, Xia C. 2009. The statistical theory of breaking entrainment depth and surface whitecap coverage of real sea waves. J Phys Oceanogr, 39: 143–161
Zhang S, Cao R, Xie L. 2012. Energy dissipation through wind-generated breaking waves. Chin J Ocean Limnol, 30: 822–825
Zhao D L. 2012. Progress in sea spay and its effects on air-sea interaction. Adv Earth Sci, 27: 624–632
Acknowledgments
This work was supported by the National High Technology Research and Development Program of China (Grant No. 2013AA09A506), the National Natural Science Foundation of China-Shandong Joint Fund for Marine Science Research Centers (Grant No. U1406404), the Youth Natural Foundation of Shandong Province (Grant No. ZR2015PD009), the Scientific and Technological Innovation Project Financially Supported by Qingdao National Laboratory for Marine Science and Technology (Grant No. 2015ASKJ01), and the Youth Science Foundation of China-Indonesia Maritime Cooperation Fund (Grant No. YZ0115005).
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Wang, H., Yang, Y., Sun, B. et al. Improvements to the statistical theoretical model for wave breaking based on the ratio of breaking wave kinetic and potential energy. Sci. China Earth Sci. 60, 180–187 (2017). https://doi.org/10.1007/s11430-016-0053-3
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11430-016-0053-3