Hostname: page-component-7c8c6479df-hgkh8 Total loading time: 0 Render date: 2024-03-27T07:52:16.342Z Has data issue: false hasContentIssue false

Growth and dissipation of wind-forced, deep-water waves

Published online by Cambridge University Press:  28 March 2013

Laurent Grare*
Affiliation:
Institut de Recherche sur les Phénomènes Hors Equilibre, CNRS UMR 6594, Aix-Marseille Université, France
William L. Peirson
Affiliation:
Water Research Laboratory, School of Civil and Environmental Engineering, University of New South Wales, King Street, Manly Vale NSW 2093, Australia
Hubert Branger
Affiliation:
Institut de Recherche sur les Phénomènes Hors Equilibre, CNRS UMR 6594, Aix-Marseille Université, France
James W. Walker
Affiliation:
Water Research Laboratory, School of Civil and Environmental Engineering, University of New South Wales, King Street, Manly Vale NSW 2093, Australia
Jean-Paul Giovanangeli
Affiliation:
Institut de Recherche sur les Phénomènes Hors Equilibre, CNRS UMR 6594, Aix-Marseille Université, France
Vladimir Makin
Affiliation:
KNMI, PO Box 201, 3730 AE De Bilt, The Netherlands
*
Email address for correspondence: lgrare@ucsd.edu

Abstract

The input of energy by wind to water waves is compared with the observed growth of the waves using a suite of microphysical measurement techniques in the laboratory. These include measured tangential stresses in the water and air immediately adjacent to the interface with corresponding form drag measurements above wind-forced freely propagating waves. The drag data sets are consistent but the comparison has highlighted important issues in relation to the measurement of fluctuating pressures above freely propagating waves. Derived normalized wind input values show good collapse as a function of mean wave steepness and are significantly in excess of the assembly of net wave growth measurements by Peirson & Garcia (J. Fluid Mech., vol. 608, 2008, pp. 243–274) at low steepness. Sheltering coefficients in the form of Jeffreys (Proc. R. Soc. Lond. Ser. A, vol. 107, 1925, pp. 189–206) are derived that are consistent with values previously obtained by Donelan & Pierson (J. Geophys. Res., vol. 92, 1987, pp. 4971–5029), Donelan (Wind-over-Wave Couplings: Perspectives and Prospects, Clarendon, 1999, pp. 183–194) and Donelan et al. (J. Phys. Oceanogr., vol. 36, 2006, pp. 1672–1689). The sheltering coefficients exhibit substantial scatter. By carefully measuring the associated growth of the surface wave fields, systematic energy budgets for the interaction between wind and waves are obtained. For non-breaking waves, there is a significant and systematic misclose in the radiative transfer equation if wave–turbulence interactions are not included. Significantly higher levels of turbulent wave attenuation are found in comparison with the theoretical estimates by Teixeira & Belcher (J. Fluid Mech., vol. 458, 2002, pp. 229–267) and Ardhuin & Jenkins (J. Phys. Oceanogr., vol. 36, 2006, pp. 551–557). Suitable normalizations of attenuation for wind-forced wave fields exhibit consistent behaviour in the presence and absence of wave breaking. Closure of the surface energy flux budget is obtained by comparing the normalized energy loss rates due to breaking with the values previously determined by Banner & Peirson (J. Fluid Mech., vol. 585, 2007, pp. 93–115) and Drazen et al.(J. Fluid Mech., vol. 611, 2008, pp. 307–332) when expressed as a function of mean wave steepness. Their normalized energy loss rates obtained for non-wind forced breaking wave groups are remarkably consistent with the levels found during this present study when breaking waves are subject to wind forcing.

Type
Papers
Copyright
©2013 Cambridge University Press

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

Footnotes

Present address: UCSD, Scripps Institution of Oceanography, La Jolla, San Diego, CA 92093, USA.

§

Present address: Sogreah Gulf – Artelia Group, PO Box 18271, Dubai, UAE.

References

Ardhuin, F., Chapron, B. & Collard, F. 2009 Observation of swell dissipation across ocean. Geophys. Res. Lett. 36, L06607.CrossRefGoogle Scholar
Ardhuin, F. & Jenkins, A. D. 2006 On the interaction of surface waves and upper ocean turbulence. J. Phys. Oceanogr. 36, 551557.Google Scholar
Banner, M. L. 1990 The influence of wave breaking on the surface pressure distribution in wind–wave interactions. J. Fluid Mech. 211, 463495.Google Scholar
Banner, M. L. & Melville, W. K. 1976 On the separation of air flow above water waves. J. Fluid Mech. 77, 825842.CrossRefGoogle Scholar
Banner, M. L. & Peirson, W. L. 1998 Tangential stress beneath wind-driven air–water interfaces. J. Fluid Mech. 364, 115145.Google Scholar
Banner, M. L. & Peirson, W. L. 2007 Wave breaking onset and strength for two-dimensional deep-water wave groups. J. Fluid Mech. 585, 93115.CrossRefGoogle Scholar
Banner, M. L. & Phillips, O. M. 1974 On the incipient breaking of small scale waves. J. Fluid Mech. 65, 647656.CrossRefGoogle Scholar
Belcher, S. E., Harris, J. A. & Street, R. L. 1994 Linear dynamics of wind waves in coupled turbulent air–water flow, part 1: theory. J. Fluid Mech. 271, 119151.Google Scholar
Benjamin, T. B. & Feir, J. E. 1967 The disintegration of wave trains on deep water. Part 1. Theory. J. Fluid Mech. 27, 417430.Google Scholar
Bole, J. B. & Hsu, E. Y. 1969 Response of gravity water waves to wind excitation. J. Fluid Mech. 35, 657675.Google Scholar
Cheung, T. K. & Street, R. L. 1988 The turbulent layer in the water at an air–water interface. J. Fluid Mech. 194, 133151.Google Scholar
Coantic, M., Ramamonjiarisoa, A., Mestayer, P., Resch, F. & Favre, A. 1981 Wind water tunnel simulation of small scale ocean atmosphere interactions. J. Geophys. Res. C7, 66076626.Google Scholar
Craig, P. D. & Banner, M. L. 1994 Modelling wave-enhanced turbulence in the ocean surface layer. J. Phys. Oceanogr. 24, 25462559.2.0.CO;2>CrossRefGoogle Scholar
Deardorff, J. W. 1967 Aerodynamic theory of growth with constant wave steepness. J. Oceanogr. Soc. Japan 23 (6), 278297.Google Scholar
Donelan, M. A. 1990 Air-sea interaction. In The Sea (ed. Le Méhauté, B. & Hanes, D.). vol. 9A. pp. 239292. Wiley.Google Scholar
Donelan, M. A. 1999 Wind-induced growth and attenuation of laboratory waves. In Wind-over-Wave Couplings: Perspectives and Prospects (ed. Sajjadi, S. G., Thomas, N. H. & Hunt, J. C. R.). pp. 183194. Clarendon.CrossRefGoogle Scholar
Donelan, M. A., Babanin, A. V., Young, I. R. & Banner, M. L. 2006 Wave-follower field measurements of the wind-input spectral function. Part II: parameterisation of wind input. J. Phys. Oceanogr. 36, 16721689.Google Scholar
Donelan, M. A., Babanin, A. V., Young, I. R., Banner, M. L. & McCormick, C. 2005 Wave-follower field measurements of the wind-input spectral function. Part I: measurements and calibrations. J. Atmos. Ocean. Technol. 22, 799813.Google Scholar
Donelan, M. A. & Pierson, W. J. 1987 Radar scattering and equilibrium ranges in wind-generated waves with application to scatterometry. J. Geophys. Res. 92 (C5), 49715029.Google Scholar
Drazen, D. A. & Melville, W. K. 2009 Turbulence and mixing in unsteady breaking surface waves. J. Fluid Mech. 628, 85119.CrossRefGoogle Scholar
Drazen, D. A., Melville, W. K. & Lenain, L. 2008 Inertial scaling of dissipation in unsteady breaking waves. J. Fluid Mech. 611, 307332.Google Scholar
Duncan, J. H. 1981 An experimental investigation of breaking waves produced by a towed hydrofoil. Proc. R. Soc. Lond. A 377, 331348.Google Scholar
Duncan, J. H. 1983 The breaking and non-breaking resistance of a two-dimensional hydrofoil. J. Fluid Mech. 126, 507520.Google Scholar
Elliott, J. A. 1970 Microscale pressure fluctuations measured within the lower atmospheric boundary layer. PhD thesis, University of Britain Columbia.Google Scholar
Elliott, J. A. 1972a Microscale pressure fluctuations measured within the lower atmospheric boundary layer. J. Fluid Mech. 53, 351384.Google Scholar
Elliott, J. A. 1972b Microscale pressure fluctuations near waves being generated by the wind. J. Fluid Mech. 54, 427448.CrossRefGoogle Scholar
Grare, L. 2009 Etude des interactions Océan-Atmosphère à proximité immediate de l’interface: Application aux vagues de vent et aux vagues extrêmes. PhD thesis, University of Aix-Marseille, http://tel.archives-ouvertes.fr/docs/00/45/45/11/PDF/These_Grare_070509.pdf.Google Scholar
Janssen, P. 2004 The Interaction of Ocean Waves and Wind. Cambridge University Press.Google Scholar
Jeffreys, H. 1925 On the formation of water waves by wind. Proc. R. Soc. Lond. Ser. A 107 (742), 189206.Google Scholar
Jessup, A. T. & Phadnis, K. R. 2005 Measurement of the geometric and kinematic properties of microscale breaking waves from infrared imagery using a PIV algorithm. Meas. Sci. Technol. 16, 19611969.CrossRefGoogle Scholar
Jones, I. S. F. & Toba, Y. 2001 Wind Stress Over the Ocean. Cambridge University Press.Google Scholar
Kawamura, H., Okuda, K., Kawai, S. & Toba, Y. 1981 Structure of turbulent boundary layer over wind waves in a wind tunnel. Tohoku Geophys. J. 28, 6986.Google Scholar
Komen, G. J., Cavaleri, M., Donelan, M., Hasselmann, K., Hasselmann, S. & Janssen, P. A. E. M. 1994 Dynamics and Modelling of Ocean Waves. Cambridge University Press.Google Scholar
Latif, M. A. 1974 Acoustic effects on pressure measurements over water waves in the laboratory. Tech. Rep. no 25. Coastal and Oceanographic Engineering Laboratory.Google Scholar
Longuet-Higgins, M. S. 1969 A nonlinear mechanism for the generation of sea waves. Proc. R. Soc. Lond. A 311, 371389.Google Scholar
Longuet-Higgins, M. S. 1992 Capillary rollers and bores. J. Fluid Mech. 240, 659679.Google Scholar
Longuet-Higgins, M. S. & Stewart, R. W. 1964 Radiation stresses in water waves: a physical discussion with applications. Deep-Sea Res. 11, 529562.Google Scholar
Makin, V. K., Branger, H., Peirson, W. L. & Giovanangeli, J.-P. 2007 Stress above wind-plus-paddle waves: modelling of laboratory experiment. J. Phys. Oceanogr. 37 (12), 28242837.CrossRefGoogle Scholar
Mastenbroek, C., Makin, V. K., Garat, M. H. & Giovanangeli, J.-P. 1996 Experimental evidence of the rapid distortion of turbulence in the air flow over water waves. J. Fluid Mech. 318, 273302.Google Scholar
Mellor, G. L. & Blumberg, A. F. 2004 Wave breaking and ocean surface layer thermal response. J. Phys. Oceanogr. 34, 693698.CrossRefGoogle Scholar
Melville, W. K. & Matusov, P. 2002 Distribution of breaking waves at the ocean surface. Nature 417, 58.Google Scholar
Melville, W. K., Veron, F. & White, J. W. 2002 The velocity field under breaking waves: coherent structures and turbulence. J. Fluid Mech. 454, 203233.CrossRefGoogle Scholar
Miles, J. W. 1957 On the generation of surface waves by shear flows. J. Fluid Mech. 3, 185204.CrossRefGoogle Scholar
Miles, J. W. 1959 On the generation of surface waves by shear flows. Part 2. J. Fluid Mech. 6, 568582.Google Scholar
Mitsuyasu, H. & Honda, T. 1982 Wind-induced growth of water waves. J. Fluid Mech. 123, 425442.Google Scholar
Papadimitrakis, Y., Hsu, E. & Street, R. 1984 Measurements of the fluctuating pressure in the turbulent boundary layer over progressive mechanically generated water waves. In Gas Transfer at Water Surfaces (ed. Brutsaert, W. & Jirka, G. H.). Kluwer.Google Scholar
Peirson, W. L. 1997 Measurement of surface velocities and shears at a wavy air–water interface using particle image velocimetry. Exp. Fluids 23, 427437.CrossRefGoogle Scholar
Peirson, W. L. & Banner, M. L. 2001 On the strength of breaking of deep water waves. In Proc. Int. Conf. Coastal Engineering. ASCE.Google Scholar
Peirson, W. L. & Banner, M. L. 2003 Aqueous surface layer flows induced by microscale breaking wind waves. J. Fluid Mech. 479, 138.Google Scholar
Peirson, W. L. & Belcher, S. E. 2005 Growth Response of Waves to the Wind Stress. In Proc. Int. Conf. Coastal Engineering. ASCE.Google Scholar
Peirson, W. L., Beya, J. F., Banner, M. L., Peral, J. S. & Azarma, S. A. 2013 Rain-induced attenuation of water waves. J. Fluid Mech. Accepted for publication 26 January 2013.Google Scholar
Peirson, W. L. & Garcia, A. W. 2008 On the wind-induced growth of slow water waves of finite steepness. J. Fluid Mech. 608, 243274.Google Scholar
Peirson, W. L., Garcia, A. W. & Pells, S. E. 2003 Water–wave attenuation due to opposing wind. J. Fluid Mech. 487, 345365.CrossRefGoogle Scholar
Peirson, W. L., Walker, J. W. & Banner, M. L. 2012 On the microphysical behaviour of wind-forced water surfaces and consequent re-aeration. J. Fluid Mech. (submitted).Google Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean. Cambridge University Press.Google Scholar
Phillips, O. M. 1985 Spectral and statistical properties of the equilibrium range in the wind-generated gravity waves. J. Fluid Mech. 156, 505531.CrossRefGoogle Scholar
Plant, W. J. 1982 A relationship between wind stress and wave slope. J. Geophys. Res. 87 (C3), 19611967.CrossRefGoogle Scholar
Plant, W. J., Dhal, P. H. Dahl, Giovanangeli, J.-P. & Branger, H. 2004 Bound and free surface waves in a large wind–wave tank. J. Geophys. Res. C: Oceans 109, C10002.CrossRefGoogle Scholar
Ramamonjiarisoa, A. & Coantic, M. 1976 Loi expérimentale de dispersion des vagues produites par le vent sur une faible longueur d’action. C. R. Acad. Sci. 282, 111114.Google Scholar
Rapp, R. J. & Melville, W. K. 1990 Laboratory measurements of deep water breaking waves. Phil. Trans. R. Soc. Lond. A 331, 735800.Google Scholar
Reul, N., Branger, H., Bliven, L. & Giovanangeli, J. P. 1999 The influence of oblique waves on the azimuthal response of a Ku-band scatterometer. IEEE Trans. Geosci. Remote Sens. 37 (1), 3647.Google Scholar
Reul, N., Branger, H. & Giovanangeli, J.-P. 2008 Air flow structure over short-gravity breaking water waves. Boundary-Layer Meteorol. 126, 477505.Google Scholar
Romero, L., Melville, K. M. & Kleiss, J. 2012 Spectral energy dissipation due to surface–wave breaking. J. Phys. Oceanogr. 42, 14211444.Google Scholar
Shemdin, O. H. & Hsu, E. Y. 1967 Direct measurements of aerodynamic pressure above a simple progressive gravity wave. J. Fluid Mech. 30, 403416.Google Scholar
Snyder, R. L., Dobson, F. W., Elliott, J. A. & Long, R. B. 1981 Array measurements of atmospheric pressure fluctuations above surface gravity waves. J. Fluid Mech. 102, 159.Google Scholar
Sullivan, P. P. & McWilliams, J. C. 2010 Dynamics of winds and currents coupled to surface waves. Annu. Rev. Fluid Mech. 42, 1942.Google Scholar
Teixeira, M. A. & Belcher, S. E. 2002 On the distortion of turbulence by a progressive surface wave. J. Fluid Mech. 458, 229267.Google Scholar
Thais, L. & Magnaudet, J. 1996 Turbulent structure beneath surface gravity waves sheared by the wind. J. Fluid Mech. 328, 313344.Google Scholar
Tian, Z., Perlin, M. & Choi, W. 2010 Energy dissipation in two-dimensional unsteady plunging breakers and an eddy viscosity model. J. Fluid Mech. 655, 217257.Google Scholar
Tolman, H. 2009 User manual and system documentation of WAVEWATCH III™version 3.14. Technical note. MMAB Contribution No. 276. NOAA.Google Scholar
Veron, F., Saxena, G. & Misra, S. K. 2007 Measurements of the viscous tangential stress in the airflow above wind waves. Geophys. Res. Lett. 34, L19603.CrossRefGoogle Scholar
Walker, J. W. 2009 The exchange of oxygen at the surface of open waters under wind forcing. PhD thesis, School of Civil and Environmental Engineering. The University of New South Wales. http://unsworks.unsw.edu.au/fapi/datastream/unsworks:5256/SOURCE02.Google Scholar
Wanninkhof, R., Asher, W. E., Ho, D. T., Sweeney, C. S. & McGillis, W. R. 2009 Advances in quantifying air–sea gas exchange and environmental forcing. Annu. Rev. Mar. Sci. 1, 213244.Google Scholar
Wilson, W. S., Banner, M. L., Flower, R. J., Michael, J. A. & Wilson, D. G. 1973 Wind-induced growth of mechanically generated water waves. J. Fluid Mech. 58, 435460.Google Scholar
Wu, J. 1975 Wind-induced drift currents. J. Fluid Mech. 68, 4970.Google Scholar
Wu, H.-Y., Hsu, E.-Y. & Street, R. L. 1977 The energy transfer due to air-input, nonlinear wave–wave interactions and white-cap dissipation associated with wind-generated waves. Dept. Civ. Eng. Tech Rep. No. 207, Stanford University, Stanford, California.Google Scholar
Wu, H.-Y., Hsu, E.-Y. & Street, R. L. 1979 Experimental study of non-linear wave–wave interaction and white-cap dissipation of wind-generated waves. Dyn. Atmos. Oceans 3, 5578.Google Scholar
Zhang, X. 2002 Enhanced dissipation of short gravity and gravity capillary waves due to parasitic capillaries. Phys. Fluids 14 (742), 8184.CrossRefGoogle Scholar