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Characteristics of the wind drift layer and microscale breaking waves

Published online by Cambridge University Press:  05 February 2007

M. H. KAMRAN SIDDIQUI  and
MARK R. LOEWEN
M. H. KAMRAN SIDDIQUI
Affiliation:
Department of Civil and Environmental Engineering, University of Alberta, 3-133 Markin/CNRL Natural Resources Engineering Facility, Edmonton, Alberta, CanadaT6G 2W2
MARK R. LOEWEN*
Affiliation:
Department of Civil and Environmental Engineering, University of Alberta, 3-133 Markin/CNRL Natural Resources Engineering Facility, Edmonton, Alberta, CanadaT6G 2W2
*
‡Author to whom correspondence should be addressed: [email protected].
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Abstract

An experimental study, investigating the mean flow and turbulence in the wind drift layer formed beneath short wind waves was conducted. The degree to which these flows resemble the flows that occur in boundary layers adjacent to solid walls (i.e. wall-layers) was examined. Simultaneous DPIV (digital particle image velocimetry) and infrared imagery were used to investigate these near-surface flows at a fetch of 5.5 m and wind speeds from 4.5 to 11 m s−1. These conditions produced short steep waves with dominant wavelengths from 6 cm to 18 cm. The mean velocity profiles in the wind drift layer were found to be logarithmic and the flow was hydrodynamically smooth at all wind speeds. The rate of dissipation of turbulent kinetic energy was determined to be significantly greater in magnitude than would occur in a comparable wall-layer. Microscale breaking waves were detected using the DPIV data and the characteristics of breaking and non-breaking waves were compared. The percentage of microscale breaking waves increased abruptly from 11% to 80% as the wind speed increased from 4.5 to 7.4 m s− and then gradually increased to 90% as the wind speed increased to 11 m s−. At a depth of 1 mm, the rate of dissipation was 1.7 to 3.2 times greater beneath microscale breaking waves compared to non-breaking waves. In the crest–trough region beneath microscale breaking waves, 40% to 50% of the dissipation was associated with wave breaking. These results demonstrated that the enhanced near-surface turbulence in the wind drift layer was the result of microscale wave breaking. It was determined that the rate of dissipation of turbulent kinetic energy due to wave breaking is a function of depth, friction velocity, wave height and phase speed as proposed by Terray et al. (1996). Vertical profiles of the rate of dissipation showed that beneath microscale breaking waves there were two distinct layers. Immediately beneath the surface, the dissipation decayed as ζ−0.7 and below this in the second layer it decayed as ζ−2. The enhanced turbulence associated with microscale wave breaking was found to extend to a depth of approximately one significant wave height. The only similarity between the flows in these wind drift layers and wall-layers is that in both cases the mean velocity profiles are logarithmic. The fact that microscale breaking waves were responsible for 40%–50% of the near-surface turbulence supports the premise that microscale breaking waves play a significant role in enhancing the transfer of gas and heat across the air–sea interface.

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Papers
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Journal of Fluid Mechanics , Volume 573 , February 2007 , pp. 417 - 456
Copyright
Copyright © Cambridge University Press 2007

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Footnotes

†

Present address: Department of Mechanical and Industrial Engineering, Concordia University, 1455 de Maisonneuve Blvd. West, Montreal, Quebec, H3G 1M8, Canada.

References

REFERENCES

Agrawal, Y. C., Terray, E. A., Donelan, M. A., Hwang, P. A., Williams, A. J. III, Drennan, W. M., Kahma, K. K. & Kitaigorodskii, S. A. 1992 Enhanced dissipation of kinetic energy beneath surface waves. Nature. 359, 219–220.CrossRefGoogle Scholar
Anis, A. & Moum, J. N. 1995 Surface wave–turbulence interactions – scaling epsilon (z) near the sea-surface. J. Phys. Oceanogr. 25, 2025–2045.2.0.CO;2>CrossRefGoogle Scholar
Banner, M. L. & Peirson, W. L. 1998 Tangential stress beneath wind-driven air–water interfaces. J. Fluid Mech. 364, 115–145.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 On the incipient breaking of small scale waves. J. Fluid Mech. 65, 647–656.CrossRefGoogle Scholar
Benilov, A. Yu, Kouznetsov, O. A. & Panin, G. N. 1974 On the analysis of wind-induced disturbances in the atmospheric turbulent surface layer. Boundary-Layer Met. 6, 269–285.CrossRefGoogle Scholar
Bock, E. J., Hara, T., Frew, N. M. & McGillis, W. R. 1999 Relationship between air–sea gas transfer and short wind waves. J. Geophys. Res. 104, 25821–25831.CrossRefGoogle Scholar
Bourassa, M. A. 2000 Shear stress model for the aqueous boundary layer near the air–sea interface. J. Geophys. Res. 105 (C1), 1167–1176.CrossRefGoogle Scholar
Bye, J. A. T. 1965 Wind-driven circulation in unstratified lakes. Limnol. Oceanogr. 10, 451–458.CrossRefGoogle Scholar
Bye, J. A. T. 1967 The wave-drift current. J. Marine Res. 25, 95–102.Google Scholar
Cheung, T. K. & Street, R. L. 1988 The turbulent layer in the water at an air–water interface. J. Fluid Mech. 194, 133–151. (Referred to herein as CS).CrossRefGoogle Scholar
Churchill, J. H. & Csanady, G. T. 1983 Near-surface measurements of quasi-Lagrangian velocities in open water. J. Phys. Oceanogr. 13, 1669–1680.2.0.CO;2>CrossRefGoogle Scholar
Csanady, G. T. 1990 The role of breaking wavelets in air–sea gas transfer. J. Geophys. Res. 95, 749–759.CrossRefGoogle Scholar
Donelan, M. A. 1990: Air–Sea Interaction. The Sea: Ocean Engineering Science, vol. 9 (ed. LeMéhauté, B. & Hanes, D.), pp. 239–292. John Wiley.Google Scholar
Donlon, C. J., Nightingale, T. J., Sheasby, T., Turner, J., Robinson, I. S. & Emery, W. J. 1999 Implications of the oceanic thermal skin temperature deviation at high wind speed. Geophys. Res. Lett. 26, 2505–2508.CrossRefGoogle Scholar
Doron, P., Bertuccioli, L., Katz, J. & Osborn, T. R. 2001 Turbulence characteristics and dissipation estimates in the coastal ocean bottom boundary layer from PIV data. J. Phys. Oceanogr. 31, 2108–2134.2.0.CO;2>CrossRefGoogle Scholar
Ebuchi, N., Kawamura, H. & Toba, Y. 1993 Bursting phenomena in the turbulent boundary layer beneath the laboratory wind-wave surface. Natural Physical Sources of Underwater Sound (ed. B. R. Kerman) pp. 263–276.CrossRefGoogle Scholar
Frew, N. M., Bock, E. J., Schimpf, U., Hara, T., Haußecker, H., Edson, J. B., McGillis, W. R., Nelson, R. K., McKenna, S. P., Uz, B. M. & Jähne, B. 2004 Air–sea gas transfer: its dependence on wind stress, small-scale roughness, and surface films. J. Geophys. Res. 109, C08S17, 1–23.Google Scholar
Gemmrich, J. R. & Farmer, D. M. 2004 Near-surface turbulence in the presence of breaking waves. J. Phys. Oceanogr. 34, 1067–1086.2.0.CO;2>CrossRefGoogle Scholar
Hinze, J. O. 1975 Turbulence. McGraw–Hill.Google 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
Hsu, C.-T., Hsu, E. Y. & Street, R. L. 1981 On the structure of turbulent flow over a progressive water wave: theory and experiment in a transformed, wave-following coordinate system. J. Fluid Mech. 105, 87–117.CrossRefGoogle Scholar
Iafrati, A. & Campana, E. F. 2005 Free-surface fluctuations behind microbreakers: space–time behaviour and subsurface flow field. J. Fluid Mech. 529, 311–347.CrossRefGoogle Scholar
Jähne, B., Munnich, K. O., Bosinger, R., Dutzi, A., Huber, W. & Libner, P. 1987 On the parameters influencing air–water gas exchange. J. Geophys. Res. 92, 1937–1949.CrossRefGoogle Scholar
Jessup, A. T., Zappa, C. J. & Yeh, H. 1997 Defining and quantifying microscale wave breaking with infrared imagery. J. Geophys. Res. 102, 23 145–23 153.CrossRefGoogle Scholar
Jiang, J.-Y., Street, R. L. & Klotz, S. P. 1990 A study of wave–turbulence interaction by use of a nonlinear water wave decomposition technique. J. Geophys. Res. 95, 16 037–16 054.CrossRefGoogle Scholar
Jiménez, J. 2004 Turbulent flow over rough walls. Annu. Rev. Fluid Mech. 36, 173–196.CrossRefGoogle Scholar
Kahma, K. K. & Donelan, M. A. 1988 A laboratory study of the minimum wind speed for wind wave generation. J. Fluid Mech. 192, 339–364.CrossRefGoogle Scholar
Keulegan, G. H. 1951 Wind tides in small closed channels. J. Res. Nat. Bur. Stand. 46, 358–381.CrossRefGoogle Scholar
Kitaigorodskii, S. A., Donelan, M. A., Lumley, J. L. & Terray, E. A. 1983 Wave–turbulence interactions in the upper ocean. Part II: Statistical characteristics of wave and turbulent components of the random velocity field in the marine surface layer. J. Phys. Oceanogr. 13, 1988–1999.2.0.CO;2>CrossRefGoogle Scholar
Komori, S., Nagaosa, R. & Murakami, Y. 1993 Turbulence structure and mass transfer across a sheared air–water interface in wind-driven turbulence. J. Fluid Mech. 249, 161–183.CrossRefGoogle Scholar
Kundu, P. K. & Cohen, I. M. 2002 Fluid Mechanics. Academic.Google Scholar
Law, C. N. S., Khoo, B. C. & Chew, T. C. 1999 Turbulence structures in the immediate vicinity of the shear-free air–water interface induced by a deeply submerged jet. Exps. Fluids 27, 321–331.CrossRefGoogle Scholar
Lin, J. T. & Gad-El-Hak, M. 1984 Turbulent current measurements in a wind wave tank. J. Geophys. Res. 89, 627–636.CrossRefGoogle Scholar
Loewen, M. R. & Siddiqui, M. H. K. 2006 Detecting microscale breaking waves. Meas. Sci. Technol. 17, 771–780.CrossRefGoogle Scholar
Longuet-Higgins, M. S. 1992 Capillary rollers and bores. J. Fluid Mech. 240, 659–679.CrossRefGoogle Scholar
Makin, V. K. & Kudryavtsev, V. N. 2002 Impact of dominant waves on sea drag. Boundary-Layer Met. 103, 83–99.CrossRefGoogle Scholar
Mei, C. C. 1983 The applied dynamics of ocean surface waves. Wiley-Interscience.Google 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. 28, 279–321.CrossRefGoogle Scholar
Melville, W. K., Veron, F. & White, C. J. 2002 The Velocity field under breaking waves: coherent structures and turbulence. J. Fluid Mech. 454, 203–233.CrossRefGoogle Scholar
Okuda, K. 1982 Internal flow structures of short wind waves. I. On the internal vorticity structures. J. Oceanogr. Soc. Japan 38, 28–42.CrossRefGoogle Scholar
Peirson, W. L. 1997 Measurements of surface velocities and shear at a wavy air–water interface using particle image velocimetry. Exps. Fluids 23, 427–437.CrossRefGoogle Scholar
Peirson, W. L. & Banner, M. L. 2003 Aqueous surface layer flows induced by microscale breaking wind waves. J. Fluid Mech. 479, 1–38.CrossRefGoogle Scholar
Schlichting, H. T. & Gersten, K. 2000 Boundary-Layer Theory. McGraw–Hill.CrossRefGoogle Scholar
Shemdin, O. H. 1972 Wind-generated current and phase speed of wind waves. J. Phys. Oceanogr. 2, 411–419.2.0.CO;2>CrossRefGoogle Scholar
Siddiqui, M. H. K., Loewen, M. R., Richardson, C., Asher, W. E. & Jessup, A. T. 2001 Simultaneous particle image velocimetry and infrared imagery of microscale breaking waves. Phys. Fluids 13, 1891–1903.CrossRefGoogle Scholar
Siddiqui, M. H. K., Loewen, M. R., Asher, W. E. & Jessup, A. T. 2004 Coherent structures beneath wind waves and their influence on air–water gas transfer. J. Geophys. Res. 109, C3, C03024.Google Scholar
Sirovich, L. & Karlsson, S. 1997 Turbulent drag reduction by passive mechanisms. Nature 388, 753–755.CrossRefGoogle Scholar
Smith, S. D. 1988 Coefficients for sea surface wind stress, heat flux, and wind profiles as a function of wind speed and temperature. J. Geophys. Res. 93 (C12), 15 467–15 472.CrossRefGoogle Scholar
Soloviev, A. & Lukas, R. 2003 Observation of wave-enhanced turbulence in the near-surface layer of the ocean during TOGA COARE. Deep-Sea Res. I, 50, 371–395.CrossRefGoogle Scholar
Soloviev, A. V., Vershinsky, N. V. & Bezverchinii, V. A. 1988 Small-scale turbulence measurements in the thin surface layer of the ocean. Deep-Sea Res. 35, 1859–1874.CrossRefGoogle Scholar
Sullivan, P. P., McWilliams, J. C. & Melville, W. K. 2004 The oceanic boundary layer driven by wave breaking with stochastic variability. Part 1. Direct numerical simulations. J. Fluid Mech. 507, 143–174.CrossRefGoogle Scholar
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence. MIT press.CrossRefGoogle Scholar
Terray, E. A., Donelan, M. A., Agrawal, Y. C., Drennan, W. M., Kahama, 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. (Referred to herein as T).2.0.CO;2>CrossRefGoogle Scholar
Thais, L. & Magnaudet, J. 1995 A triple decomposition of the fluctuating motion below laboratory wind water-waves. J. Geophys. Res. 100 (C1), 741–755.CrossRefGoogle Scholar
Thais, L. & Magnaudet, J. 1996 Turbulent structure beneath surface gravity waves sheared by the wind. J. Fluid Mech. 328, 313–344.CrossRefGoogle Scholar
Turner, J. S. 1973 Buoyancy Effects in Fluids. Cambridge University Press.CrossRefGoogle Scholar
Van Dorn, W. G. 1953 Wind Stress on an Artificial Pond. J. Mar. Res. 12, 249–276.Google Scholar
Veron, F. & Melville, W. K. 1999 Pulse-to-pulse coherent Doppler measurements of waves and turbulence. J. Atmos. Oceanic. Technol. 16, 1580–1597.2.0.CO;2>CrossRefGoogle Scholar
Wu, J. 1975 Wind-induced drift currents. J. Fluid Mech. 68, 49–70.CrossRefGoogle Scholar
Zappa, C. J., Asher, W. E. & Jessup, A. T. 2001 Microscale wave breaking and air–water gas transfer. J. Geophys. Res. 106, 9385–9391.CrossRefGoogle Scholar
Zappa, C. J., Asher, W. E., Jessup, A. T., Klinke, J. & Long, S. R. 2004 Microbreaking and the enhancement of air–water gas transfer velocities. J. Geophys. Res. 109, C8, C08S16.Google Scholar