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Turbulence beneath finite amplitude water waves

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Abstract

Babanin and Haus (J Phys Oceanogr 39:2675–2679, 2009) recently presented evidence of near-surface turbulence generated below steep non-breaking deep-water waves. They proposed a threshold wave parameter a 2ω/ν = 3,000 for the spontaneous occurrence of turbulence beneath surface waves. This is in contrast to conventional understanding that irrotational wave theories provide a good approximation of non-wind-forced wave behaviour as validated by classical experiments. Many laboratory wave experiments were carried out in the early 1960s (e.g. Wiegel 1964). In those experiments, no evidence of turbulence was reported, and steep waves behaved as predicted by the high-order irrotational wave theories within the accuracy of the theories and experimental techniques at the time. This contribution describes flow visualisation experiments for steep non-breaking waves using conventional dye techniques in the wave boundary layer extending above the wave trough level. The measurements showed no evidence of turbulent mixing up to a value of a 2ω/ν = 7,000 at which breaking commenced in these experiments. These present findings are in accord with the conventional understandings of wave behaviour.

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References

  • Agrawal Y, Terray E, Donelan M, Hwang P, Williams A, Drennan W, Kahma K, Kitaigorodskii S (1992) Enhanced dissipation of kinetic energy beneath surface waves. Nature 359:219–220

    Article  Google Scholar 

  • Anis A, Moum J (1995) Surface wave-turbulence interaction: Scaling ε (z) near the sea surface. J Phys Oceanogr 25:2025–2045

    Article  Google Scholar 

  • Ardhuin F, Jenkins A (2006) On the interaction of surface waves and upper ocean turbulence. J Phys Oceanogr 36:551–557

    Article  Google Scholar 

  • Babanin A (2006) On a wave-induced turbulence and a wave-mixed upper ocean layer. J Phys Oceanogr L20605(33):1–6

    Google Scholar 

  • Babanin A, Haus B (2009) On the existence of water turbulence induced by non-breaking surface waves. J Phys Oceanogr 39:2675–2679 (Notes and Correspondence)

    Article  Google Scholar 

  • Bradshaw P (1971) An introduction to turbulence and its measurement. Pergamon Press, First edition

    MATH  Google Scholar 

  • Burchard H, Craig P, Gemmrich J, van Haren H, Mathieu P, Meier H, Smith W, Prandke H, Rippeth T, Skyllingstad E, Smyth W, Welsh D, Wijesekera H (2008) Observational and numerical modeling methods for quantifying coastal ocean turbulence and mixing. Prog Oceanogr 76–4:399–442

    Article  Google Scholar 

  • Chang K, Liu P (1999) Experimental investigation of turbulence generated by breaking waves in water of intermediate depth. Phys Fluids 11–11:3390–3400

    Article  Google Scholar 

  • Chang K, Liu P (2000) Pseudo turbulence in PIV breaking-wave measurements. Exp Fluids 29:331–338

    Article  Google Scholar 

  • Cheung T, Street R (1988) The turbulent layer in the water at an air-water interface. J Fluid Mech 194:133–151

    Article  Google Scholar 

  • CEM, Coastal Engineering Manual (2008) US Army Corps of Engineers, Washington, DC (in 6 volumes)

  • Craig P, Banner M (1994) Modelling wave-enhanced turbulence in the ocean surface layer. J Phys Oceanogr 24:2546–2559

    Article  Google Scholar 

  • Drazen D, Melville W (2009) Turbulence and mixing in unsteady breaking surface waves. J Fluid Mech 628:85–119

    Article  MATH  Google Scholar 

  • Fenton J (1985) A fifth-order stokes theory for steady waves. J Waterw Port Coast Ocean Eng 111(2):216–234

    Article  MathSciNet  Google Scholar 

  • Gemmrich J, Farmer D (2004) Near-surface turbulence in the presence of breaking waves. J Phys Oceanogr 34:1067–1086

    Article  MathSciNet  Google Scholar 

  • Hughes S (1993) Physical models and laboratory techniques in coastal engineering. Advanced Series on Ocean Eng, vol 7. World Scientific Publications, Singapore

    Book  Google Scholar 

  • Jahne B, Haußecker H (1998) Air-water gas exchange. Annu Rev Fluid Mech 30:443–468

    Article  Google Scholar 

  • Janssen P (2004) The interaction of ocean waves and wind. Cambridge University Press, Cambridge

    Book  Google Scholar 

  • Jiang L, Perlin M, Shultz W (1998) Period tripling and energy dissipation of breaking standing waves. J Fluid Mech 369:273–299

    MathSciNet  MATH  Google Scholar 

  • Kinsman B (1984) Wind waves, their generation and propagation on the ocean surface. Dover publications, Inc., New York

    Google Scholar 

  • Longuet-Higgins M (1953) Mass transport in water waves. Phil Trans R Soc Lond A 245:535–581

    Article  MathSciNet  MATH  Google Scholar 

  • Longuet-Higgins M (1960) Mass transport in the boundary layer at a free oscillating surface. J Fluid Mech 8:293–306

    Article  MathSciNet  MATH  Google Scholar 

  • Magnaudet J, Thais L (1995) Orbital rotational motion and turbulence below laboratory wind water waves. J Geophys Res 100(C1):757–771

    Article  Google Scholar 

  • Matlab® R (2010a)

  • Nikora V, Goring D (1998) ADV Measurements of turbulence: Can we improve their interpretation? JHydr Eng ASCE 124–6:630–634

    Article  Google Scholar 

  • Peirson W (1997) Measurement of surface velocities and shears at a wavy air-water interface using particle image velocimetry. Exp Fluids 23:427–437

    Article  Google Scholar 

  • Peregrine D, Svendsen L (1978) Spilling breakers, bores and hydraulic jumps. In: Proceedings of the 16th international conference on coastal engineering, 2nd edn., vol 1, pp 540–550

  • Phillips O (1961) A note on the turbulence generated by gravity waves. J Geophys Res 66–9:2889–2893

    Article  Google Scholar 

  • Rapp R, Melville W (1990) Laboratory measurements of deep water breaking waves. Philos Trans R Soc A 331:735–800

    Article  Google Scholar 

  • Reynolds O (1883) An experimental investigation of the circumstances which determine whether the motion of water shall be direct or sinuous, and of the law of resistance in parallel channels. Phil Trans R Soc Lond 174:935–982

    Article  MATH  Google Scholar 

  • Sheng J, Meng H, Fox R (2000) A large eddy PIV method for turbulence dissipation rate estimation. Chem Eng Sci 55:4423–4434 (Pergamon-Elsevier Science Ltd)

    Article  Google Scholar 

  • Siddiqui K, Loewen M (2007) Characteristics of the wind drift layer and microscale breaking waves. J Fluid Mech 573:417–456

    Article  MATH  Google Scholar 

  • SPM84, Shore Protection Manual (1984) 4th edn., 2 vol. US Army Engineer Waterways Experiment Station US Government Printing Office, Washington, DC

    Google Scholar 

  • Stokes G (1847) On the theory of oscillatory waves. Trans Cambr Philos Soc 8:441–455

    Google Scholar 

  • Swan C (1990a) Wave kinematics within the crest to trough region. Environ Forces offshore Struct Predict 26:45–60

    Google Scholar 

  • Swan C (1990b) Convection within an experimental wave flume. J Hydraul Res 28:273–282

    Google Scholar 

  • Teixeira M, Belcher S (2002) On the distortion of turbulence by a progressive surface wave. J Fluid Mech 458:229–267

    Article  MathSciNet  MATH  Google Scholar 

  • Tennekes H, Lumley J (1972) A first course in turbulence. 15th printing MIT Press Design Department, Cambridge

    Google Scholar 

  • Terray E, Donelan M, Agrawal Y, Drennan W, Kahma K, Williams A III, Hwang P, Kitaigorodskii S (1996) Estimates of kinetic energy dissipation under breaking waves. J Phys Oceanogr 26:792–807

    Article  Google Scholar 

  • Tolman H (2009) User manual and system documentation of WAVEWATCH III TM version 3.14. Technical note. MMAB Contribution No. 276. NOAA

  • Voulgaris G, Trowbridge J (1998) Evaluation of the acoustic Doppler velocimeter (ADV) for turbulence measurements. J Atmos Ocean Technol 15:272–289

    Article  Google Scholar 

  • Wiegel R (1964) Oceanographical engineering. Prentice Hall International in Theoretical and Applied Mechanics. N. M. Newmark editor, Englewood Cliffs

    Google Scholar 

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Authors and Affiliations

  1. Escuela de Ingeniería Civil Oceánica, Facultad de Ingeniería, Universidad de Valparaíso, Av. Brasil 1786 of. 30, Valparaíso, Chile

    J. F. Beyá

  2. Water Research Laboratory, School of Civil and Environmental Engineering, The University of New South Wales, Sydney, NSW, 2052, Australia

    J. F. Beyá & W. L. Peirson

  3. School of Mathematics and Statistics, The University of New South Wales, Sydney, NSW, 2052, Australia

    M. L. Banner

Authors
  1. J. F. Beyá
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  2. W. L. Peirson
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  3. M. L. Banner
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Correspondence to J. F. Beyá.

Appendix

Appendix

See Figs. 8, 9 and 10.

Fig. 8
figure 8

Image sequence from t = 0 to t = 5T, Case 1, No zoom, no rectification, no image geometric distortion, contrast and brightness adjusted

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Fig. 9
figure 9

Image sequence from t = 0 to t = 5T, Case 2, zoomed out images, no rectification, images with geometric distortion (H41%:V65%), contrast and brightness adjusted

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Fig. 10
figure 10

Image sequence from t = 0 to t = 5T, Case 3, zoomed out images, no rectification, images with geometric distortion (H51%:V60%), contrast and brightness adjusted

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Beyá, J.F., Peirson, W.L. & Banner, M.L. Turbulence beneath finite amplitude water waves. Exp Fluids 52, 1319–1330 (2012). https://doi.org/10.1007/s00348-011-1254-4

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  • DOI: https://doi.org/10.1007/s00348-011-1254-4

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