Experiments in Fluids

, Volume 53, Issue 2, pp 369–390 | Cite as

Turbulent structure of air flow over wind-induced gravity waves

Research Article


This is the second paper in a group of three that reports the systematic measurements of wind-generated water waves in a wind tunnel experiment. Here, the structure of the boundary layer on the air side of the water–air interface was analysed and compared with the boundary layer over a smooth plane rigid wall. The contribution of the wave-induced Reynolds stress was detected through filtering the spectrum of velocity fluctuations. Wave-induced Reynolds stresses became negligible for z > 5 H rms. The intermittency factor in the boundary layer over water waves was similar to that in a boundary layer over a rigid plane wall, with several differences near the interface. Here, the presence/absence of water damps out the turbulence. The quadrant analyses revealed that ejection and sweep events were dominant and more concentrated. At small fetches, the large-amplitude negative streamwise perturbations were preferentially lifted. Turbulence energy production peaked at z/δ = 0.2 and had a distribution similar to that observed for a self-preserving boundary layer with a strong adverse gradient pressure. The quadrant analysis contribution to the energy production revealed that ejections still dominated the balance and that the production was spatially modulated in the wind direction with a couple of cells and with a minimum in the area of the free surface wave height reduction.


\( \overline{ \ldots } \)

Time average operator

\( \widetilde{ \ldots } \)

Oscillating term operator

\( \widehat{ \ldots } \)

Phasic average operator


Volume fraction or concentration for water


Boundary layer thickness


Intermittency factor


Mass density


Angle between wind and wave propagation direction


Turbulent kinetic energy


Kinematic fluid viscosity




Crest height


Trough height




Celerity of propagation of the gravity waves


Water depth


Wave height, threshold coefficient

Hrms, Hmean

Root mean square wave height, mean wave height


Highest one-third wave


Coefficient, von Karman constant


Wave length


Probability distribution function

Re, Rex

Reynolds number, based on the abscissa x



Tmean, T1/3,…

Period of the waves, mean value, mean value of the first third


Turbulent kinetic energy


Streamwise wind velocity


Asymptotic wind velocity


Wind velocity at the reference level of 10 m


Drift velocity

U, V

Streamwise, vertical wind velocity

U′, V′

Streamwise, vertical fluctuating wind velocity


Friction velocity in the air boundary layer

x, y, z, xi

Spatial co-ordinates


Instantaneous level of the free surface



The experimental data presented herein were obtained during the author’s sabbatical spent at CEAMA, Grupo de Dinámica de Flujos Ambientales, University of Granada, Spain, kindly hosted by Miguel A. Losada. Financial support from CEAMA is gratefully acknowledged. Special thanks to Luca Chiapponi, Simona Bramato and Christian Mans who provided great help with the experiments.


  1. Alfredsson RJ, Johansson AV (1984) On the detection of turbulence-generating events. J Fluid Mech 139(1):325–345CrossRefGoogle Scholar
  2. Anisimova YP, Makova VI, Nikitina YA, Speranskaya AA (1982) Momentum flux spectrum above a developing wind wave. Atmos Oceanic Phys 18:435–439Google Scholar
  3. Antonia RA, Chambers AJ (1980) Wind wave induced disturbances in the marine surface layer. J Phys Oceanogr 10:611–622CrossRefGoogle Scholar
  4. Brocchini M (2002) Free surface boundary conditions at a bubbly/weakly-splashing air-water interface. Phys Fluids 14(6):1834–1840MathSciNetCrossRefGoogle Scholar
  5. Brocchini M, Peregrine DH (2001) The dynamics of strong turbulence at free surfaces. Part 2. Free-surface boundary conditions. J Fluid Mech 449:255–290MathSciNetCrossRefGoogle Scholar
  6. Chang PC, Plate EJ, Hidy GM (1971) Turbulent air flow over the dominant component of wind-generated water waves. J Fluid Mech 47:183–208CrossRefGoogle Scholar
  7. Chiapponi L, Longo S, Bramato S, Mans C, Losada A M (2011) Free-surface turbulence, Wind generated waves: laboratory data. Technical report on experimental activity in Granada, University of Parma (Italy), CEAMA (Granada, Spain)Google Scholar
  8. Donelan MA, Babanin AV, Young IR, Banner ML (2006) Wave-follower field measurements of the wind-input spectral function. Part II: parameterization of the wind input. J Phys Oceanogr 36:1672–1689CrossRefGoogle Scholar
  9. Foster RC, Vianey F, Drobinski P, Carlotti P (2006) Near-surface coherent structures and the vertical momentum flux in a large-eddy simulation of the neutrally-stratified boundary layer. Boundary Layer Meteorol 120:229–255CrossRefGoogle Scholar
  10. Hsu C-T, Hsu E-Y (1983) On the structure of turbulent flow over a progressive water wave: theory and experiment in a transformed, wave-following coordinate system. Part 2. J Fluid Mech 131:123–153CrossRefGoogle Scholar
  11. Hsu C-T, Hsu E-Y, Street RL (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 105:87–117CrossRefGoogle Scholar
  12. Hunt JCR, Stretch DD, Belcher SE (2011) Viscous coupling of shear-free turbulence across nearly flat fluid interfaces. J Fluid Mech 671(iii):96–120Google Scholar
  13. Janssen PAEM (1999) On the effect of ocean waves on the kinetic energy balance and consequences for the inertial dissipation technique. J Phys Oceanogr 29:530–534CrossRefGoogle Scholar
  14. Kato H, Sano K (1971) An experimental study of the turbulent structure of wind over water waves. Rep Port Harb Res Inst 10:3–42Google Scholar
  15. Klebanoff PS (1955) Characteristics of turbulence in a boundary layer with zero pressure gradient. NACA Report 1247Google Scholar
  16. Krostad PÅ, Antonia RA (1999) Surface roughness effects in turbulent boundary layers. Exp Fluids 27:450–460CrossRefGoogle Scholar
  17. Lam K, Banerjee S (1992) On the condition of streak formation in a bounded turbulent flow. Phys Fluids A Fluid Dyn 4(2):306–320Google Scholar
  18. Letchford CW, Zachry BC (2009) On wind, waves, and surface drag. Presented at the 5th European and African conference on wind engineering, Florence, ItalyGoogle Scholar
  19. Longo S (2010) Experiments on turbulence beneath a free surface in a stationary field generated by a Crump weir: free surface characteristics and the relevant scales. Exp Fluids 49:1325–1338CrossRefGoogle Scholar
  20. Longo S (2011) Experiments on turbulence beneath a free surface in a stationary field generated by a Crump weir: turbulence structure and correlation with the free surface. Exp Fluids 50:201–215Google Scholar
  21. Longo S (2012) Wind-generated water waves in a wind tunnel: free surface statistics wind friction and mean air flow properties. Coastal Eng 61:27–41CrossRefGoogle Scholar
  22. Longo S, Liang D, Chiapponi L, Aguilera Jiménez L (2012) Turbulent flow structure in experimental laboratory wind-generated gravity waves. Accepted in Coastal Engineering. doi: 10.1016/j.coastaleng.2012.02.006
  23. Miles JW (1957) On the generation of surface waves by shear flows. J Fluid Mech 3:185–204MathSciNetMATHCrossRefGoogle Scholar
  24. Miles JW (1959) On the generation of surface waves by shear flows. J Fluid Mech 6:568–582MathSciNetMATHCrossRefGoogle Scholar
  25. Nagarajan S, Lele SK, Ferziger JH (2007) Leading-edge effects in bypass transition. J Fluid Mech 572:471–504MATHCrossRefGoogle Scholar
  26. Nolan KP, Walsh EJ, McEligot DM (2010) Quadrant analysis of a transitional boundary layer subject to free-stream turbulence. J Fluid Mech 658:310–335MATHCrossRefGoogle Scholar
  27. Rashidi M, Banerjee S (1990) The effect of boundary conditions and shear rate on streak formation and breakdown in turbulent channel flows. Phys Fluids A 2(10):1827–1838Google Scholar
  28. Schlichting H, Gersten K (2000) Boundary layer theory. Springer, BerlinMATHGoogle Scholar
  29. Shaikh N, Siddiqui K (2011a) Near-surface flow structure over wind-generated water waves, part I: wave-induced flow characteristics. Ocean Dyn 61:127–141CrossRefGoogle Scholar
  30. Shaikh N, Siddiqui K (2011b) Near-surface flow structure over wind-generated water waves, part II: characteristics of separated and non-separated flows. Ocean Dyn 61:143–154CrossRefGoogle Scholar
  31. Sjöblom A, Smedman AS (2002) The turbulent kinetic energy budget in the marine atmospheric surface layer. J Geophys Res 107(C10):3142Google Scholar
  32. Sjöblom A, Smedman AS (2003) Vertical structure in the marine atmospheric boundary layer and its implication for the inertial dissipation method. Boundary-Layer Meteorol 109:1–25CrossRefGoogle Scholar
  33. Stewart RH (1970) Laboratory studies of the velocity field over deep-water waves. J Fluid Mech 42:733–754CrossRefGoogle Scholar
  34. Sullivan PP, McWilliams JC, Moeng C-H (2000) Simulation of turbulent flow over idealized water waves. J Fluid Mech 404:47–85MATHCrossRefGoogle Scholar
  35. Sullivan PP, Edson JB, Hristov T, McWilliams JC (2008) Large-Eddy simulations and observations of atmospheric marine boundary layers above nonequilibrium surface waves. J Atmos Sci 65:1225–1245CrossRefGoogle Scholar
  36. Townsend AA (1948) Local isotropy in the turbulent wake of a cylinder. Aust J Sci Res Ser A Phys Sci 1:161–174Google Scholar
  37. Townsend AA (1976) The structure of turbulent shear flow. Cambridge University Press, CambridgeMATHGoogle Scholar
  38. Yelland M, Taylor PK (1996) Wind stress measurements from the open ocean. J Phys Oceanogr 26(4):541–558CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 2012

Authors and Affiliations

  1. 1.Department of Civil EngineeringUniversity of ParmaParmaItaly
  2. 2.Centro Andaluz de Medio AmbienteUniversidad de GranadaGranadaSpain

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