Hostname: page-component-cd9895bd7-8ctnn Total loading time: 0 Render date: 2024-12-19T03:52:38.106Z Has data issue: false hasContentIssue false
  • English
  • Français

Turbulent structure beneath surface gravity waves sheared by the wind

Published online by Cambridge University Press:  26 April 2006

L. Thais  and
J. Magnaudet
L. Thais
Affiliation:
Institut de Mécanique des Fluides de Toulouse, UMR CNRS 5502, 2 Avenue Camille Soula, 31400 Toulouse, France Present address: School of Mathematics, University of Bristol, Bristol, BS8 1TW, UK.
J. Magnaudet
Affiliation:
Institut de Mécanique des Fluides de Toulouse, UMR CNRS 5502, 2 Avenue Camille Soula, 31400 Toulouse, France
Get access Rights & Permissions [Opens in a new window]

Abstract

New experiments have been carried out in a large laboratory channel to explore the structure of turbulent motion in the water layer beneath surface gravity waves. These experiments involve pure wind waves as well as wind-ruffled mechanically generated waves. A submersible two-component LDV system has been used to obtain the three components of the instantaneous velocity field along the vertical direction at a single fetch of 26 m. The displacement of the free surface has been determined simultaneously at the same downstream location by means of wave gauges. For both types of waves, suitable separation techniques have been used to split the total fluctuating motion into an orbital contribution (i.e. a motion induced by the displacement of the surface) and a turbulent contribution. Based on these experimental results, the present paper focuses on the structure of the water turbulence. The most prominent feature revealed by the two sets of experiments is the enhancement of both the turbulent kinetic energy and its dissipation rate with respect to values found near solid walls. Spectral analysis provides clear indications that wave–turbulence interactions greatly affect energy transfers over a significant frequency range by imposing a constant timescale related to the wave-induced strain. For mechanical waves we discuss several turbulent statistics and their modulation with respect to the wave phase, showing that the turbulence we observed was deeply affected at both large and small scales by the wave motion. An analysis of the phase variability of the bursting suggests that there is a direct interaction between the waves and the underlying turbulence, mainly at the wave crests. Turbulence budgets show that production essentially takes place in the wavy region of the flow, i.e. above the wave troughs. These results are finally used to address the nature of the basic mechanisms governing wave–turbulence interactions.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 328 , 10 December 1996 , pp. 313 - 344
Copyright
© 1996 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.)

References

Agrawal, Y. C, Terray, E. A., Donelan, M. A., Hwang, P. A., Williams, A. J., Drennan, W. M., Kahma, K. K. & Kitaigorodskii, S. A. 1992 Enhanced dissipation of kinetic energy beneath surface waves. Nature 359, 219–220.Google Scholar
Alfredsson, P. H. & Johansson, A. V. 1984 On the detection of turbulence-generating events. J. Fluid Mech. 139, 325–345.Google Scholar
Banner, M. L. & Peregrine, D. H. 1993 Wave breaking in deep water. Ann. Rev. Fluid Mech. 25, 373–397.Google Scholar
Belcher, S. E. & Hunt, J. C. R. 1993 Turbulent shear flow over slowly moving waves. J. Fluid Mech. 251, 109–148.Google 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, 119–151.Google Scholar
Belcher, S. E., Newley, T. M. J. & Hunt, J. C. R. 1993 The drag on an undulated surface induced by the flow of a turbulent boundary layer. J. Fluid Mech. 249, 557–596.Google Scholar
Benilov, A. Yu., Kouznetzov, O. A. & Panin, G. N. 1974 On the analysis of wind wave induced disturbances in the atmospheric turbulent surface layer. Boundary-Layer Met. 6, 269–285.Google Scholar
Blackwelder, A. F. & Kaplan, R. E. 1976 On the bursting phenomenon near the wall in turbulent shear flows. J. Fluid Mech. 76, 89–112.Google Scholar
Bogard, D. G. & Coughran, M. T. 1987 Bursts and ejections in a LEBU-modified boundary layer. In 6th Symp. on Turbulent Shear Flows, Toulouse.
Bogard, D. G. & Tiedermann, W. G. 1986 Burst detection with a single-point velocity measurement. J. Fluid Mech. 162, 389–413.Google Scholar
Buckles, J., Hanratty, T. J. & Adrian, R. J. 1984 Turbulent flow over large-amplitude wavy surfaces. J. Fluid Mech. 140, 27–44.Google Scholar
Cheung, T. K. & Street, R. L. 1988 Turbulent layers in the water at an air-water interface. J. Fluid Mech. 194, 133–151 (referred to herein as CS).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. 86, C7, 6607–6626.Google Scholar
Dillon, T. M., Richman, J. G., Hansen, C. G. & Pearson, M. D. 1981 Near-surface measurements in a lake. Nature 290, 390–392.Google Scholar
Donelan, M. A. 1978 Whitecaps and momentum transfer. In Turbulent Fluxes through the Sea Surface. Wave dynamics and Prediction (ed. A. J Favre & K Hasselmann). Plenum.
Donelan, M. A., Anctil, F. & Doering, J. C. 1992 A simple method for calculating the velocity field beneath irregular waves. Coastal Engng, 16, 399–424.Google Scholar
Ebuchi, N., Kawamura, H. & Toba, Y. 1987 Fine structure of laboratory wind-wave surfaces studied using an optical method. Boundary-Layer Met. 39, 133–151.Google Scholar
Gargett, A. E. 1989 Ocean turbulence. Ann. Rev. Fluid Mech. 21, 419–451.Google Scholar
Houdeville, R. & Corjon, A. 1988 Phénomène de Bursting dans une couche limite pulsée de plaque plane. Rapport ONERA RSF OA 69/2259. CER, Toulouse.Google 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.Google Scholar
Jiang, J. S. & Street, R. L. 1991 Modulated flows beneath wind-ruffled, mechanically generated water waves. J. Geophys. Res. 96, C2, 2711–2721.Google Scholar
Jiang, J. S., 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, C9, 16037–16054.Google Scholar
Jones, I. S. F. 1985 Turbulence below wind waves. In The Ocean Surface (ed. Y Toba & H Mitsuyasu). Reidel.
Kitaigorodskii, S. A. K., 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
Kitaigorodskii, S. A. K. & Lumley, J. L. 1983 Wave-turbulence interactions in the upper ocean. Part I: The energy balance of the interacting fields of surface wind waves and wind-induced three-dimensional turbulence. J. Phys. Oceanogr. 13, 1977–1987.2.0.CO;2>CrossRefGoogle Scholar
Klebanoff, P. S. 1955 Characteristics of turbulence in a boundary layer flow with zero pressure gradient. NACA Rep. 1247.Google 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.Google Scholar
Lake, B. M. & Yuen, H. C. 1978 A new model for nonlinear wind waves. Part 1, Physical model and experimental evidence. J. Fluid Mech. 88, 33–62.Google Scholar
Leibovich, S. 1983 The form and dynamics of Langmuir circulations. Ann. Rev. Fluid Mech. 15, 391–427.Google Scholar
Lemmin, U., Scott, J. T. & Czapski, U. H. 1974 The development from two-dimensional to three-dimensional turbulence generated by breaking waves. J. Geophys. Res. 79, 3442–3448.Google Scholar
Lin, J. T. & Gad-el-Hak, M. 1984 Turbulent current measurements in a wind-wave tank. J. Geophys. Res. 89, C1, 627–636.Google Scholar
Longuet-Higgins, M. S. 1963 The generation of capillary waves by steep gravity waves. J. Fluid Mech. 16, 138–159.Google Scholar
Longuet-Higgins, M. S. 1992 Capillary rollers and bores. J. Fluid Mech. 240, 659–679.Google Scholar
Lumley, J. L. & Terray, E. A. 1983 Kinematics of turbulence convected by a random wave field. J. Phys. Oceanogr. 13, 2000–2007.Google Scholar
Magnaudet, J. & Masbernat, L. 1990 Interactions des vagues de vent avec le courant moyen et la turbulence. C.R. Acad. Sci. Paris II 311, 1461–1466.Google Scholar
Magnaudet, J. & Thais, L. 1995 Orbital rotational motion and turbulence bellow laboratory wind water waves. J. Geophys. Res. 100, C1, 757–771 (referred to herein as 1).Google Scholar
Monismith, S. G., Magnaudet, J., Nepf, H., Thais, L., & Cowen, E. A. 1996 Mean flows under surface gravity waves. To be submitted to J. Fluid Mech.Google Scholar
Nepf, H. M., Cowen, E. A., Kimmel, S. J. & Monismith, S. G. 1995 Langmuir vortices beneath breaking waves. J. Geophys. Res. 100, C8 16211–16222.Google Scholar
Pedlosky, J. 1987 Geophysical Fluid Dynamics.. Springer.
Phillips, O. M. 1961 A note on the turbulence generated by gravity waves. J. Geophys. Res., 66, 2889–2893.Google Scholar
Phillips, O. M. 1977 The Dynamics of the Upper Ocean. Cambridge University Press.
Phillips, O. M. 1981 Dispersion of short wavelets in the presence of a dominant long wave. J. Fluid Mech. 107, 465–485.Google Scholar
Phillips, O. M. & Banner, M. L. 1974 Wave breaking in the presence of wind drift and swell. J. Fluid Mech. 66, 625–640.Google Scholar
Ramamonjiarisoa, A. 1974 Contribution à l’étude de la structure statistique et des mécanismes de génération des vagues de vent. Thèse d'Etat, Université de Provence, Aix-Marseille I.
Rashidi, M., Hestroni, G. & Banerjee, S. 1992 Wave-induced interaction in free-surface channel flows. Phys. Fluids A 2227–2238.Google Scholar
Revault d'Allonnes, M. 1982 Une hypothèse sur la structure de la turbulence induite dans l'eau par les vagues fortement cambrées. C.R. Acad. Sci. 295, 201–203.Google Scholar
Reynolds, W. C. & Hussain, A. K. M. F. 1972 The mechanics of an organized wave in turbulent shear flow. Part 3. Theoretical model and comparisons with experiments. J. Fluid Mech. 54, 263–288.Google Scholar
Sommeria, J. & Moreau, R. 1982 Why, how, and when, MHD turbulence becomes two-dimensional. J. Fluid Mech. 118, 507–518.Google Scholar
Tardu, F. S., Binder, G. & Blackwelder, R. 1987 Modulation of bursting by periodic oscillations imposed on channel flow. In 6th Symp. on Turbulent Shear Flows, Toulouse.
Tennekes, H. & Lumley, J. L. 1972 A First Course in Turbulence.. MIT Press.
Terray, E. A. & Bliven, L. F. 1985 The vertical structure of turbulence beneath gently breaking waves. In The Ocean Surface (ed. Y Toba & H Mitsuyasu). Reidel.
Terray, E. A., Donelan, M. A., Agrawal, Y. C., Drennan, W. M., Kahma, K. K., Willams, A. J., Hwang, P. A., & Kitaigorodskii, S. A. 1996 Estimates of kinetic energy dissipation under breaking waves. J. Phys. Oceanogr. 26, 792–807.Google Scholar
Thais, L. 1994 Contribution à l’étude du mouvement turbulent sous des vagues de surface cisaillés par le vent. Thèse Inst. Nat. Polytech. Toulouse.
Thais, L. & Magnaudet, J. 1995 A triple decomposition of the fluctuating motion below laboratory wind water waves. J. Geophys. Res. 100, C1, 741–755 (referred to herein as II).Google Scholar
Veynante, D. & Candel, S. 1988 Application of nonlinear spectral analysis and signal reconstruction to laser Doppler velocimetry. Exps. Fluids 6, 534–540.Google Scholar
Yoshikawa, I., Kawamura, H., Okuda, K. & Toba, Y. 1988 Turbulent structure in water under laboratory wind waves. J. Ocean. Soc. Japan 44, 143–156.Google Scholar