On the Interaction of Surface Waves and Upper Ocean Turbulence

Fabrice Ardhuin Centre Militaire d'Océanographie, Service Hydrographique et Océanographique de la Marine, Brest, France

Search for other papers by Fabrice Ardhuin in
Current site
Google Scholar
PubMed
Close
and
Alastair D. Jenkins Bjerknes Centre for Climate Research, Geophysical Institute, Bergen, Norway

Search for other papers by Alastair D. Jenkins in
Current site
Google Scholar
PubMed
Close
Restricted access

Abstract

The phase-averaged energy evolution for random surface waves interacting with oceanic turbulence is investigated. The change in wave energy balances the change in the production of turbulent kinetic energy (TKE). Outside the surface viscous layer and the bottom boundary layer the turbulent flux is not related to the wave-induced shear so that eddy viscosity parameterizations cannot be applied. Instead, it is assumed that the wave motion and the turbulent fluxes are not correlated on the scale of the wave period. Using a generalized Lagrangian average it is found that the mean wave-induced shears, despite zero vorticity, yield a production of TKE as if the Stokes drift shear were a mean flow shear. This result provides a new interpretation of a previous derivation from phase-averaged equations by McWilliams et al. It is found that the present source or sink of wave energy is smaller but is still on the order of the empirically adjusted functions used for the dissipation of swell energy in operational wave models, as well as observations of that phenomenon by Snodgrass et al.

Corresponding author address: Dr. Fabrice Ardhuin, Centre Militaire d'Océanographie, Service Hydrographique et Océanographique de la Marine, 13, rue du Chatellier, 29609 Brest Cedex, France. Email: ardhuin@shom.fr

Abstract

The phase-averaged energy evolution for random surface waves interacting with oceanic turbulence is investigated. The change in wave energy balances the change in the production of turbulent kinetic energy (TKE). Outside the surface viscous layer and the bottom boundary layer the turbulent flux is not related to the wave-induced shear so that eddy viscosity parameterizations cannot be applied. Instead, it is assumed that the wave motion and the turbulent fluxes are not correlated on the scale of the wave period. Using a generalized Lagrangian average it is found that the mean wave-induced shears, despite zero vorticity, yield a production of TKE as if the Stokes drift shear were a mean flow shear. This result provides a new interpretation of a previous derivation from phase-averaged equations by McWilliams et al. It is found that the present source or sink of wave energy is smaller but is still on the order of the empirically adjusted functions used for the dissipation of swell energy in operational wave models, as well as observations of that phenomenon by Snodgrass et al.

Corresponding author address: Dr. Fabrice Ardhuin, Centre Militaire d'Océanographie, Service Hydrographique et Océanographique de la Marine, 13, rue du Chatellier, 29609 Brest Cedex, France. Email: ardhuin@shom.fr

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

    • Search Google Scholar
    • Export Citation
  • Andrews, D. G., and M. E. McIntyre, 1978: An exact theory of nonlinear waves on a Lagrangian-mean flow. J. Fluid Mech, 89 , 609–646.

    • Search Google Scholar
    • Export Citation
  • Ardhuin, F., and A. D. Jenkins, 2005: On the effect of wind and turbulence on ocean swell. Proc. of the 15th Int. Polar and Offshore Engineering Conf., Vol. III, Seoul, South Korea, ISOPE, 429–434.

  • Bal, G., and T. Chou, 2002: Capillary-gravity wave transport over spatially random drift. Wave Motion, 35 , 107–124.

  • Banner, M. L., A. V. Babanin, and I. R. Young, 2000: Breaking probability for dominant waves on the sea surface. J. Phys. Oceanogr, 30 , 3145–3160.

    • Search Google Scholar
    • Export Citation
  • Craig, P. D., and M. L. Banner, 1994: Modeling wave-enhanced turbulence in the ocean surface layer. J. Phys. Oceanogr, 24 , 2546–2559.

    • Search Google Scholar
    • Export Citation
  • Grant, W. D., and O. S. Madsen, 1979: Combined wave and current interaction with a rough bottom. J. Geophys. Res, 84 , 1797–1808.

  • Holm, D. D., 1996: The ideal Craik-Leibovich equations. Physica D, 98 , 415–441.

  • Janssen, P., 2004: The Interaction of Ocean Waves and Wind. Cambridge University Press, 300 pp.

  • Janssen, P. A. E. M., O. Saetra, C. Wettre, and H. Hersbach, 2004: Impact of the sea state on the atmosphere and ocean. Ann. Hydrograph, 3 .(772), 3-1–3-23.

    • Search Google Scholar
    • Export Citation
  • Jenkins, A. D., 1989: The use of a wave prediction model for driving a near-surface current model. Deut. Hydrogr. Z, 42 , 133–149.

    • Search Google Scholar
    • Export Citation
  • Jenkins, A. D., 2004: Lagrangian and surface-following coordinate approaches to wave-induced currents and air-sea momentum flux in the open ocean. Ann. Hydrograph, 3 , 772. 4-1–4-6.

    • Search Google Scholar
    • Export Citation
  • Kantha, L., 2006: A note on the decay rate of swell. Ocean Modell, 11 , 167–173.

  • Kantha, L. H., and C. A. Clayson, 2004: On the effect of surface gravity waves on mixing in the oceanic mixed layer. Ocean Modell, 6 , 101–124.

    • Search Google Scholar
    • Export Citation
  • Kenyon, K. E., 1969: Stokes drift for random gravity waves. J. Geophys. Res, 74 , 6991–6994.

  • Kitaigorodskii, S. A., and J. L. Lumley, 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.

    • Search Google Scholar
    • Export Citation
  • Komen, G. J., L. Cavaleri, M. Donelan, K. Hasselmann, S. Hasselmann, and P. A. E. M. Janssen, 1994: Dynamics and Modelling of Ocean Waves. Cambridge University Press, 554 pp.

    • Search Google Scholar
    • Export Citation
  • Kudryavtsev, V. N., and V. K. Makin, 2004: Impact of swell on the marine atmospheric boundary layer. J. Phys. Oceanogr, 34 , 934–949.

    • Search Google Scholar
    • Export Citation
  • Kudryavtsev, V. N., V. K. Makin, and B. Chapron, 1999: Coupled sea surface-atmosphere model. 2. Spectrum of short wind waves. J. Geophys. Res, 104 , 7625–7639.

    • Search Google Scholar
    • Export Citation
  • Leibovich, S., 1980: On wave-current interaction theory of Langmuir circulations. J. Fluid Mech, 99 , 715–724.

  • Longuet-Higgins, M. S., 1987: A stochastic model of sea-surface roughness. I. Wave crests. Proc. Roy. Soc. London, 410A , 19–34.

  • Longuet-Higgins, M. S., 2005: On wave set-up in shoaling water with a rough sea bed. J. Fluid Mech, 527 , 217–234.

  • Longuet-Higgins, M. S., and J. S. Turner, 1974: An ‘entraining plume’ model of a spilling breaker. J. Fluid Mech, 63 , 1–20.

    • Search Google Scholar
    • Export Citation
  • Marin, F., 2004: Eddy viscosity and Eulerian drift over rippled beds in waves. Coastal Eng, 50 , 139–159.

  • McKee, W. D., 1996: A model for surface wave propagation across a shearing current. J. Phys. Oceanogr, 26 , 276–278.

  • McWilliams, J. C., P. P. Sullivan, and C-H. Moeng, 1997: Langmuir turbulence in the ocean. J. Fluid Mech, 334 , 1–30.

  • McWilliams, J. C., J. M. Restrepo, and E. M. Lane, 2004: An asymptotic theory for the interaction of waves and currents in coastal waters. J. Fluid Mech, 511 , 135–178.

    • Search Google Scholar
    • Export Citation
  • Mellor, G., and A. Blumberg, 2004: Wave breaking and ocean surface layer thermal response. J. Phys. Oceanogr, 34 , 693–698.

  • Melville, W. K., 1996: The role of surface wave breaking in air-sea interaction. Annu. Rev. Fluid Mech, 28 , 279–321.

  • Melville, W. K., F. Verron, and C. J. White, 2002: The velocity field under breaking waves: Coherent structures and turbulence. J. Fluid Mech, 454 , 203–233.

    • Search Google Scholar
    • Export Citation
  • Phillips, O. M., 1961: A note on the turbulence generated by gravity waves. J. Geophys. Res, 66 , 2889–2893.

  • Phillips, O. M., 1977: The Dynamics of the Upper Ocean. Cambridge University Press, 336 pp.

  • Rogers, W. E., 2002: An investigation into sources of error in low frequency energy predictions. Oceanography division, Naval Research Laboratory, Stennis Space Center Tech. Rep. 7320-02-10035, 63 pp.

  • Rogers, W. E., P. A. Hwang, and D. W. Wang, 2003: Investigation of wave growth and decay in the SWAN model: Three regional-scale applications. J. Phys. Oceanogr, 33 , 366–389.

    • Search Google Scholar
    • Export Citation
  • Smith, J. A., 1980: Waves, currents, and Langmuir circulation. Ph.D. thesis, Dalhousie University, 242 pp.

  • Snodgrass, F. E., G. W. Groves, K. Hasselmann, G. R. Miller, W. H. Munk, and W. H. Powers, 1966: Propagation of ocean swell across the Pacific. Philos. Trans. Roy. Soc. London, A249 , 431–497.

    • Search Google Scholar
    • Export Citation
  • Teixeira, M. A. C., and S. E. Belcher, 2002: On the distortion of turbulence by a progressive surface wave. J. Fluid Mech, 458 , 229–267.

    • Search Google Scholar
    • Export Citation
  • Tolman, H. L., 2002: Validation of WAVEWATCH-III version 1.15. NOAA/NWS/NCEP/MMAB Tech. Rep. 213, 33 pp.

  • Tolman, H. L., and D. Chalikov, 1996: Source terms in a third-generation wind wave model. J. Phys. Oceanogr, 26 , 2497–2518.

  • White, B. S., 1999: Wave action on currents with vorticity. J. Fluid Mech, 386 , 329–344.

  • Xu, Z., and A. J. Bowen, 1994: Wave- and wind-driven flow in water of finite depth. J. Phys. Oceanogr, 24 , 1850–1866.

All Time Past Year Past 30 Days
Abstract Views 0 0 0
Full Text Views 1306 654 154
PDF Downloads 670 159 21