Skip to main content
×
Home
    • Aa
    • Aa

Surface gravity wave effects in the oceanic boundary layer: large-eddy simulation with vortex force and stochastic breakers

  • PETER P. SULLIVAN (a1), JAMES C. McWILLIAMS (a2) and W. KENDALL MELVILLE (a3)
Abstract

The wind-driven stably stratified mid-latitude oceanic surface turbulent boundary layer is computationally simulated in the presence of a specified surface gravity-wave field. The gravity waves have broad wavenumber and frequency spectra typical of measured conditions in near-equilibrium with the mean wind speed. The simulation model is based on (i) an asymptotic theory for the conservative dynamical effects of waves on the wave-averaged boundary-layer currents and (ii) a boundary-layer forcing by a stochastic representation of the impulses and energy fluxes in a field of breaking waves. The wave influences are shown to be profound on both the mean current profile and turbulent statistics compared to a simulation without these wave influences and forced by an equivalent mean surface stress. As expected from previous studies with partial combinations of these wave influences, Langmuir circulations due to the wave-averaged vortex force make vertical eddy fluxes of momentum and material concentration much more efficient and non-local (i.e. with negative eddy viscosity near the surface), and they combine with the breakers to increase the turbulent energy and dissipation rate. They also combine in an unexpected positive feedback in which breaker-generated vorticity seeds the creation of a new Langmuir circulation and instigates a deep strong intermittent downwelling jet that penetrates through the boundary layer and increases the material entrainment rate at the base of the layer. These wave effects on the boundary layer are greater for smaller wave ages and higher mean wind speeds.

Copyright
References
Hide All
Alves J. G. M., Banner M. L. & Young I. R. 2003 Revisiting the Pierson–Moskowitz asymptotic limits for fully developed wind waves. J. Phys. Oceanogr. 33, 13011323.
Ardhuin F. & Jenkins A. D. 2006 On the interaction of surface waves and upper ocean turbulence. J. Phys. Oceanogr. 36, 551557.
Armfield S. & Street R. 1999 The fractional step method for the Navier–Stokes equations on staggered grids: The accuracy of three variations. J. Comput. Phys. 153, 660665.
Banner M. L. 1990 Equilibrium spectra of wind waves. J. Phys. Oceanogr. 20, 966984.
Banner M. L. & Peirson W. L. 1998 Tangential stress beneath wind-driven air–water interfaces. J. Fluid Mech. 364, 115145.
Belcher S. E. & Vassilicos J. C. 1997 Breaking waves and the equilibrium range of wind–wave spectra. J. Fluid Mech. 342, 377401.
Chini G. P. & Leibovich S. 2003 Resonant Langmuir-circulation internal-wave interaction. Part 1. Internal wave reflection. J. Fluid Mech. 495, 3555.
Craig P. D. & Banner M. L. 1994 Modeling wave-enhanced turbulence in the ocean surface layer. J. Phys. Oceanogr. 24, 25462559.
Craik A. D. D. & Leibovich S. 1976 A rational model for Langmuir circulations. J. Fluid Mech. 73, 401426.
Csanady G. T. 1994 Vortex pair model of Langmuir circulation. J. Mar. Res. 52, 559581.
Donelan M. A. 1998 Air–water exchange processes. In Physical Processes in Lakes and Oceans, Coastal and Estuarine Studies, vol. 54, pp. 1936. American Geophysical Union.
Donelan M. A. 2001 A nonlinear dissipation function due to wave breaking. In Workshop on Ocean Wave Forcasting. European Centre for Medium Range Weather Forecasting, Reading, England.
Donelan M. A., Hamilton J. & Hui W. H. 1985 Directional spectra of wind-generated waves. Phil. Trans. R. Soc. Lond. A 315, 509562.
Donelan M. A., Haus B. K., Reul N., Plant W. J., Stiassnie M., Graber H. C., Brown O. B. & Saltzman E. S. 2004 On the limiting aerodynamic roughness of the ocean in very strong winds. Geophys. Res. Lett. 31, L18306.
Donelan M. A., Longuet-Higgins M. S. & Turner J. S. 1972 Whitecaps. Nature 239, 449451.
Donelan M. A. & Pierson W. J. 1987 Radar scattering and equilibrium ranges in wind generated waves with applications to scatterometry. J. Geophys. Res. 92, 49715029.
Drennan W. M., Donelan M. A., Terray E. A. & Katsaros K. B. 1996 Oceanic turbulence dissipation measurements in SWADE. J. Phys. Oceanogr. 26, 808815.
Emanuel K. 2004 Tropical cyclone energetics and structure. In Atmospheric Turbulence and Mesoscale Meteorology (ed. Fedorovich E., Rotunno R. & Stevens B.), pp. 165191. Cambridge University Press.
Emanuel K. A. 1999 Thermodynamic control of hurricane intensity. Nature 401, 665669.
Enstad L. I., Nagaosa R. & Alendal G. 2006 Low shear turbulence structures beneath stress-driven interface with neutral and stable stratification. Phys. Fluids 18, 055106–1 055106–23.
Fairall C. W., Bradley E. F., Hare J. E., Grachev A. A. & Edson J. B. 2003 Bulk parameterization of air–sea fluxes: Updates and verification for the COARE algorithm. J. Clim. 16, 571591.
Ferziger J. H. & Perić M. 2002 Computational Methods for Fluid Dynamics, 3rd edn. Springer.
Gargett A., Tejada-Martínez A. E. & Grosch C. E. 2004 Langmuir supercells: A mechanism for sediment resuspension and transport in shallow seas. Science 306, 19251928.
Gemmrich J. R. 2005 On the occurrence of wave breaking. In 14th 'Aha Huliko'a Hawaiian Winter Workshop on Rogue Waves, pp. 123130. Office of Naval Research.
Gemmrich J. R. & Farmer D. M. 1999 Near-surface turbulence and thermal structure in a wind-driven sea. J. Phys. Oceanogr. 29, 480499.
Hara T. & Belcher S. E. 2002 Wind forcing in the equilibrium range of wind–wave spectra. J. Fluid Mech. 470, 223245.
Kantha L. H. & Clayson C. A. 2004 On the effect of surface gravity waves on mixing in the oceanic mixed layer. Ocean Modelling 6, 101124.
Kawamura T. 2000 Numerical investigation of turbulence near a sheared air-water interface. Part 2: Interaction of turbulent shear flow with surface waves. J. Mar. Sci. Technology 5, 161175.
Kenyon K. E. 1969 Stokes drift for random gravity waves. J. Geophys. Res. 74, 69916994.
Klemp J. & Durran D. 1983 An upper boundary condition permitting internal gravity wave radiation in numercal mesoscale models. Mon. Wea. Rev. 11, 430444.
Komen G. J., Cavaleri L., Donelan M., Hasselmann K., Hasselmann S. & Janssen P. A. E. M. 1994 Dynamics and Modelling of Ocean Waves. Cambridge University Press.
Lamarre E. & Melville W. K. 1991 Air entrainment and dissipation in breaking waves. Nature 351, 469472.
Large W. G., McWilliams J. C. & Doney S. C. 1995 Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization. Rev. Geophys. 32, 363403.
Large W. G. & Pond S. 1982 Sensible and latent heat flux measurements over the ocean. J. Phys. Oceanogr. 12, 464484.
Leibovich S. 1983 The form and dynamics of Langmuir circulations. Ann. Rev. Fluid Mech. 15, 391427.
Lewis D. M. & Belcher S. E. 2004 Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans 37, 313351.
Li M., Garrett C. & Skyllingstad E. 2005 A regime diagram for classifying turbulent large eddies in the upper ocean. Deep-Sea Res. I 52, 259278.
Lin C.-L., McWilliams J. C., Moeng C.-H. & Sullivan P. P. 1996 Coherent structures and dynamics in a neutrally stratified planetary boundary layer flow. Phys. Fluids 8, 26262639.
Liu W. T., Katsaros K. B. & Businger J. A. 1979 Bulk parameterization of air–sea exchanges in heat and water vapor including the molecular constraints at the interface. J. Atmos. Sci. 36, 17221735.
Loewen M. R. & Melville W. K. 1990 Microwave backscatter and acoustic radiation from breaking waves. J. Fluid Mech. 2, 297299.
Longuet-Higgins M. S. 1975 Integral properties of periodic gravity waves of finite amplitude. Proc. Roy. Soc. Lond. A 342, 157174.
Makin V. K., Kudryavtsev V. N. & Mastenbroek C. 1995 Drag of the sea surface. Boundary-Layer Met. 73, 159182.
McWilliams J. C. 1996 Modeling the oceanic general circulation. Annu. Rev. Fluid Mech. 28, 215248.
McWilliams J. C. & Huckle E. 2006 Ekman layer rectification. J. Phys. Oceanogr. 36, 16461659.
McWilliams J. C. & Restrepo J. M. 1999 The wave-driven ocean circulation. J. Phys. Oceanogr. 29, 25232540.
McWilliams J. C., Restrepo J. R. & Lane E. M. 2004 An asymptotic theory for the interaction of waves and currents in shallow coastal water. J. Fluid Mech. 511, 135178.
McWilliams J. C. & Sullivan P. P. 2000 Vertical mixing by Langmuir circulations. Spill Sci. Technol. Bull. 6, 225237.
McWilliams J. C., Sullivan P. P. & Moeng C-H. 1997 Langmuir turbulence in the ocean. J. Fluid Mech. 334, 130.
Mellor G. L. & Yamada T. 1982 Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. 20, 851875.
Melsom A. & SÆtra Ø. 2004 Effects of wave breaking on the near-surface profiles of velocity and turbulent kinetic energy. J. Phys. Oceanogr. 34, 490504.
Melville W. K. 1994 Energy dissipation by breaking waves. J. Phys. Oceanogr. 24, 20412049.
Melville W. K. 1996 The role of wave breaking in air–sea interaction. Ann. Rev. Fluid Mech. 28, 279321.
Melville W. K. & Matusov P. 2002 Distribution of breaking waves at the ocean surface. Nature 417, 5863.
Melville W. K., Veron F. & White C. J. 2002 The velocity field under breaking waves: coherent structures and turbulence. J. Fluid Mech. 454, 203233.
Moeng C-H. 1984 A large-eddy simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci. 41, 20522062.
Moeng C-H. & Rotunno R. 1990 Vertical velocity skewness in the buoyancy-driven boundary layer. J. Atmos. Sci. 47, 11491162.
Moeng C. H. & Wyngaard J. C. 1989 Evaluation of turbulent transport and dissipation closures in second-order modeling. J. Atmos. Sci. 46, 23112330.
Nepf H. M., Cowen E. A., Kimmel S. J. & Monismith S. G. 1995 Longitudinal vortices beneath breaking waves. J. Geophys. Res. 100, 16,21116,221.
Noh Y., Min H. S. & Raasch S. 2004 Large eddy simulation of the ocean mixed layer: The effects of wave breaking and Langmuir circulation. J. Phys. Oceanogr. 34, 720735.
Phillips O. M. 1977 Dynamics of the Upper Ocean. Cambridge University Press.
Phillips O. M. 1985 Spectral and statistical properties of the equilibrium range in wind-generated gravity waves. J. Fluid Mech. 156, 505531.
Phillips W. R. C. 2002 Langmuir circulations beneath growing or decaying surface waves. J. Fluid Mech. 469, 317342.
Pierson W. J. & Moskowitz L. 1964 A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigorodskii. J. Geophys. Res. 69, 51815190.
Polton J. A., Lewis D. M. & Belcher S. E. 2004 The role of wave-induced Coriolis–Stokes forcing on the wind-driven mixed layer. J. Phys. Oceanogr. 34, 23452358.
Powell M. D., Vickery P. J. & Reinhold T. A. 2003 Reduced drag coefficient for high wind speeds in tropical cyclones. Nature 422, 279283.
Price J. F., Weller R. A. & Pinkel R. 1986 Diurnal cycling: Observations and models of the upper ocean response to diurnal heating, cooling, and wind mixing. J. Geophys. Res. 91, 84118427.
Rapp R. J. & Melville W. K. 1990 Laboratory measurements of deep-water breaking waves. Phil. Trans. R. Soc. Lond. A 331, 735800.
Rascale N., Ardhuin F. & Terray E. A. 2006 Drift and mixing under the ocean surface: A coherent one-dimensional description with application to unstratified conditions. J. Geophys. Res. 111, C03016.
Scotti A., Meneveau C. & Lilly D. K. 1993 Generalized Smagorinsky model for anisotropic grids. Phys. Fluids A 5, 23062308.
Skyllingstad E. 2005 Langmuir circulation. In Marine Turbulence: Theories, Observations, and Models (ed. Baumert H. Z., Simpson J. & Sündermann J.), pp. 277282. Cambridge University Press.
Skyllingstad E. D. & Denbo D. W. 1995 An ocean large-eddy simulation of Langmuir circulations and convection in the surface mixed layer. J. Geophys. Res. 100, 85018522.
Smyth W. D., Skyllingstad E. D., Crawford G. B. & Wijesekera H. 2002 Nonlocal fluxes and Stokes drift effects in the K-profile parameterization. Ocean Dyn. 52, 104115.
Sullivan P. P., McWilliams J. C. & Melville W. K. 2004 The oceanic boundary layer driven by wave breaking with stochastic variability. I: Direct numerical simulations. J. Fluid Mech. 507, 143174.
Sullivan P. P., McWilliams J. C. & Melville W. K. 2005 Surface waves and ocean mixing: Insights from numerical simulations with stochastic surface forcing. In 14th 'Aha Huliko'a Hawaiian Winter Workshop on Rogue Waves, pp. 147–154.
Sullivan P. P., McWilliams J. C. & Moeng C-H. 1994 A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows. Boundary-Layer Met. 71, 247276.
Sullivan P. P., McWilliams J. C. & Moeng C-H. 1996 A grid nesting method for large-eddy simulation of planetary boundary layer flows. Boundary-Layer Met. 80, 167202.
Sullivan P. P., Moeng C-H., Stevens B., Lenschow D. H. & Mayor S. D. 1998 Structure of the entrainment zone capping the convective atmospheric boundary layer. J. Atmos. Sci. 55, 30423064.
Terray E. A., Donelan M. A., Agrawal Y. C., Drennan W. M., Kahma K. K., Williams A. J. 3rd, Hwang P. A. & Kitaigorodskii S. A. 1996 Estimates of kinetic energy dissipation under breaking waves. J. Phys. Oceanogr. 26, 792807.
Terray E. A., Drennan W. M. & Donelan M. A. 1999 The vertical structure of shear and dissipation in the ocean surface layer. In Proc. Symp. on the Wind-Driven Air–Sea Interface—Electromagnetic and Acoustic Sensing, Wave Dynamics, and Turbulent Fluxes, pp. 239245. University of New South Wales, Sydney Australia.
Thorpe Thorpe, S. A. 2004 Langmuir circulation. Ann. Rev. Fluid Mech. 36, 5579.
Thorpe S. A. 2005 The Turbulent Ocean. Cambridge University Press.
Tsai W-T. 1998 A numerical study of the evolution and structure of a turbulent shear layer under a free surface. J. Fluid Mech. 354, 239276.
Tsai W-T. & Yue D. K. P. 1996 Computation of nonlinear free-surface flows. Ann. Rev. Fluid Mech. 28, 249278.
Wu J. 1983 Sea-surface drift currents induced by wind and waves. J. Phys. Oceanogr. 13, 14411451.
Wu J. 1988 Variations of whitecap coverage with wind stress and water temperature. J. Phys. Oceanogr. 18, 14481453.
Zhou H. 1999 Numerical simulation of Langmuir circulations in a wavy domain and its comparison with the Craik-Leibovich theory. PhD thesis, Stanford University.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

Metrics

Altmetric attention score

Full text views

Total number of HTML views: 0
Total number of PDF views: 66 *
Loading metrics...

Abstract views

Total abstract views: 169 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 20th October 2017. This data will be updated every 24 hours.