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
Linked references
Hide All

This list contains references from the content that can be linked to their source. For a full set of references and notes please see the PDF or HTML where available.

J. G. M. Alves , M. L. Banner & I. R. Young 2003 Revisiting the Pierson–Moskowitz asymptotic limits for fully developed wind waves. J. Phys. Oceanogr. 33, 13011323.

F. Ardhuin & A. D. Jenkins 2006 On the interaction of surface waves and upper ocean turbulence. J. Phys. Oceanogr. 36, 551557.

S. Armfield & R. Street 1999 The fractional step method for the Navier–Stokes equations on staggered grids: The accuracy of three variations. J. Comput. Phys. 153, 660665.

M. L. Banner 1990 Equilibrium spectra of wind waves. J. Phys. Oceanogr. 20, 966984.

P. D. Craig & M. L. Banner 1994 Modeling wave-enhanced turbulence in the ocean surface layer. J. Phys. Oceanogr. 24, 25462559.

G. T. Csanady 1994 Vortex pair model of Langmuir circulation. J. Mar. Res. 52, 559581.

M. A. Donelan 1998 Air–water exchange processes. In Physical Processes in Lakes and Oceans, Coastal and Estuarine Studies, vol. 54, pp. 1936. American Geophysical Union.

M. A. Donelan , J. Hamilton & W. H. Hui 1985 Directional spectra of wind-generated waves. Phil. Trans. R. Soc. Lond. A 315, 509562.

M. A. Donelan , B. K. Haus , N. Reul , W. J. Plant , M. Stiassnie , H. C. Graber , O. B. Brown & E. S. Saltzman 2004 On the limiting aerodynamic roughness of the ocean in very strong winds. Geophys. Res. Lett. 31, L18306.

M. A. Donelan , M. S. Longuet-Higgins & J. S. Turner 1972 Whitecaps. Nature 239, 449451.

M. A. Donelan & W. J. Pierson 1987 Radar scattering and equilibrium ranges in wind generated waves with applications to scatterometry. J. Geophys. Res. 92, 49715029.

W. M. Drennan , M. A. Donelan , E. A. Terray & K. B. Katsaros 1996 Oceanic turbulence dissipation measurements in SWADE. J. Phys. Oceanogr. 26, 808815.

K. Emanuel 2004 Tropical cyclone energetics and structure. In Atmospheric Turbulence and Mesoscale Meteorology (ed. E. Fedorovich , R. Rotunno & B. Stevens ), pp. 165191. Cambridge University Press.

K. A. Emanuel 1999 Thermodynamic control of hurricane intensity. Nature 401, 665669.

L. I. Enstad , R. Nagaosa & G. Alendal 2006 Low shear turbulence structures beneath stress-driven interface with neutral and stable stratification. Phys. Fluids 18, 055106–1 055106–23.

C. W. Fairall , E. F. Bradley , J. E. Hare , A. A. Grachev & J. B. Edson 2003 Bulk parameterization of air–sea fluxes: Updates and verification for the COARE algorithm. J. Clim. 16, 571591.

J. H. Ferziger & M. Perić 2002 Computational Methods for Fluid Dynamics, 3rd edn. Springer.

A. Gargett , A. E. Tejada-Martínez & C. E. Grosch 2004 Langmuir supercells: A mechanism for sediment resuspension and transport in shallow seas. Science 306, 19251928.

J. R. Gemmrich & D. M. Farmer 1999 Near-surface turbulence and thermal structure in a wind-driven sea. J. Phys. Oceanogr. 29, 480499.

L. H. Kantha & C. A. Clayson 2004 On the effect of surface gravity waves on mixing in the oceanic mixed layer. Ocean Modelling 6, 101124.

T. Kawamura 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.

K. E. Kenyon 1969 Stokes drift for random gravity waves. J. Geophys. Res. 74, 69916994.

G. J. Komen , L. Cavaleri , M. Donelan , K. Hasselmann , S. Hasselmann & P. A. E. M. Janssen 1994 Dynamics and Modelling of Ocean Waves. Cambridge University Press.

E. Lamarre & W. K. Melville 1991 Air entrainment and dissipation in breaking waves. Nature 351, 469472.

W. G. Large , J. C. McWilliams & S. C. Doney 1995 Oceanic vertical mixing: A review and a model with a nonlocal boundary layer parameterization. Rev. Geophys. 32, 363403.

W. G. Large & S. Pond 1982 Sensible and latent heat flux measurements over the ocean. J. Phys. Oceanogr. 12, 464484.

S. Leibovich 1983 The form and dynamics of Langmuir circulations. Ann. Rev. Fluid Mech. 15, 391427.

D. M. Lewis & S. E. Belcher 2004 Time-dependent, coupled, Ekman boundary layer solutions incorporating Stokes drift. Dyn. Atmos. Oceans 37, 313351.

M. Li , C. Garrett & E. Skyllingstad 2005 A regime diagram for classifying turbulent large eddies in the upper ocean. Deep-Sea Res. I 52, 259278.

C.-L. Lin , J. C. McWilliams , C.-H. Moeng & P. P. Sullivan 1996 Coherent structures and dynamics in a neutrally stratified planetary boundary layer flow. Phys. Fluids 8, 26262639.

W. T. Liu , K. B. Katsaros & J. A. Businger 1979 Bulk parameterization of air–sea exchanges in heat and water vapor including the molecular constraints at the interface. J. Atmos. Sci. 36, 17221735.

M. S. Longuet-Higgins 1975 Integral properties of periodic gravity waves of finite amplitude. Proc. Roy. Soc. Lond. A 342, 157174.

V. K. Makin , V. N. Kudryavtsev & C. Mastenbroek 1995 Drag of the sea surface. Boundary-Layer Met. 73, 159182.

J. C. McWilliams 1996 Modeling the oceanic general circulation. Annu. Rev. Fluid Mech. 28, 215248.

J. C. McWilliams & E. Huckle 2006 Ekman layer rectification. J. Phys. Oceanogr. 36, 16461659.

J. C. McWilliams & J. M. Restrepo 1999 The wave-driven ocean circulation. J. Phys. Oceanogr. 29, 25232540.

J. C. McWilliams & P. P. Sullivan 2000 Vertical mixing by Langmuir circulations. Spill Sci. Technol. Bull. 6, 225237.

G. L. Mellor & T. Yamada 1982 Development of a turbulence closure model for geophysical fluid problems. Rev. Geophys. 20, 851875.

A. Melsom & Ø SÆtra . 2004 Effects of wave breaking on the near-surface profiles of velocity and turbulent kinetic energy. J. Phys. Oceanogr. 34, 490504.

W. K. Melville 1994 Energy dissipation by breaking waves. J. Phys. Oceanogr. 24, 20412049.

W. K. Melville 1996 The role of wave breaking in air–sea interaction. Ann. Rev. Fluid Mech. 28, 279321.

W. K. Melville & P. Matusov 2002 Distribution of breaking waves at the ocean surface. Nature 417, 5863.

C-H. Moeng 1984 A large-eddy simulation model for the study of planetary boundary-layer turbulence. J. Atmos. Sci. 41, 20522062.

C-H. Moeng & R. Rotunno 1990 Vertical velocity skewness in the buoyancy-driven boundary layer. J. Atmos. Sci. 47, 11491162.

C. H. Moeng & J. C. Wyngaard 1989 Evaluation of turbulent transport and dissipation closures in second-order modeling. J. Atmos. Sci. 46, 23112330.

H. M. Nepf , E. A. Cowen , S. J. Kimmel & S. G. Monismith 1995 Longitudinal vortices beneath breaking waves. J. Geophys. Res. 100, 16,21116,221.

Y. Noh , H. S. Min & S. Raasch 2004 Large eddy simulation of the ocean mixed layer: The effects of wave breaking and Langmuir circulation. J. Phys. Oceanogr. 34, 720735.

W. J. Pierson & L. Moskowitz 1964 A proposed spectral form for fully developed wind seas based on the similarity theory of S. A. Kitaigorodskii. J. Geophys. Res. 69, 51815190.

M. D. Powell , P. J. Vickery & T. A. Reinhold 2003 Reduced drag coefficient for high wind speeds in tropical cyclones. Nature 422, 279283.

J. F. Price , R. A. Weller & R. Pinkel 1986 Diurnal cycling: Observations and models of the upper ocean response to diurnal heating, cooling, and wind mixing. J. Geophys. Res. 91, 84118427.

R. J. Rapp & W. K. Melville 1990 Laboratory measurements of deep-water breaking waves. Phil. Trans. R. Soc. Lond. A 331, 735800.

A. Scotti , C. Meneveau & D. K. Lilly 1993 Generalized Smagorinsky model for anisotropic grids. Phys. Fluids A 5, 23062308.

E. D. Skyllingstad & D. W. Denbo 1995 An ocean large-eddy simulation of Langmuir circulations and convection in the surface mixed layer. J. Geophys. Res. 100, 85018522.

W. D. Smyth , E. D. Skyllingstad , G. B. Crawford & H. Wijesekera 2002 Nonlocal fluxes and Stokes drift effects in the K-profile parameterization. Ocean Dyn. 52, 104115.

P. P. Sullivan , J. C. McWilliams & C-H. Moeng 1994 A subgrid-scale model for large-eddy simulation of planetary boundary-layer flows. Boundary-Layer Met. 71, 247276.

P. P. Sullivan , J. C. McWilliams & C-H. Moeng 1996 A grid nesting method for large-eddy simulation of planetary boundary layer flows. Boundary-Layer Met. 80, 167202.

P. P. Sullivan , C-H. Moeng , B. Stevens , D. H. Lenschow & S. D. Mayor 1998 Structure of the entrainment zone capping the convective atmospheric boundary layer. J. Atmos. Sci. 55, 30423064.

E. A. Terray , M. A. Donelan , Y. C. Agrawal , W. M. Drennan , K. K. Kahma , A. J. Williams 3rd, P. A. Hwang & S. A. Kitaigorodskii 1996 Estimates of kinetic energy dissipation under breaking waves. J. Phys. Oceanogr. 26, 792807.

Thorpe, S. A. Thorpe 2004 Langmuir circulation. Ann. Rev. Fluid Mech. 36, 5579.

S. A. Thorpe 2005 The Turbulent Ocean. Cambridge University Press.

W-T. Tsai & D. K. P. Yue 1996 Computation of nonlinear free-surface flows. Ann. Rev. Fluid Mech. 28, 249278.

J. Wu 1983 Sea-surface drift currents induced by wind and waves. J. Phys. Oceanogr. 13, 14411451.

J. Wu 1988 Variations of whitecap coverage with wind stress and water temperature. J. Phys. Oceanogr. 18, 14481453.

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