Thickness-weighted mean theory for the effect of surface gravity waves on mean flows in the upper ocean

Journal of Physical Oceanography

Volumn 42, Issue 5, 2012, Pages 725-747

  Aiki, Hidenori ^a   Greatbatch, Richard J ^b  

^a JAPAN AGENCY FOR MARINE EARTH SCIENCE AND TECHNOLOGY   (Japan)

^b GEOMAR HELMHOLTZ CENTRE FOR OCEAN RESEARCH KIEL   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

CONSERVATION OF VOLUME; DEPTH DEPENDENTS; EULERIAN; EULERIAN COORDINATE SYSTEM; FINITE AMPLITUDE; LAGRANGIAN; LARGE-SCALE CIRCULATION; MEAN FLOW; MEAN VELOCITIES; MOMENTUM FLUX; MONOCHROMATIC WAVE; RESIDUAL EFFECTS; SEA SURFACES; SURFACE GRAVITY WAVES; TURBULENT VISCOSITY; UPPER OCEAN; WAVE STRESS;

LAGRANGE MULTIPLIERS; MOMENTUM; SURFACE WAVES;

GRAVITY WAVES;

EKMAN LAYER; FLUID FLOW; GRAVITY WAVE; LAGRANGIAN ANALYSIS; OCEANIC CURRENT; SEA SURFACE; THEORETICAL STUDY; TURBULENT FLOW; UPPER OCEAN; VISCOSITY;

EID: 84864526846     PISSN: 00223670     EISSN: 15200485     Source Type: Journal    
DOI: 10.1175/JPO-D-11-095.1     Document Type: Article

References (65)

1. Aiki, H., and T. Yamagata, 2006: Energetics of the layer-thickness form drag based on an integral identity. Ocean Sci., 2, 161-171.
2. Aiki, H., and K. J. Richards, 2008: Energetics of the global ocean: The role of layer-thickness form drag. J. Phys. Oceanogr., 38, 1845- 1869.
3. 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.
4. Andrews, D. G., J. R. Holton, and C. B. Leovy, 1987: Middle Atmosphere Dynamics. Academic Press, 489 pp.
5. Ardhuin, F., N. Rascle, and K. Belibassakis, 2008: Explicit waveaveraged primitive equations using a generalized Lagrangian mean. Ocean Modell., 20, 35-60.
6. Bleck, R., 1985: On the conversion between mean and eddy components of potential and kinetic energy in isentropic and isopycnic coordinates. Dyn. Atmos. Oceans, 9, 17-37.
7. Booij, N., R. C. Ris, and L.H. Holthuijsen, 1999:A third-generation wave model for coastal regions 1. Model description and validation. J. Geophys. Res., 104 (C4), 7649-7666.
8. Broströ m, G., K. H. Christensen, and J. E. H. Weber, 2008:Aquasi-Eulerian, quasi-Lagrangian view of surface-wave-induced flow in the ocean. J. Phys. Oceanogr., 38, 1122-1130.
9. Chang, M.-S., 1969: Mass transport in deep-water long-crested random-gravity waves. J. Geophys. Res., 6, 1515-1536.
10. Craik, A. D. D., and S. Leibovich, 1976: A rational model for Langmuir circulations. J. Fluid Mech., 73, 401-426.
11. de Szoeke, R. A., and A. F. Bennett, 1993: Microstructure fluxes across density surfaces. J. Phys. Oceanogr., 23, 2254-2264.
12. Favre, A., 1965: Equations des gaz turbulents compressibles I.- Forme géné rale. J. Mé c., 4, 361-390.
13. Favre, A., 1983: Turbulence: Space-time statistical properties and behavior in supersonic flows. Phys. Fluids, 23A, 2851-2863.
14. Gallimore, R. G., and D. R. Johnson, 1981: The forcing of the meridional circulation of the isentropic zonally averaged circumpolar vortex. J. Atmos. Sci., 38, 583-599.
15. Gent, P. R., 2011: The Gent-McWilliams parameterization: 20/20 hindsight. Ocean Modell., 39, 2-9.
16. Gent, P. R., J. Willebrand, T. J. McDougall, and J. C. McWilliams, 1995: Parameterizing eddy-induced tracer transports in ocean circulation models. J. Phys. Oceanogr., 25, 463-474.
17. Gnanadesikan, A., and R. A. Weller, 1995: Structure and instability of the Ekman spiral in the presence of surface gravity waves. J. Phys. Oceanogr., 25, 3148-3171.
18. Greatbatch, R. J., 1998: Exploring the relationship between eddyinduced transport velocity, vertical momentum transfer, and the isopycnal flux of potential vorticity. J. Phys. Oceanogr., 28, 422-432.
19. Greatbatch, R. J., and T. J. McDougall, 2003: The non-Boussinesq temporal residual mean. J. Phys. Oceanogr., 33, 1231-1239.
20. Griffies, S. M., 2004: Fundamentals of Ocean Climate Models. Princeton University Press, 518 pp.
21. Hasselmann, K., 1970: Wave-driven inertial oscillations. Geophys. Astrophys. Fluid Dyn., 1, 463-502.
22. Hesselberg, T., 1926: Die Gesetze der ausgegleichenen atmospha ̈rischen Bewegungen. Beitr. Phys. Atmos., 12, 141-160.
23. Huang, N. E., 1979: On surface drift currents in the ocean. J. Fluid Mech., 91, 191-208.
24. Iwasaki, T., 2001: Atmospheric energy cycle viewed from wave- mean-flow interaction and Lagrangian mean circulation. J. Atmos. Sci., 58, 3036-3052.
25. Jacobson, T., and H. Aiki, 2006: An exact energy for TRM theory. J. Phys. Oceanogr., 36, 558-564.
26. Jenkins, A. D., 1986: A theory for steady and variable wind- and wave-induced currents. J. Phys. Oceanogr., 16, 1370-1377.
27. Jenkins, A. D., 1987a: A Lagrangian model for wind- and wave-induced near-surface currents. Coastal Eng., 11, 513-526.
28. Jenkins, A. D., 1987b: Wind and wave induced currents in a rotating sea with depth-varying eddy viscosity. J. Phys. Oceanogr., 17, 938-951.
29. Jenkins, A. D., 1989: The use of a wave prediction model for driving a nearsurface current model. Dtsch. Hydrogr. Z., 42, 133-149.
30. Jenkins, A. D., and F. Ardhuin, 2004: Interaction of ocean waves and currents: How different approaches may be reconciled. Proc. 14th Int. Offshore and Polar Engineering Conf., Toulon, France, International Society of Offshore and Polar Engineers, Vol. 3, 105-111.
31. 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.
32. Komen, G. J., L. Cavaleri, M. Donelan, K. Hasselmann, S. Hasselmann, and P. A. E. M. Janssen, 1994: Dynamics and Modelling ofOceanWaves,CambridgeUniversity Press, 532 pp.
33. Lamb, H., 1932: Hydrodynamics. 6th ed. Cambridge University Press, 738 pp.
34. Longuet-Higgins, M. L., 1953: Mass transport in water waves. Philos. Trans. Roy. Soc. London, 245A, 535-581.
35. Longuet-Higgins, M. L., 1960: Mass transport in the boundary layer at a free oscillating surface. J. Fluid Mech., 8, 293-306.
36. Longuet-Higgins, M. L., 1969: A nonlinear mechanism for the generation of sea waves. Proc. Roy. Soc., 311A, 371-389.
37. Madsen, O. S., 1978: Mass transport in deep-water waves. J. Phys. Oceanogr., 8, 1009-1015.
38. McDougall, T. J., and P. C. McIntosh, 2001: The temporal-residualmean velocity. Part II: Isopycnal interpretation and the tracer and momentum equations. J. Phys. Oceanogr., 31, 1222-1246.
39. 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.
40. Mellor, G., 2003: The three-dimensional current and surface wave equations. J. Phys. Oceanogr., 33, 1978-1989.
41. Mellor, G., 2008: The depth-dependent current and wave interaction equations: A revision. J. Phys. Oceanogr., 38, 2587-2596.
42. Mellor, G., M. A. Donelan, and L.-Y. Oey, 2008: A surface wave model for coupling with numerical ocean circulation models. J. Atmos. Oceanic Technol., 25, 1785-1807.
43. Moon, I.-J., 2005: Impact of a coupled ocean wave-tide-circulation system on coastal modeling. Ocean Modell., 8, 203-236.
44. Ng, C.-O., 2004: Mass transport in gravity waves revisited. J. Geophys. Res., 109, C04012.
45. Phillips, O. M., 1977: Dynamics of the Upper Ocean. Cambridge University Press, 336 pp.
46. Piedra-Cueva, I., 1995: Drift velocity of spatially decaying waves in a two-layer viscous system. J. Fluid Mech., 299, 217-239.
47. Pierson, W. J., 1962: Perturbation analysis of the Navier-Stokes equations in Lagrangian form with selected linear solutions. J. Geophys. Res., 67, 3151-3160.
48. Pollard, R. T., 1970: Surface waves with rotation:An exact solution. J. Geophys. Res., 75, 5895-5898.
49. Polton, J. A., D. M. Lewis, and S. E. Belcher, 2005: The role of wave-induced Coriolis-Stokes forcing on the wind-driven mixed layer. J. Phys. Oceanogr., 35, 444-457.
50. Rhines, P., 1982: Basic dynamics of the large-scale geostrophic circulation. Proc. 24th Summer Study Program in Geophysical Fluid Dynamics, Woods Hole, MA, Woods Hole Oceanographic Institution, 1-47.
51. Røed, L. P., 1997: Energy diagnostics in a 11/2-layer, nonisopycnic model. J. Phys. Oceanogr., 27, 1472-1476.
52. Wave-current interactions in finite depth
53. Song, J.-B., and Y.-S. Huang, 2011: An approximate solution of wave-modified Ekman current for gradually varying eddy viscosity. Deep-Sea Res., 58, 668-676.
54. Stokes, G. G., 1847: On the theory of oscillatory waves. Trans. Cambridge Phyilos. Soc., 8, 441-455.
55. Tamura, H., T. Waseda, and Y. Miyazawa, 2010: Impact of nonlinear energy transfer on the wave field in Pacific hindcast experiments. J. Geophys. Res., 115, C12036, doi:10.1029/2009JC006014.
56. Tang, C. L., W. Perrie, A. D. Jenkins, B. M. DeTracey, Y. Hu, B. Toulany, and P. C. Smith, 2007: Observation and modeling of surface currents on the Grand Banks: A study of the wave effects on surface currents. J. Geophys. Res., 112, C10025, doi:10.1029/2006JC004028.
57. 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.
58. Tolman, H. L., 1991: A third-generation model for wind waves on slowly varying, unsteady, and inhomogeneous depths and currents. J. Phys. Oceanogr., 21, 782-797.
59. Ü nlü ata, U., and C. C. Mei, 1970: Mass transport in water waves. J. Geophys. Res., 75, 7611-7618.
60. Ursell, F., 1950: On the theoretical form of ocean swell on a rotating earth. Mon. Not. Roy. Astron. Soc. Geophys., 6 (Suppl.), 1-8.
61. Waseda, T., M. Hallerstig, K. Ozaki, and H. Tomita, 2011: Enhanced freak wave occurrence with narrow directional spectrum in the North Sea. Geophys. Res. Lett., 38, L13605, doi:10.1029/2011GL047779.
62. Weber, J. E., 1983: Steady wind- and wave-induced currents in the open ocean. J. Phys. Oceanogr., 13, 524-530.
63. Weber, J. E., 2003: Wave-induced mass transport in the oceanic surface layer. J. Phys. Oceanogr., 33, 2527-2533.
64. Weber, J. E., G. Broström, and O. Saetra, 2006: Eulerian versus Lagrangian approaches to the wave-induced transport in the upper ocean. J. Phys. Oceanogr., 36, 2106-2118.
65. Xu, Z., and A. J. Bowen, 1994: Wave- and wind-driven flow in water of finite depth. J. Phys. Oceanogr., 24, 1850-1866.