An energy compartment model for propagation, nonlinear interaction, and dissipation of internal gravity waves

Journal of Physical Oceanography

Volumn 44, Issue 8, 2014, Pages 2093-2106

  Eden, Carsten ^a   Olbers, Dirk ^b  

^a UNIVERSITY OF HAMBURG   (Germany)

^b ALFRED WEGENER INSTITUTE FOR POLAR AND MARINE RESEARCH   (Germany)

Author keywords

Atm Ocean Structure Phenomena; Circulation Dynamics; Internal waves; Mixing; Models and modeling; Parameterization; Tides; Wave breaking; Wave properties

Indexed keywords

GRAVITY WAVES; MIXING; PARAMETERIZATION; TIDES; WAVE ENERGY CONVERSION;

GLOBAL NUMERICAL SIMULATIONS; INTERNAL WAVES; NONLINEAR INTERACTIONS; RADIATIVE TRANSFER EQUATIONS; SUBHARMONIC INSTABILITY; WAVE PROPERTIES; WAVE-WAVE INTERACTIONS; WAVEBREAKING;

TIDAL POWER;

BOTTOM TOPOGRAPHY; GRAVITY WAVE; INTERNAL WAVE; MIXING; NONLINEAR WAVE; NUMERICAL MODEL; OCEAN TIDE; OCEANIC CIRCULATION; PARAMETERIZATION; STRATIFICATION; WAVE BREAKING; WAVE ENERGY; WAVE PROPAGATION; WAVE SCATTERING;

EID: 84905640606     PISSN: 00223670     EISSN: 15200485     Source Type: Journal    
DOI: 10.1175/JPO-D-13-0224.1     Document Type: Article

References (43)

1. Alford, M. H., and Z. Zhao, 2007: Global patterns of low-mode internal-wave propagation. Part I: Energy and energy flux. J. Phys. Oceanogr., 37, 1829-1848, doi:10.1175/JPO3085.1.
2. Cairns, J. L., and G. O. Williams, 1976: Internal wave observations from a midwater float, 2. J. Geophys. Res., 81, 1943-1950, doi:10.1029/JC081i012p01943.
3. Furuichi, N., T. Hibiya, and Y. Niwa, 2008: Model-predicted distribution of wind-induced internal wave energy in the world's oceans. J. Geophys. Res., 113, C09034, doi:10.1029/2008JC004768.
4. Garrett, C., 2001: What is the near-inertial wave band and why is it different from the rest of the internal wave spectrum? J. Phys. Oceanogr., 31, 962-971, doi:10.1175/1520-0485(2001)031<0962: WITNIB>2.0.CO;2.
5. Goff, J. A., and B. K. Arbic, 2010: Global prediction of abyssal hill roughness statistics for use in ocean models from digital maps of paleo-spreading rate, paleo-ridge orientation, and sediment thickness. Ocean Modell., 32, 36-43, doi:10.1016/j.ocemod.2009.10.001.
6. Gouretski, V., and K. Koltermann, 2004: WOCE global hydrographic climatology. Berichte des BSH 35, 52 pp.
7. Gregg,M. C., 1989: Scaling turbulent dissipation in the thermocline. J. Geophys. Res., 94, 9686-9698, doi:10.1029/JC094iC07p09686.
8. Hasselmann, K., 1968: Weak-interaction theory of ocean waves. Basic Dev. Fluid Dyn., 2, 117-182, doi:10.1016/B978-0-12-395520-3.50008-6.
9. Hibiya, T., and M. Nagasawa, 2004: Latitudinal dependence of diapycnal diffusivity in the thermocline estimated using a finescale parameterization. Geophys. Res. Lett., 31, L01301, doi:10.1029/2003GL017998.
10. Jayne, S., 2009: The impact of abyssal mixing parameterizations in an ocean general circulation model. J. Phys. Oceanogr., 39, 1756-1775, doi:10.1175/2009JPO4085.1.
11. Jochum, M., B. P. Briegleb, G. Danabasoglu, W. G. Large, N. J. Norton, S. R. Jayne, M. H. Alford, and F. O. Bryan, 2013: The impact of oceanic near-inertial waves on climate. J. Climate, 26, 2833-2844, doi:10.1175/JCLI-D-12-00181.1.
12. Kelly, S.,N. Jones, J. Nash, and A. Waterhouse, 2013: The geography of semidiurnal mode-1 internal-tide energy loss. Geophys. Res. Lett., 40, 4689-4693, doi:10.1002/grl.50872.
13. Kunze, E., and S. L. Smith, 2004: The role of small-scale topography in turbulent mixing of the global ocean. Oceanography, 17, 55-64, doi:10.5670/oceanog.2004.67.
14. Large, W., and G. Crawford, 1995: Observations and simulations of upper-ocean response to wind events during the ocean storms experiment. J. Phys. Oceanogr., 25, 2831-2852, doi:10.1175/1520-0485(1995)025<2831:OASOUO>2.0.CO;2.
15. MacKinnon, J., and K. Winters, 2005: Subtropical catastrophe: Significant loss of low-mode tidal energy at 28.98. Geophys. Res. Lett., 32, L15605, doi:10.1029/2005GL023376.
16. MacKinnon, J., M. H. Alford, O. Sun, R. Pinkel, Z. Zhao, and J. Klymak, 2013: Parametric subharmonic instability of the internal tide at 298N. J. Phys. Oceanogr., 43, 17-28, doi:10.1175/JPO-D-11-0108.1.
17. Marshall, J., A. Adcroft, C. Hill, L. Perelman, and C. Heisey, 1997: A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. J. Geophys. Res., 102, 5753-5766, doi:10.1029/96JC02775.
18. McComas, C., and P. Müller, 1981: Time scales of resonant interactions among oceanic internal waves. J. Phys. Oceanogr., 11, 139-147, doi:10.1175/1520-0485(1981)011<0139: TSORIA>2.0.CO;2.
19. Molemaker, M. J., J. C. McWilliams, and X. Capet, 2010: Balanced and unbalanced routes to dissipation in an equilibrated Eady flow. J. Fluid Mech., 654, 35-63, doi:10.1017/S0022112009993272.
20. Müller, M., J. Cherniawsky, M. Foreman, and J.-S. Storch, 2012: Global M2 internal tide and its seasonal variability from high resolution ocean circulation and tide modeling. Geophys. Res. Lett., 39, L19607, doi:10.1029/2012GL053320.
21. Müller, P., and N. Xu, 1992: Scattering of oceanic internal gravity waves off random bottom topography. J. Phys. Oceanogr., 22, 474-488, doi:10.1175/1520-0485(1992)022<0474: SOOIGW>2.0.CO;2.
22. Müller, P., and M. Briscoe, 1999: Diapycnal mixing and internal waves. Dynamics of Oceanic Internal Gravity Waves: Proc. 11th 'Aha Huliko'a Hawaiian Winter Workshop, Honolulu, HI, University of Hawai'i at Manoa, 289-294.
23. Müller, P., and A. Natarov, 2003: The internal wave action model (IWAM). Near-Boundary Processes and Their Parameterization: Proc. 13th 'Aha Huliko'a Hawaiian Winter Workshop, Honolulu, HI, University of Hawai'i at Manoa, 95-105.
24. Müller, P., G. Holloway, F. Henyey, and N. Pomphrey, 1986: Nonlinear interactions among internal gravity waves. Rev. Geophys., 24, 493-536, doi:10.1029/RG024i003p00493.
25. Munk, W., 1981: Internal waves and small-scale processes. Evolution of Physical Oceanography, B. A. Warren and C. Wunsch, Eds., MIT Press, 264-291.
26. Nikurashin,M., and R. Ferrari, 2011: Global energy conversion rate fromgeostrophic flows into internal lee waves in the deep ocean. Geophys. Res. Lett., 38, L08610, doi:10.1029/2011GL046576.
27. Nycander, J., 2005: Generation of internal waves in the deep ocean by tides. J. Geophys. Res., 110, C10028, doi:10.1029/2004JC002487.
28. Olbers, D. J., 1974: On the Energy Balance of Small-Scale Internal Waves in the Deep Sea. Hamb. Geophys. Einzelschriften, No. 24, G. M. L. Wittenborn, 91 pp.
29. Olbers, D. J., 1976: Nonlinear energy transfer and the energy balance of the internal wave field in the deep ocean. J. Fluid Mech., 74, 375-399, doi:10.1017/S0022112076001857.
30. Olbers, D. J., 1983: Models of the oceanic internal wave field. Rev. Geophys. Space Phys., 21, 1567-1606, doi:10.1029/RG021i007p01567.
31. Olbers, D. J., and K. Herterich, 1979: The spectral energy transfer from surface waves to internal waves. J. Fluid Mech., 92, 349-379, doi:10.1017/S0022112079000653.
32. Olbers, D. J., and N. Pomphrey, 1981: Disqualifying two candidates for the energy balance of the oceanic internal wave field. J. Phys. Oceanogr., 11, 1423-1425, doi:10.1175/1520-0485(1981)011<1423: DTCFTE>2.0.CO;2.
33. Olbers, D. J., and C. Eden, 2013: A global model for the diapycnal diffusivity induced by internal gravity waves. J. Phys. Oceanogr., 43, 1759-1779, doi:10.1175/JPO-D-12-0207.1.
34. Olbers, D. J., J. Willebrand, and C. Eden, 2012: Ocean Dynamics, Springer, 704 pp.
35. Osborn, T. R., and C. S. Cox, 1972: Oceanic fine structure. Geophys. Astrophys. Fluid Dyn., 3, 321-345, doi:10.1080/03091927208236085.
36. Polzin, K. L., 2010: Mesoscale eddy-internal wave coupling. Part II: Energetics and results from POLYMODE. J. Phys. Oceanogr., 40, 789-801, doi:10.1175/2009JPO4039.1.
37. Pomphrey, N., J. D. Meiss, and K. M. Watson, 1980: Description of nonlinear internal wave interactions using Langevin methods. J. Geophys. Res., 85, 1085-1094, doi:10.1029/JC085iC02p01085.
38. Rimac, A., J.-S. von Storch, C. Eden, and H. Haak, 2013: The influence of high-resolution wind stress field on the power input to near-inertial motions in the ocean. Geophys. Res. Lett., 40, 4882-4886, doi:10.1002/grl.50929.
39. Simmons, H. L., 2008: Spectral modification and geographic redistribution of the semi-diurnal internal tide. Ocean Modell., 21, 126-138, doi:10.1016/j.ocemod.2008.01.002.
40. St. Laurent, L., and C. Garrett, 2002: The role of internal tides in mixing the deep ocean. J. Phys. Oceanogr., 32, 2882-2899, doi:10.1175/1520-0485(2002)032<2882:TROITI>2.0.CO;2.
41. St. Laurent, L., M. H. Alford, and T. Paluszkiewicz, 2012: An introduction to the special issue on internal waves. Oceanography, 25, 15-19, doi:10.5670/oceanog.2012.37.
42. Wunsch, C., and R. Ferrari, 2004: Vertical mixing, energy and the general circulation of the oceans. Annu. Rev. Fluid Mech., 36, 281-314, doi:10.1146/annurev.fluid.36.050802.122121.
43. Zhai, X., R. J. Greatbatch, and C. Eden, 2007: Spreading of nearinertial energy in a 1/128 model of the North Atlantic Ocean. Geophys. Res. Lett., 34, L10609, doi:10.1029/2007GL029895.