• Alford, M. H., , and Z. Zhao, 2007: Global patterns of low-mode internal-wave propagation. Part II: Group velocity. J. Phys. Oceanogr., 37 , 18491858.

    • Search Google Scholar
    • Export Citation
  • Britter, R. E., , and J. E. Simpson, 1978: Experiments on the dynamics of a gravity current head. J. Fluid Mech., 88 , 223240.

  • Chang, M-H., , R-C. Lein, , T. Y. Tang, , E. A. D’Asaro, , and Y. J. Yang, 2006: Energy flux of nonlinear internal waves in northern South China Sea. Geophys. Res. Lett., 33 .L03607, doi:10.1029/2005GL025196.

    • Search Google Scholar
    • Export Citation
  • Christie, D. R., , K. J. Muirhead, , and R. H. Clarke, 1981: Solitary waves in the lower atmosphere. Nature, 293 , 4649.

  • Clarke, R. H., , R. K. Smith, , and D. G. Reid, 1981: The morning glory of the Gulf of Carpenteria: An atmospheric undular bore. Mon. Wea. Rev., 109 , 17261750.

    • Search Google Scholar
    • Export Citation
  • Crook, N. A., 1988: Trapping of low-level internal gravity waves. J. Atmos. Sci., 45 , 15331541.

  • Gear, J., , and R. Grimshaw, 1983: A second order theory for solitary waves in shallow fluids. Phys. Fluids, 26 , 1429.

  • Hebert, D., 1988: The available potential energy of an isolated feature. J. Geophys. Res., 93 , 556564.

  • Helfrich, K. R., , and W. K. Melville, 2006: Long nonlinear internal waves. Annu. Rev. Fluid Mech., 38 , 395425.

  • Henyey, F. S., , and A. Hoering, 1997: Energetics of borelike internal waves. J. Geophys. Res., 102 , 33233330.

  • Holloway, P. E., 1987: Internal hydraulic jumps and solitons at a shelf break region on the Australian North West shelf. J. Geophys. Res., 92 , 54055416.

    • Search Google Scholar
    • Export Citation
  • Hosegood, P., , and H. van Haren, 2003: Near-bed solibores over the continental slope in the Faeroe-Shetland Channel. Deep-Sea Res., 51 , 29432971.

    • Search Google Scholar
    • Export Citation
  • Huyer, A., , R. L. Smith, , and E. J. C. Sobey, 1978: Seasonal differences in low-frequency current fluctuations over the Oregon continental shelf. J. Geophys. Res., 83 , 50775089.

    • Search Google Scholar
    • Export Citation
  • Klymak, J. M., , and J. N. Moum, 2003: Internal solitary waves of elevation advancing on a shoaling shelf. Geophys. Res. Lett., 30 .2045, doi:10.1029/2003GL017706.

    • Search Google Scholar
    • Export Citation
  • Klymak, J. M., , R. Pinkel, , C-T. Liu, , A. K. Liu, , and L. David, 2006: Prototypical solitons in the South China Sea. Geophys. Res. Lett., 33 .L11607, doi:10.1029/2006GL025932.

    • Search Google Scholar
    • Export Citation
  • Kundu, P. K., , and I. M. Cohen, 2004: Fluid Mechanics. 3d ed. Elsevier Academic, 759 pp.

  • Kunze, E., , L. K. Rosenfeld, , G. S. Carter, , and M. C. Gregg, 2002: Internal waves in Monterey Submarine Canyon. J. Phys. Oceanogr., 32 , 18901913.

    • Search Google Scholar
    • Export Citation
  • Lamb, K. G., 2003: Shoaling solitary internal waves: On a criterion for the formation of waves with trapped cores. J. Fluid Mech., 478 , 81100.

    • Search Google Scholar
    • Export Citation
  • Lamb, K. G., 2007: Energy and pseudoenergy flux in the internal wave field generated by tidal flow over topography. Cont. Shelf Res., 27 , 12081232.

    • Search Google Scholar
    • Export Citation
  • Lien, R-C., , T. Y. Tang, , M. H. Chang, , and E. A. D’Asaro, 2005: Energy of nonlinear internal waves in the South China Sea. Geophys. Res. Lett., 32 .L05615, doi:10.1029/2004GL022012.

    • Search Google Scholar
    • Export Citation
  • Lumley, J. L., , and E. A. Terray, 1983: Kinematics of turbulence convected by a random wave field. J. Phys. Oceanogr., 13 , 20002007.

  • MacKinnon, J. A., , and M. C. Gregg, 2003: Shear and baroclinic energy flux on the summer New England shelf. J. Phys. Oceanogr., 33 , 14621475.

    • Search Google Scholar
    • Export Citation
  • Marks, J., 1974: Acoustic radar investigations of boundary layer phenomena. NASA Contractor Rep. CR-2432, 65 pp.

  • Mehta, A. P., , B. R. Sutherland, , and P. J. Kyba, 2002: Interfacial gravity currents. II. Wave excitation. Phys. Fluids, 14 , 35583569.

  • Moum, J. N., , and W. D. Smyth, 2006: The pressure disturbance of a nonlinear internal wave train. J. Fluid Mech., 558 , 153177.

  • Moum, J. N., , M. C. Gregg, , R. C. Lien, , and M. Carr, 1995: Comparison of turbulence kinetic energy dissipation rate estimates from two ocean microstructure profilers. J. Atmos. Oceanic Technol., 12 , 346366.

    • Search Google Scholar
    • Export Citation
  • Moum, J. N., , D. M. Farmer, , W. D. Smyth, , L. Armi, , and S. Vagle, 2003: Structure and generation of turbulence at interfaces strained by internal solitary waves propagating shoreward over the continental shelf. J. Phys. Oceanogr., 33 , 20932112.

    • Search Google Scholar
    • Export Citation
  • Moum, J. N., , D. M. Farmer, , E. L. Shroyer, , W. D. Smyth, , and L. Armi, 2007: Dissipative losses in nonlinear internal waves propagating across the continental shelf. J. Phys. Oceanogr., 37 , 19891995.

    • Search Google Scholar
    • Export Citation
  • Nash, J. D., , and J. N. Moum, 2005: River plumes as a source of large amplitude internal waves in the ocean. Nature, 437 , 400403.

  • Nash, J. D., , M. H. Alford, , and E. Kunze, 2005: On estimating internal wave energy fluxes in the ocean. J. Atmos. Oceanic Technol., 22 , 15511570.

    • Search Google Scholar
    • Export Citation
  • Osborne, A. R., , and T. L. Burch, 1980: Internal solitons in Andaman Sea. Science, 208 , 451460.

  • Perlin, A., , J. N. Moum, , and J. M. Klymak, 2005a: Response of the bottom boundary layer over the continental shelf to variations in alongshore winds. J. Geophys. Res., 110 .C10S09, doi:10.1029/2004JC002500.

    • Search Google Scholar
    • Export Citation
  • Perlin, A., , J. N. Moum, , J. M. Klymak, , M. D. Levine, , T. Boyd, , and P. M. Kosro, 2005b: A modified law-of-the-wall to describe velocity profiles in the bottom boundary layer. J. Geophys. Res., 110 .C10S10, doi:10.1029/2004JC002310.

    • Search Google Scholar
    • Export Citation
  • Pinkel, R., 2000: Internal solitary waves in the warm pool of the western equatorial pacific. J. Phys. Oceanogr., 30 , 29062926.

  • Reid, R. O., , B. A. Elliott, , and D. B. Olson, 1981: Available potential energy: A clarification. J. Phys. Oceanogr., 11 , 1529.

  • Rottman, J. W., , and J. E. Simpson, 1989: The formation of internal bores in the atmosphere: A laboratory model. Quart. J. Roy. Meteor. Soc., 115 , 941963.

    • Search Google Scholar
    • Export Citation
  • Sandstrom, H., , and J. A. Elliott, 1984: Internal tide and solitons on the Scotian Shelf. J. Geophys. Res., 89 , 64196426.

  • Scotti, A., , R. C. Beardsley, , and R. Butman, 2006: On the interpretation of energy and energy fluxes of nonlinear internal waves: An example from Massachusetts Bay. J. Fluid Mech., 561 , 103112.

    • Search Google Scholar
    • Export Citation
  • Simpson, J. E., 1997: Gravity Currents in the Environment and Laboratory. 2d ed. Cambridge University Press, 244 pp.

  • Smith, R. K., , N. Crook, , and G. Roff, 1982: The Morning Glory: An extraordinary atmospheric undular bore. Quart. J. Roy. Meteor. Soc., 108 , 937956.

    • Search Google Scholar
    • Export Citation
  • Smyth, W. D., , P. O. Zavialov, , and J. N. Moum, 1997: Decay of turbulence in the upper ocean following sudden isolation from surface forcing. J. Phys. Oceanogr., 27 , 810822.

    • Search Google Scholar
    • Export Citation
  • Sun, J., and Coauthors, 2004: Atmospheric disturbances that generate intermittent turbulence in nocturnal boundary layers. Bound.-Layer Meteor., 110 , 255279.

    • Search Google Scholar
    • Export Citation
  • Trowbridge, J. H., , and S. Elgar, 2001: Turbulence measurements in the surf zone. J. Phys. Oceanogr., 31 , 24032417.

  • Venayagamoorthy, S. K., , and O. B. Fringer, 2005: Nonhydrostatic and nonlinear contributions to the energy flux budget in nonlinear internal waves. Geophys. Res. Lett., 32 .L15603, doi:10.1029/2005GL023432.

    • Search Google Scholar
    • Export Citation
  • Winters, K. B., , P. N. Lombard, , J. J. Riley, , and E. A. D’Asaro, 1995: Available potential energy and mixing in density-stratified fluids. J. Fluid Mech., 289 , 115128.

    • Search Google Scholar
    • Export Citation
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Energy Transport by Nonlinear Internal Waves

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  • 1 College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon
  • | 2 University of Victoria, Victoria, British Columbia, Canada
  • | 3 College of Oceanic and Atmospheric Sciences, Oregon State University, Corvallis, Oregon
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Abstract

Winter stratification on Oregon’s continental shelf often produces a near-bottom layer of dense fluid that acts as an internal waveguide upon which nonlinear internal waves propagate. Shipboard profiling and bottom lander observations capture disturbances that exhibit properties of internal solitary waves, bores, and gravity currents. Wavelike pulses are highly turbulent (instantaneous bed stresses are 1 N m−2), resuspending bottom sediments into the water column and raising them 30+ m above the seafloor. The wave cross-shelf transport of fluid often counters the time-averaged Ekman transport in the bottom boundary layer. In the nonlinear internal waves that were observed, the kinetic energy is roughly equal to the available potential energy and is O(0.1) megajoules per meter of coastline. The energy transported by these waves includes a nonlinear advection term 〈uE〉 that is negligible in linear internal waves. Unlike linear internal waves, the pressure–velocity energy flux 〈up〉 includes important contributions from nonhydrostatic effects and surface displacement. It is found that, statistically, 〈uE〉 ≃ 2〈up〉. Vertical profiles through these waves of elevation indicate that up(z) is more important in transporting energy near the seafloor while uE(z) dominates farther from the bottom. With the wave speed c estimated from weakly nonlinear wave theory, it is verified experimentally that the total energy transported by the waves is 〈up〉 + 〈uE〉 ≃ cE〉. The high but intermittent energy flux by the waves is, in an averaged sense, O(100) watts per meter of coastline. This is similar to independent estimates of the shoreward energy flux in the semidiurnal internal tide at the shelf break.

Corresponding author address: J. N. Moum, College of Oceanic and Atmospheric Sciences, Oregon State University, COAS Admin. Bldg. 104, Corvallis, OR 97331-5503. Email: moum@coas.oregonstate.edu

Abstract

Winter stratification on Oregon’s continental shelf often produces a near-bottom layer of dense fluid that acts as an internal waveguide upon which nonlinear internal waves propagate. Shipboard profiling and bottom lander observations capture disturbances that exhibit properties of internal solitary waves, bores, and gravity currents. Wavelike pulses are highly turbulent (instantaneous bed stresses are 1 N m−2), resuspending bottom sediments into the water column and raising them 30+ m above the seafloor. The wave cross-shelf transport of fluid often counters the time-averaged Ekman transport in the bottom boundary layer. In the nonlinear internal waves that were observed, the kinetic energy is roughly equal to the available potential energy and is O(0.1) megajoules per meter of coastline. The energy transported by these waves includes a nonlinear advection term 〈uE〉 that is negligible in linear internal waves. Unlike linear internal waves, the pressure–velocity energy flux 〈up〉 includes important contributions from nonhydrostatic effects and surface displacement. It is found that, statistically, 〈uE〉 ≃ 2〈up〉. Vertical profiles through these waves of elevation indicate that up(z) is more important in transporting energy near the seafloor while uE(z) dominates farther from the bottom. With the wave speed c estimated from weakly nonlinear wave theory, it is verified experimentally that the total energy transported by the waves is 〈up〉 + 〈uE〉 ≃ cE〉. The high but intermittent energy flux by the waves is, in an averaged sense, O(100) watts per meter of coastline. This is similar to independent estimates of the shoreward energy flux in the semidiurnal internal tide at the shelf break.

Corresponding author address: J. N. Moum, College of Oceanic and Atmospheric Sciences, Oregon State University, COAS Admin. Bldg. 104, Corvallis, OR 97331-5503. Email: moum@coas.oregonstate.edu

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