• Alford, M. H., and Coauthors, 2015: The formation and fate of internal waves in the South China Sea. Nature, 521, 6573, https://doi.org/10.1038/nature14399.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Bordes, G., A. Venaille, S. Joubaud, P. Odier, and T. Dauxois, 2012: Experimental observation of a strong mean flow induced by internal gravity waves. Phys. Fluids, 24, 086602, https://doi.org/10.1063/1.4745880.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Carter, G. S., and M. C. Gregg, 2006: Persistent near-diurnal internal waves observed above a site of M2 barotropic-to-baroclinic conversion. J. Phys. Oceanogr., 36, 11361147, https://doi.org/10.1175/JPO2884.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Carter, G. S., and Coauthors, 2008: Energetics of M2 barotropic to baroclinic tidal conversion at the Hawaiian Islands. J. Phys. Oceanogr., 38, 22052223, https://doi.org/10.1175/2008JPO3860.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Chou, S. H., D. S. Luther, M. D. Guiles, G. S. Carter, and T. Decloedt, 2014: An empirical investigation of nonlinear energy transfer from the M2 internal tide to diurnal wave motions in the Kauai Channel, Hawaii. Geophys. Res. Lett., 41, 505512, https://doi.org/10.1002/2013GL058320.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • de Lavergne, C., G. Madec, J. Le Sommer, A. G. Nurser, and A. C. Naveira Garabato, 2016: On the consumption of Antarctic Bottom Water in the abyssal ocean. J. Phys. Oceanogr., 46, 635661, https://doi.org/10.1175/JPO-D-14-0201.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Elgar, S., and R. Guza, 1988: Statistics of bicoherence. IEEE Trans. Acoust. Speech, 36, 16671668, https://doi.org/10.1109/29.7555.

  • Emery, W. J., and R. E. Thomson, 2001: Data Analysis Methods in Physical Oceanography. 2nd ed. Elsevier Science, 638 pp.

  • Eriksen, C. C., 1982: Observations of internal wave reflection off sloping bottoms. J. Geophys. Res., 87, 525538, https://doi.org/10.1029/JC087iC01p00525.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Ferrari, R., A. Mashayek, T. J. McDougall, M. Nikurashin, and J. M. Campin, 2016: Turning ocean mixing upside down. J. Phys. Oceanogr., 46, 22392261, https://doi.org/10.1175/JPO-D-15-0244.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gayen, B., and S. Sarkar, 2013: Degradation of an internal wave beam by parametric subharmonic instability in an upper ocean pycnocline. J. Geophys. Res. Oceans, 118, 46894698, https://doi.org/10.1002/jgrc.20321.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Gill, A. E., 1982: Atmosphere–Ocean Dynamics. Academic Press, 662 pp.

  • Grisouard, N., M. Leclair, L. Gostiaux, and C. Staquet, 2013: Large scale energy transfer from an internal gravity wave reflecting on a simple slope. Proc. IUTAM, 8, 119128, https://doi.org/10.1016/j.piutam.2013.04.016.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Huang, R., 1994: Thermohaline circulation: Energetics and variability in a single-hemisphere basin model. J. Geophys. Res., 99, 12 47112 485, https://doi.org/10.1029/94JC00522.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kelly, S. M., N. L. Jones, J. D. Nash, and A. F. Waterhouse, 2013a: The geography of semidiurnal mode-1 internal-tide energy loss. Geophys. Res. Lett., 40, 46894693, https://doi.org/10.1002/grl.50872.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kelly, S. M., N. L. Jones, and J. D. Nash, 2013b: A coupled model for Laplace’s tidal equations in a fluid with one horizontal dimension and variable depth. J. Phys. Oceanogr., 43, 17801797, https://doi.org/10.1175/JPO-D-12-0147.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Klymak, J. M., and Coauthors, 2006: An estimate of tidal energy lost to turbulence at the Hawaiian Ridge. J. Phys. Oceanogr., 36, 11481164, https://doi.org/10.1175/JPO2885.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Klymak, J. M., M. H. Alford, R.-C. Lien, Y. J. Yang, and T.-Y. Tang, 2011: The breaking and scattering of the internal tide on a continental slope. J. Phys. Oceanogr., 41, 926945, https://doi.org/10.1175/2010JPO4500.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Lamb, K. G., 2004: Nonlinear interaction among internal wave beams generated by tidal flow over supercritical topography. Geophys. Res. Lett., 31, L09313, https://doi.org/10.1029/2003GL019393.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Liu, Q., X. Xie, X. Shang, G. Chen, and H. Wang, 2019: Modal structure and propagation of internal tides in the northeastern South China Sea. Acta Oceanol. Sin., 38, 1223, https://doi.org/10.1007/s13131-019-1473-1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • MacKinnon, J. A., M. H. Alford, O. Sun, R. Pinkel, Z. Zhao, and J. Klymak, 2013: Parametric subharmonic instability of the internal tide at 29°N. J. Phys. Oceanogr., 43, 1728, https://doi.org/10.1175/JPO-D-11-0108.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Martini, K. I., M. H. Alford, E. Kunze, J. D. Nash, and S. M. Kelly, 2013: Internal bores and breaking internal tides on the Oregon continental slope. J. Phys. Oceanogr., 43, 120139, https://doi.org/10.1175/JPO-D-12-030.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • McDougall, T. J., and R. Ferrari, 2017: Abyssal upwelling and downwelling driven by near-boundary mixing. J. Phys. Oceanogr., 47, 261283, https://doi.org/10.1175/JPO-D-16-0082.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Mercier, M. J., M. Mathur, L. Gostiaux, T. Gerkema, J. M. Magalhães, J. C. B. Da Silva, and T. Dauxois, 2012: Soliton generation by internal tidal beams impinging on a pycnocline: Laboratory experiments. J. Fluid Mech., 704, 3760, https://doi.org/10.1017/jfm.2012.191.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Moum, J. N., D. R. Caldwell, J. D. Nash, and G. D. Gunderson, 2002: Observations of boundary mixing over the continental slope. J. Phys. Oceanogr., 32, 21132130, https://doi.org/10.1175/1520-0485(2002)032<2113:OOBMOT>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Müller, P., and X. Liu, 2000: Scattering of internal waves at finite topography in two dimensions. Part I: Theory and case studies. J. Phys. Oceanogr., 30, 532549, https://doi.org/10.1175/1520-0485(2000)030<0532:SOIWAF>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Munk, W., and C. Wunsch, 1998: Abyssal recipes. II: Energetics of tidal and wind mixing. Deep-Sea Res. I, 45, 19772010, https://doi.org/10.1016/S0967-0637(98)00070-3.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nash, J. D., E. Kunze, J. M. Toole, and R. W. Schmitt, 2004: Internal tide reflection and turbulent mixing on the continental slope. J. Phys. Oceanogr., 34, 11171134, https://doi.org/10.1175/1520-0485(2004)034<1117:ITRATM>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nash, J. D., M. H. Alford, and E. Kunze, 2005: Estimating internal wave energy fluxes in the ocean. J. Atmos. Oceanic Technol., 22, 15511570, https://doi.org/10.1175/JTECH1784.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Nash, J. D., E. Kunze, J. M. Toole, K. Martini, and S. Kelly, 2007: Hotspots of deep ocean mixing on the Oregon continental slope. Geophys. Res. Lett., 34, L01605, https://doi.org/10.1029/2006GL028170.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • New, A. L., and R. D. Pingree, 1992: Local generation of internal soliton packets in the central Bay of Biscay. Deep Sea Res., 39A, 15211534, https://doi.org/10.1016/0198-0149(92)90045-U.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Pinkel, R., 1984: Doppler sonar observations of internal waves: The wavenumber-frequency spectrum. J. Phys. Oceanogr., 14, 12491270, https://doi.org/10.1175/1520-0485(1984)014<1249:DSOOIW>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • St. Laurent, L., and C. Garrett, 2002: The role of internal tides in mixing the deep ocean. J. Phys. Oceanogr., 32, 28822899, https://doi.org/10.1175/1520-0485(2002)032<2882:TROITI>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Sun, O., and R. Pinkel, 2013: Subharmonic energy transfer from the semidiurnal internal tide to near-diurnal motions over Kaena Ridge, Hawaii. J. Phys. Oceanogr., 43, 766789, https://doi.org/10.1175/JPO-D-12-0141.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Tabaei, A., T. R. Akylas, and K. G. Lamb, 2005: Nonlinear effects in reflecting and colliding internal wave beams. J. Fluid Mech., 526, 217243, https://doi.org/10.1017/S0022112004002769.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., 1992: Thermal fronts caused by internal gravity waves reflecting from a slope. J. Phys. Oceanogr., 22, 105108, https://doi.org/10.1175/1520-0485(1992)022<0105:TFCBIG>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., 1998: Nonlinear reflection of internal waves at a density discontinuity at the base of the mixed layer. J. Phys. Oceanogr., 28, 18531860, https://doi.org/10.1175/1520-0485(1998)028<1853:NROIWA>2.0.CO;2.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Thorpe, S. A., and A. P. Haines, 1987: On the reflection of a train of finite-amplitude internal waves from a uniform slope. J. Fluid Mech., 178, 279302, https://doi.org/10.1017/S0022112087001228.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • van Haren, H., 2004: Incoherent internal tidal currents in the deep ocean. Ocean Dyn., 54, 6676, https://doi.org/10.1007/s10236-003-0083-2.

  • van Haren, H., A. Cimatoribus, and L. Gostiaux, 2015: Where large deep-ocean waves break. Geophys. Res. Lett., 42, 23512357, https://doi.org/10.1002/2015GL063329.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Waterhouse, A. F., and Coauthors, 2014: Global patterns of diapycnal mixing from measurements of the turbulent dissipation rate. J. Phys. Oceanogr., 44, 18541872, https://doi.org/10.1175/JPO-D-13-0104.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wunsch, S., 2017: Harmonic generation by nonlinear self-interaction of a single internal wave mode. J. Fluid Mech., 828, 630647, https://doi.org/10.1017/jfm.2017.532.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xie, X., X. Shang, H. van Haren, and G. Chen, 2013: Observations of enhanced nonlinear instability in the surface reflection of internal tides. Geophys. Res. Lett., 40, 15801586, https://doi.org/10.1002/grl.50322.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xie, X., Q. Liu, Z. Zhao, X. Shang, S. Cai, D. Wang, and D. Chen, 2018: Deep sea currents driven by breaking internal tides on the continental slope. Geophys. Res. Lett., 45, 61606166, https://doi.org/10.1029/2018GL078372.

    • Search Google Scholar
    • Export Citation
  • Xie, X.-H., G.-Y. Chen, X.-D. Shang, and W.-D. Fang, 2008: Evolution of the semidiurnal (M2) internal tide on the continental slope of the northern South China Sea. Geophys. Res. Lett., 35, L13604, https://doi.org/10.1029/2008GL034179.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Xie, X.-H., X.-D. Shang, H. van Haren, G.-Y. Chen, and Y.-Z. Zhang, 2011: Observations of parametric subharmonic instability-induced near-inertial waves equatorward of the critical diurnal latitude. Geophys. Res. Lett., 38, L05603, https://doi.org/10.1029/2010GL046521.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhao, Z., 2014: Internal tide radiation from the Luzon Strait. J. Geophys. Res. Oceans, 119, 54345448, https://doi.org/10.1002/2014JC010014.

  • Zhao, Z., and M. H. Alford, 2009: New altimetric estimates of mode-1 M2 internal tides in the central North Pacific Ocean. J. Phys. Oceanogr., 39, 16691684, https://doi.org/10.1175/2009JPO3922.1.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Zhou, Q., and P. J. Diamessis, 2013: Reflection of an internal gravity wave beam off a horizontal free-slip surface. Phys. Fluids, 25, 036601, https://doi.org/10.1063/1.4795407.

    • Crossref
    • Search Google Scholar
    • Export Citation
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Near-Surface Reflection and Nonlinear Effects of Low-Mode Internal Tides on a Continental Slope

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  • 1 State Key Laboratory of Satellite Ocean Environment Dynamics, Second Institute of Oceanography, Ministry of Natural Resources, Hangzhou, China
  • 2 School of Oceanography, Shanghai Jiao Tong University, Shanghai, China
  • 3 Southern Marine Science and Engineering Guangdong Laboratory, Zhuhai, China
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Abstract

Two sets of mooring data were collected at two sites (MA and MB) along a cross-slope section on the northeastern continental slope in the South China Sea (SCS). These data are used to investigate evolution and energy decay of low-mode semidiurnal (M2) internal tides on a subcritical slope with respect to M2. At the deep portion of the slope (~1250 m; MA), the M2 internal tides show upward energy propagation, while vertically standing M2 internal tides are often observed at shallow MB (~845 m). A two-dimensional linear internal tide model with realistic topography and stratification reproduces the observations, suggesting that low-mode M2 internal tides incident on subcritical slopes evolve into vertically propagating internal waves due to topographic scattering, propagate upward to the boundary, and reflect from the sea surface. The reflection point largely depends on the phase between the modal components of the incoming flux. In the near-surface reflection region, two kinds of nonlinear effects are observed to decay energy of the incoming internal tides. One is the resonant parametric subharmonic instability which transfers M2 internal tides to diurnal subharmonics M1 (=M2/2), but the instability is found to mainly depend on the incident waves. The other one is the nonresonant wave–wave interaction, producing two higher-harmonic M4 (=2M2) rays with opposite vertical propagation. A strong westward mean flow is observed in the interacting region, with amplitude comparable to that of the incident waves. This mean flow also appears to be generated by the nonlinear reflection of the M2 internal tides.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Xiaohui Xie, xhxie2013@gmail.com

Abstract

Two sets of mooring data were collected at two sites (MA and MB) along a cross-slope section on the northeastern continental slope in the South China Sea (SCS). These data are used to investigate evolution and energy decay of low-mode semidiurnal (M2) internal tides on a subcritical slope with respect to M2. At the deep portion of the slope (~1250 m; MA), the M2 internal tides show upward energy propagation, while vertically standing M2 internal tides are often observed at shallow MB (~845 m). A two-dimensional linear internal tide model with realistic topography and stratification reproduces the observations, suggesting that low-mode M2 internal tides incident on subcritical slopes evolve into vertically propagating internal waves due to topographic scattering, propagate upward to the boundary, and reflect from the sea surface. The reflection point largely depends on the phase between the modal components of the incoming flux. In the near-surface reflection region, two kinds of nonlinear effects are observed to decay energy of the incoming internal tides. One is the resonant parametric subharmonic instability which transfers M2 internal tides to diurnal subharmonics M1 (=M2/2), but the instability is found to mainly depend on the incident waves. The other one is the nonresonant wave–wave interaction, producing two higher-harmonic M4 (=2M2) rays with opposite vertical propagation. A strong westward mean flow is observed in the interacting region, with amplitude comparable to that of the incident waves. This mean flow also appears to be generated by the nonlinear reflection of the M2 internal tides.

© 2021 American Meteorological Society. For information regarding reuse of this content and general copyright information, consult the AMS Copyright Policy (www.ametsoc.org/PUBSReuseLicenses).

Corresponding author: Xiaohui Xie, xhxie2013@gmail.com
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