Editorial Type:
Article
Article Type:
Research Article

Multimodal Internal Waves Generated over a Subcritical Ridge: Impact of the Upper-Ocean Stratification

Jieshuo Xie State Key Laboratory of Tropical Oceanography, South China Sea Institute of Oceanology, Chinese Academy of Sciences, Guangzhou, and Institute of Space and Earth Information Science, Chinese University of Hong Kong, Hong Kong, and University of Chinese Academy of Sciences, Beijing, China

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Jiayi Pan Institute of Space and Earth Information Science, Chinese University of Hong Kong, Hong Kong, China

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David A. Jay Department of Civil and Environmental Engineering, Portland State University, Portland, Oregon

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Print Publication:
01 Mar 2015
DOI:
https://doi.org/10.1175/JPO-D-14-0132.1
Page(s):
904–926
Restricted access

Abstract

Interaction of barotropic tides with subsurface topography is vital to ocean mixing. Yet the behavior of large-amplitude, nonlinear, internal solitary waves (ISWs) that can cause strong mixing remains poorly understood, especially that of higher-mode and multimodal internal waves. Therefore, a 2.5-dimensional, nonhydrostatic model with adjustable vertical resolution was developed to investigate effects of upper-ocean stratification on tidally induced multimodal internal waves and to show how they are generated by the subcritical ridge where only upward-propagating internal wave beams (IWBs) are present. The effects of the stratification on properties and characteristics of the excited IWBs and on the energy partition of the radiated mode-1 and mode-2 internal waves were investigated based on the model results. Higher modes of internal waves can also be effectively generated in the IWBs by the subcritical topography, and the contribution to IWBs from higher modes increases with the upper-ocean stratification. Mode-2 ISWs can be excited from the IWBs if both the tidal Froude number and the contribution to IWBs from mode-2 waves are sufficiently high (U0 is the tidal current speed, and c2 is the phase speed of mode-2 waves). In a moderately stratified upper ocean, both mode-1 and mode-2 ISWs can be produced, but for weak (strong) stratification, only mode-1 (mode-2) ISWs are generated. Further, it is found that the distance between two successive mode-1 or mode-2 ISW trains increases linearly with the upper-ocean stratification. The ratio of the kinetic energy to the available potential energy for the mode-2 ISWs increases with the upper-ocean stratification in a strongly stratified ocean.

Corresponding author address: Jiayi Pan, Institute of Space and Earth Information Science, Chinese University of Hong Kong, Shatin, N. T., Hong Kong, China. E-mail: panj@cuhk.edu.hk

Abstract

Interaction of barotropic tides with subsurface topography is vital to ocean mixing. Yet the behavior of large-amplitude, nonlinear, internal solitary waves (ISWs) that can cause strong mixing remains poorly understood, especially that of higher-mode and multimodal internal waves. Therefore, a 2.5-dimensional, nonhydrostatic model with adjustable vertical resolution was developed to investigate effects of upper-ocean stratification on tidally induced multimodal internal waves and to show how they are generated by the subcritical ridge where only upward-propagating internal wave beams (IWBs) are present. The effects of the stratification on properties and characteristics of the excited IWBs and on the energy partition of the radiated mode-1 and mode-2 internal waves were investigated based on the model results. Higher modes of internal waves can also be effectively generated in the IWBs by the subcritical topography, and the contribution to IWBs from higher modes increases with the upper-ocean stratification. Mode-2 ISWs can be excited from the IWBs if both the tidal Froude number and the contribution to IWBs from mode-2 waves are sufficiently high (U0 is the tidal current speed, and c2 is the phase speed of mode-2 waves). In a moderately stratified upper ocean, both mode-1 and mode-2 ISWs can be produced, but for weak (strong) stratification, only mode-1 (mode-2) ISWs are generated. Further, it is found that the distance between two successive mode-1 or mode-2 ISW trains increases linearly with the upper-ocean stratification. The ratio of the kinetic energy to the available potential energy for the mode-2 ISWs increases with the upper-ocean stratification in a strongly stratified ocean.

Corresponding author address: Jiayi Pan, Institute of Space and Earth Information Science, Chinese University of Hong Kong, Shatin, N. T., Hong Kong, China. E-mail: panj@cuhk.edu.hk
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  • Akylas, T. R., and R. H. J. Grimshaw, 1992: Solitary internal waves with oscillatory tails. J. Fluid Mech., 242, 279–298, doi:10.1017/S0022112092002374.

    • Search Google Scholar
    • Export Citation

  • Akylas, T. R., R. H. J. Grimshaw, S. R. Clarke, and A. Tabaei, 2007: Reflecting tidal wave beams and local generation of solitary waves in the ocean thermocline. J. Fluid Mech., 593, 297–313, doi:10.1017/S0022112007008786.

    • Search Google Scholar
    • Export Citation

  • Baines, P. G., 1977: Upstream influence and Long’s model in stratified flows. J. Fluid Mech., 82, 147–159, doi:10.1017/S0022112077000573.

    • Search Google Scholar
    • Export Citation

  • Balmforth, N. J., G. R. Ierley, and W. R. Young, 2002: Tidal conversion by subcritical topography. J. Phys. Oceanogr., 32, 2900–2914, doi:10.1175/1520-0485(2002)032<2900:TCBST>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Bogucki, D., L. G. Redekopp, and J. Barth, 2005: Internal solitary waves in the Coastal Mixing and Optics 1996 experiment: Modal structure and resuspension. J. Geophys. Res., 110, C02024, doi:10.1029/2003JC002253.

    • Search Google Scholar
    • Export Citation

  • Buijsman, M. C., Y. Kanarska, and J. C. McWilliams, 2010: On the generation and evolution of nonlinear internal waves in the South China Sea. J. Geophys. Res., 115, C02012, doi:10.1029/2009JC005275.

    • Search Google Scholar
    • Export Citation

  • Buijsman, M. C., S. Legg, and J. Klymak, 2012: Double-ridge internal tide interference and its effect on dissipation in Luzon Strait. J. Phys. Oceanogr., 42, 1337–1356, doi:10.1175/JPO-D-11-0210.1.

    • Search Google Scholar
    • Export Citation

  • Cai, S., J. Xie, and J. He, 2012: An overview of internal solitary waves in the South China Sea. Surv. Geophys., 33, 927–943, doi:10.1007/s10712-012-9176-0.

    • Search Google Scholar
    • Export Citation

  • Colosi, J. A., and W. Munk, 2006: Tales of the venerable Honolulu tide gauge. J. Phys. Oceanogr., 36, 967–996, doi:10.1175/JPO2876.1.

    • Search Google Scholar
    • Export Citation

  • Farmer, D. M., and J. D. Smith, 1980: Tidal interaction of stratified flow with a sill in Knight Inlet. Deep-Sea Res.,27A, 239–254, doi:10.1016/0198-0149(80)90015-1.

    • Search Google Scholar
    • Export Citation

  • Gerkema, T., 2001: Internal and interfacial tides: Beam scattering and local generation of solitary waves. J. Mar. Res., 59, 227–255, doi:10.1357/002224001762882646.

    • Search Google Scholar
    • Export Citation

  • Gerkema, T., and J. T. F. Zimmerman, 2008: An introduction to internal waves. Royal NIOZ Lecture Notes, 207 pp. [Available online at www.nioz.nl/files/upload/users/258010/book.pdf.]

  • Grisouard, N., C. Staquet, and T. Gerkema, 2011: Generation of internal solitary waves in a pycnocline by an internal wave beam: A numerical study. J. Fluid Mech., 676, 491–513, doi:10.1017/jfm.2011.61.

    • Search Google Scholar
    • Export Citation

  • Hall, R. A., J. M. Huthnance, and R. G. Williams, 2013: Internal wave reflection on shelf slopes with depth-varying stratification. J. Phys. Oceanogr., 43, 248–258, doi:10.1175/JPO-D-11-0192.1.

    • Search Google Scholar
    • Export Citation

  • Helfrich, K. R., and W. K. Melville, 1986: On long nonlinear internal waves over slope-shelf topography. J. Fluid Mech., 167, 285–308, doi:10.1017/S0022112086002823.

    • Search Google Scholar
    • Export Citation

  • Jackson, C. R., 2004: An atlas of internal solitary–like waves and their properties. 2nd ed. Global Ocean Associates Rep., 560 pp. [Available online at www.internalwaveatlas.com/Atlas2_index.html.]

  • Kang, D., 2010: Energetics and dynamics of internal tides in Monterey Bay using numerical simulations. Ph.D. dissertation, Stanford University, 170 pp.

  • Kantha, L. H., and C. A. Clayson, 2000: Numerical Models of Oceans and Oceanic Processes. Academic Press, 940 pp.

  • Klymak, J. M., S. Legg, and R. Pinkel, 2010: A simple parameterization of turbulent tidal mixing near supercritical topography. J. Phys. Oceanogr., 40, 2059–2074, doi:10.1175/2010JPO4396.1.

    • 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, doi:10.1029/2003GL019393.

    • Search Google Scholar
    • Export Citation

  • Lamb, K. G., 2008: On the calculation of the available potential energy of an isolated perturbation in a density stratified fluid. J. Fluid Mech., 597, 415–427, doi:10.1017/S0022112007009743.

    • Search Google Scholar
    • Export Citation

  • Lamb, K. G., and V. T. Nguyen, 2009: Calculating energy flux in internal solitary waves with an application to reflectance. J. Phys. Oceanogr., 39, 559–580, doi:10.1175/2008JPO3882.1.

    • Search Google Scholar
    • Export Citation

  • Legg, S., and J. Klymak, 2008: Internal hydraulic jumps and overturning generated by tidal flow over a tall steep ridge. J. Phys. Oceanogr., 38, 1949–1964, doi:10.1175/2008JPO3777.1.

    • Search Google Scholar
    • Export Citation

  • Levitus, S., Ed., 2009: World Ocean Atlas 2009. U.S. Government Printing Office, 1110 pp. [Available online at www.nodc.noaa.gov/OC5/WOA09/pr_woa09.html.]

  • Liu, A. K., F. C. Su, M. K. Hsu, N. J. Kuo, and C. R. Ho, 2013: Generation and evolution of mode-two internal waves in the South China Sea. Cont. Shelf Res., 59, 18–27, doi:10.1016/j.csr.2013.02.009.

    • Search Google Scholar
    • Export Citation

  • Llewellyn Smith, S. G., and W. R. Young, 2002: Conversion of the barotropic tide. J. Phys. Oceanogr., 32, 1554–1566, doi:10.1175/1520-0485(2002)032<1554:COTBT>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Llewellyn Smith, S. G., and W. R. Young, 2003: Tidal conversion at a very steep ridge. J. Fluid Mech., 495, 175–191, doi:10.1017/S0022112003006098.

    • 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, 37–60, doi:10.1017/jfm.2012.191.

    • Search Google Scholar
    • Export Citation

  • Nash, J. D., E. Kunze, C. M. Lee, and T. B. Sanford, 2006: Structure of the baroclinic tide generated at Kaena Ridge, Hawaii. J. Phys. Oceanogr., 36, 1123–1135, doi:10.1175/JPO2883.1.

    • Search Google Scholar
    • Export Citation

  • New, A. L., and R. D. Pingree, 1990: Large-amplitude internal soliton packets in the central Bay of Biscay. Deep-Sea Res., 37, 513–524, doi:10.1016/0198-0149(90)90022-N.

    • Search Google Scholar
    • Export Citation

  • North, G. R., L. B. Thomas, F. C. Robert, and J. M. Fanthune, 1982: Sampling errors in the estimation of empirical orthogonal functions. Mon. Wea. Rev., 110, 699–706, doi:10.1175/1520-0493(1982)110<0699:SEITEO>2.0.CO;2.

    • Search Google Scholar
    • Export Citation

  • Osborne, A. R., and T. L. Burch, 1980: Internal solitons in the Andaman Sea. Science, 208, 451–460, doi:10.1126/science.208.4443.451.

    • Search Google Scholar
    • Export Citation

  • Pickering, A., and M. H. Alford, 2012: Velocity structure of internal tide beams emanating from Kaena Ridge, Hawaii. J. Phys. Oceanogr., 42, 1039–1044, doi:10.1175/JPO-D-12-018.1.

    • Search Google Scholar
    • Export Citation

  • Ramp, S. R., Y. J. Yang, D. B. Reeder, and F. L. Bahr, 2012: Observations of a mode-2 nonlinear internal wave on the northern Heng-Chun Ridge south of Taiwan. J. Geophys. Res., 117, C03043, doi:10.1029/2011JC007662.

    • Search Google Scholar
    • Export Citation

  • Scotti, A., R. Beardsley, and B. Butman, 2006: On the interpretation of energy and energy fluxes of nonlinear internal waves: An example from Massachusetts Bay. J. Fluid Mech., 561, 103–112, doi:10.1017/S0022112006000991.

    • Search Google Scholar
    • Export Citation

  • Shen, C. Y., T. E. Evans, R. M. Oba, and S. Finette, 2009: Three-dimensional hindcast simulation of internal soliton propagation in the Asian Seas International Acoustics Experiment area. J. Geophys. Res., 114, C01014, doi:10.1029/2008JC004937.

    • Search Google Scholar
    • Export Citation

  • Shroyer, E. L., J. N. Moum, and J. D. Nash, 2010: Mode 2 waves on the continental shelf: Ephemeral components of the nonlinear internal wavefield. J. Geophys. Res., 115, C07001, doi:10.1029/2009JC005605.

    • Search Google Scholar
    • Export Citation

  • Staquet, C., and J. Sommeria, 2002: Internal gravity waves: From instabilities to turbulence. Annu. Rev. Fluid Dyn., 34, 559–593, doi:10.1146/annurev.fluid.34.090601.130953.

    • Search Google Scholar
    • Export Citation

  • Stastna, M., and W. Peltier, 2005: On the resonant generation of large amplitude internal solitary waves and solitary-like waves. J. Fluid Mech., 543, 267–292, doi:10.1017/S002211200500652X.

    • Search Google Scholar
    • Export Citation

  • Turkington, B., A. Eydeland, and S. Wang, 1991: A computational method for solitary internal waves in a continuously stratified fluid. Stud. Appl. Math., 85, 93–127.

    • Search Google Scholar
    • Export Citation

  • Vazquez, A., N. Stashchuk, V. Vlasenko, M. Bruno, A. Izquierdo, and P. C. Gallacher, 2006: Evidence of multimodal structure of the baroclinic tide in the Strait of Gibraltar. Geophys. Res. Lett., 33, L17605, doi:10.1029/2006GL026806.

    • Search Google Scholar
    • Export Citation

  • Venayagamoorthy, S. K., and O. B. Fringer, 2007: On the formation and propagation of nonlinear internal boluses across a shelf break. J. Fluid Mech., 577, 137–159, doi:10.1017/S0022112007004624.

    • Search Google Scholar
    • Export Citation

  • Vitousek, S., and O. B. Fringer, 2011: Physical vs. numerical dispersion in nonhydrostatic ocean modeling. Ocean Modell., 40, 72–86, doi:10.1016/j.ocemod.2011.07.002.

    • Search Google Scholar
    • Export Citation

  • Vlasenko, V., and W. Alpers, 2005: Generation of secondary internal waves by the interaction of an internal solitary wave with an underwater bank. J. Geophys. Res., 110, C02019, doi:10.1029/2004JC002467.

    • Search Google Scholar
    • Export Citation

  • Vlasenko, V., N. Stashchuk, and K. Hutter, 2005: Baroclinic Tides: Theoretical Modeling and Observational Evidence. Cambridge University Press, 351 pp.

  • Vlasenko, V., N. Stashchuk, C. Guo, and X. Chen, 2010: Multimodal structure of baroclinic tides in the South China Sea. Nonlinear Processes Geophys., 17, 529–543, doi:10.5194/npg-17-529-2010.

    • Search Google Scholar
    • Export Citation

  • Winters, B. K., and L. Armi, 2013: The response of a continuously stratified fluid to an oscillating flow past an obstacle. J. Fluid Mech., 727, 83–118, doi:10.1017/jfm.2013.247.

    • Search Google Scholar
    • Export Citation

  • Xie, J., S. Cai, and Y. He, 2010: A continuously stratified nonlinear model for internal solitary waves in the northern South China Sea. Chin. J. Oceanol. Limnol., 28, 1040–1048, doi:10.1007/s00343-010-9077-3.

    • Search Google Scholar
    • Export Citation

  • Yang, Y. J., Y. C. Feng, M.-H. Chang, S. R. Ramp, C.-C. Kao, and T.-Y. Tang, 2009: Observations of second baroclinic mode internal solitary waves on the continental slope of the northern South China Sea. J. Geophys. Res., 114, C10003, doi:10.1029/2009JC005318.

    • Search Google Scholar
    • Export Citation

  • Zheng, Q., R. D. Susanto, C.-R. Ho, Y. Song, and Q. Xu, 2007: Statistical and dynamical analyses of generation mechanisms of solitary internal waves in the northern South China Sea. J. Geophys. Res., 112, C03021, doi:10.1029/2006JC003551.

    • Search Google Scholar
    • Export Citation
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