Generation of second-mode internal solitary waves during winter in the northern South China Sea

  • Jianjun Liang
  • Xiao-Ming LiEmail author


Field measurements of second-mode internal solitary waves (mode 2 ISWs) during the winter on the upper continental slope of the northern South China Sea were reported in Yang et al. (J Geophys Res 114, 2009), but their generation mechanism remains elusive. We investigated this issue with a multi-modal evolution model and theoretical analysis, which suggest that the observed mode 2 ISWs were generated by a shoaling mode 2 semidiurnal internal tide (IT). The results show that two groups of mode 2 ISWs usually appear within one semidiurnal tidal period, successively riding on expanded and subsequently compressed pycnoclines. The number of wave groups largely depends on the amplitudes of the ITs, and a larger IT produces larger and more mode 2 ISWs. Furthermore, intermodal coupling dominates the evolution of a mode 1 IT, highlighting the importance of considering mode scattering in the propagation of low-mode ITs. Finally, the barotropic body force is calculated, and we deduce that the mode 2 semidiurnal IT originates from the Luzon Strait.


Second-mode internal solitary waves South China Sea 



The WOA13 product, ETOPO1 global relief model, TEOS-10 software, and the OTIS regional tidal solutions for the China Seas were downloaded from the websites at,,, and, respectively. The study was partially supported by grants from the Natural Science Foundation of Hainan Province Project (2016CXTD016), National Natural Science Foundation of China Project (41876201), and the Director Foundation of RADI. Finally, the authors wish to thank the two reviewers for their useful comments and suggestions.


  1. Alford MH et al (2015) The formation and fate of internal waves in the South China Sea. Nature 521:65. CrossRefGoogle Scholar
  2. Bai XL, Liu ZY, Li XF, Hu JY (2014) Generation sites of internal solitary waves in the southern Taiwan Strait revealed by MODIS true-colour image observations. Int J Remote Sens 35:4086–4098. CrossRefGoogle Scholar
  3. Baines PG (1982) On internal tide generation models. Deep Sea Res A 29:307–338. CrossRefGoogle Scholar
  4. Chen ZW, Xie JS, Wang DX, Zhan JM, Xu JX, Cai SQ (2014) Density stratification influences on generation of different modes internal solitary waves. J Geophys Res 119:7029–7046. CrossRefGoogle Scholar
  5. da Silva JCB, New AL, Magalhaes JM (2009) Internal solitary waves in the Mozambique Channel: Observations and interpretation. J Geophys Res 114.
  6. Dong D, Yang XF, Li XF, Li ZW (2016) SAR observation of eddy-Induced mode-2 internal solitary waves in the South China Sea. IEEE T Geosci Remote 54:6674–6686. CrossRefGoogle Scholar
  7. Egbert GD, Erofeeva SY (2002) Efficient inverse modeling of Barotropic Ocean tides. J Atmos Ocean Technol 19:183–204.<0183:eimobo>;2 CrossRefGoogle Scholar
  8. Grimshaw R (2002) Internal solitary waves. In: Grimshaw R (ed) Environmental stratified flows. Kluwer Academic Publishers, New York, Boston, Dordrecht, London, Moscow, pp 1–28Google Scholar
  9. Grimshaw R, Pelinovsky E, Talipova T (2007) Modelling Internal Solitary Waves in the Coastal Ocean. Surv Geophys 28:273–298. CrossRefGoogle Scholar
  10. Grisouard N, Staquet C, Gerkema T (2011) Generation of internal solitary waves in a pycnocline by an internal wave beam: a numerical study. J Fluid Mech 676:491–513. CrossRefGoogle Scholar
  11. Guo CC, Chen XE (2012) Numerical investigation of large amplitude second mode internal solitary waves over a slope-shelf topography. Ocean Model 42:80–91. CrossRefGoogle Scholar
  12. Guo CC, Chen XE (2014) A review of internal solitary wave dynamics in the northern South China Sea. Prog Oceanogr 121:7–23. CrossRefGoogle Scholar
  13. Helfrich KR, Melville WK (1986) On long nonlinear internal waves over slope-shelf topography. J Fluid Mech 167:285–308. CrossRefGoogle Scholar
  14. Holloway PE, Pelinovsky E, Talipova T, Barnes B (1997) A nonlinear model of internal tide transformation on the Australian North West Shelf. J Phys Oceanogr 27:871–896.<0871:anmoit>;2 CrossRefGoogle Scholar
  15. Holloway PE, Pelinovsky E, Talipov T (1999) A generalized Korteweg-de Vries model of internal tide transformation in the coastal zone. J Geophys Res 104:18333–18350. CrossRefGoogle Scholar
  16. Jackson CR, da Silva JCB, Jeans G (2012) The generation of nonlinear internal waves. Oceanography 25:108–123. CrossRefGoogle Scholar
  17. Lamb KG, Warn-Varnas A (2015) Two-dimensional numerical simulations of shoaling internal solitary waves at the ASIAEX site in the South China Sea. Nonlin Processes Geophys 22:289–312. CrossRefGoogle Scholar
  18. Li Q, Farmer DM (2011) The generation and evolution of nonlinear internal waves in the deep basin of the South China Sea. J Phys Oceanogr 41:1345–1363. CrossRefGoogle Scholar
  19. Li XF, Zhao ZX, Pichel WG (2008) Internal solitary waves in the northwestern South China Sea inferred from satellite images. Geo Res Lett 35.
  20. Liu AK, Chang YS, Hsu M-K, Liang NK (1998) Evolution of nonlinear internal waves in the East and South China Seas. J Geophys Res 103:7995–8008. CrossRefGoogle Scholar
  21. Liu AK, Su F-C, Hsu M-K, Kuo N-J, Ho C-R (2013) Generation and evolution of mode-two internal waves in the South China Sea. Cont Shelf Res 59:18–27. CrossRefGoogle Scholar
  22. Locarnini RA, Mishonov AV, Antonov JI, Boyer TP, Garcia HE, Barnova OK (2013) World Ocean Atlas 2013, Volume 1: Temperature. S. Levitus, Ed.; A. Mishonov, Technical Ed.; NOAA Atlas NESDIS 73, 40 pp.
  23. Lozovatsky I, Liu ZY, Fernando H, Armengol J, Roget E (2012) Shallow water tidal currents in close proximity to the seafloor and boundary-induced turbulence. Ocean Dyn 62:177–191. CrossRefGoogle Scholar
  24. Mehta AP, Sutherland BR, Kyba PJ (2002) Interfacial gravity currents. II. Wave excitation. Phys Fluids 14:3558–3569. CrossRefGoogle Scholar
  25. Ramp SR, Yang YJ, Bahr FL (2010) Characterizing the nonlinear internal wave climate in the northeastern South China Sea. Nonlin Processes Geophys 17:481–498. CrossRefGoogle Scholar
  26. Ramp SR, Yang YJ, Reeder DB, Bahr FL (2012) Observations of a mode-2 nonlinear internal wave on the northern Heng-Chun Ridge south of Taiwan. J Geophys Res 117:C03043. CrossRefGoogle Scholar
  27. Sakai T, Redekopp LG (2009) A weakly nonlinear model for multi-modal evolution of wind-generated long internal waves in a closed basin. Nonlin Processes Geophys 16:487–502. CrossRefGoogle Scholar
  28. Shroyer EL, Moum JN, Nash JD (2010) Mode 2 waves on the continental shelf: Ephemeral components of the nonlinear internal wavefield. J Geophys Res 115.
  29. Stastna M, Peltier WR (2005) On the resonant generation of large-amplitude internal solitary and solitary-like waves. J Fluid Mech 543:267–292. CrossRefGoogle Scholar
  30. Vlasenko VI, Hutter K (2001) Generation of second mode solitary waves by the interaction of a first mode soliton with a sill. Nonlin Processes Geophys 8:223–239. CrossRefGoogle Scholar
  31. Wu LD, Miao CB, Zhao W (2013) Patterns of K1 and M2 internal tides and their seasonal variations in the northern South China Sea. J Oceanogr 69:481–494. CrossRefGoogle Scholar
  32. Yang YJ, Tang TY, Chang MH, Liu AK, Hsu M-K, Ramp SR (2004) Solitons northeast of Tung-Sha Island during the ASIAEX pilot studies IEEE J Oceanic Eng 29:1182–1199.
  33. Yang YJ, Fang YC, Chang M-H, Ramp SR, Kao C-C, Tang TY (2009) Observations of second baroclinic mode internal solitary waves on the continental slope of the northern South China Sea. J Geophys Res 114.
  34. Yang YJ, Fang YC, Tang TY, Ramp SR (2010) Convex and concave types of second baroclinic mode internal solitary waves. Nonlin Processes Geophys 17:605–614. CrossRefGoogle Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Key Laboratory of Digital Earth Science, Institute of Remote Sensing and Digital EarthChinese Academy of SciencesBeijingChina
  2. 2.Laboratory for Regional Oceanography and Numerical ModelingQingdao National Laboratory for Marine Science and TechnologyQingdaoChina
  3. 3.Hainan Key Laboratory of Earth ObservationSanyaChina

Personalised recommendations