Skip to main content
SpringerLink
Log in

Modelling the propagation of an internal solitary wave across double ridges and a shelf-slope

  • Original Article
  • Published:
Environmental Fluid Mechanics Aims and scope Submit manuscript

Abstract

Evolution of the internal solitary waves (ISWs) in the northern South China Sea (SCS) has recently attracted the attention of many oceanographers in Taiwan and the United States. These ISWs are believed to have been induced by a branch of the Kuroshio current over Luzon Strait, which propagates westward over two ridges in the Luzon Strait between Taiwan and the Philippines, and further onto the continental margin with a shelf-slope in the SCS. This paper presents some preliminary results for the evolution of a depression ISW across two triangular obstacles using numerical modelling and laboratory experiments. The experimental results confirm that the intervals and relative height between the two obstacles are important factors in the interaction of an ISW with the obstacles. However, in the case of the movement of an ISW of depression-type across the Luzon Strait, the effect of the two ridges on the characteristics of the ISW might be less significant than that from the shelf-slope, due to the variations in relative water depth. Results from numerical experiments also show that the amplitude of an ISW can be augmented once the wave commences its contact with a shelf-slope, where an internal hydraulic jump and wave breaking with vortex motion are evident in the laboratory experiments. Eventually, an ISW of depression-type could become an elevation-type at the edge of the continental shelf landwards beyond the turning point, where the upper layer is larger than the bottom layer in a stratified water column.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Apel JR, Badiey M, Chiu CS, Finette S, Headrick R, Kemp J, Lynch JF, Newhall A, Orr MH, Pasewark BH, Tielbuerger D, Turgut A, Heydt K, Wolf S (1997) An overview of the 1995 SWARM shallow-water internal wave acoustic scattering experiment. IEEE J Ocean Eng 22: 465–500

    Article  Google Scholar 

  2. Baines PG (1983) Tidal motion in submarine canyons—a laboratory experiment. J Phys Oceanogr 13: 310–328

    Article  Google Scholar 

  3. Bole JB, Ebbesmeyer JJ, Romea RD (1994) Soliton currents in South China Sea: measurements and theoretical modelling. In: Proceedings of 26th Annual Offshore Technical Conference, Houston, Texas, pp 367–375

  4. Chen CY (2007) An experimental study of stratified mixing caused by internal solitary waves in a two-layered fluid system over variable seabed topography. Ocean Eng 34(14–15): 1995–2008

    Article  Google Scholar 

  5. Chen CY, Hsu JRC, Chen CW, Cheng MH (2006a) Numerical model of an internal solitary wave evolution on impermeable variable seabed in a stratified two-layer fluid system. China Ocean Eng 20(2): 303–313

    Google Scholar 

  6. Chen CY, Hsu JRC, Kuo CF, Chen HH, Cheng MH (2006b) Laboratory observations on internal solitary wave evolution over a submarine ridge. China Ocean Eng 20(1): 61–72

    CAS  Google Scholar 

  7. Chen CY, Hsu JRC, Chen HH, Kuo CF, Cheng MH (2007a) Laboratory observations of internal solitary wave evolution on steep and inverse uniform slopes. Ocean Eng 34(1): 157–170

    Article  Google Scholar 

  8. Chen CY, Hsu JRC, Cheng MH, Chen HH, Kuo CF (2007b) An investigation on internal solitary waves in a two-layer fluid: propagation and reflection from steep slopes. Ocean Eng 34(1): 171–184

    Article  CAS  Google Scholar 

  9. Chen CY, Hsu JRC, Chen CW, Kuo CF, Chen HH, Cheng MH (2007c) Wave propagation at the interface of a two-layer system in the laboratory. J Mar Sci Technol 15(1): 8–16

    Google Scholar 

  10. Chen CY, Hsu JRC, Cheng MH, Chen CW (2008) Experiments on mixing and dissipation in internal solitary waves over variable ridges. Environ Fluid Mech 8(3): 199–215

    Article  Google Scholar 

  11. Helfrich KR (1992) Internal solitary wave breaking and run-up on a uniform slope. J Fluid Mech 243: 133–154

    Article  Google Scholar 

  12. Helfrich KR, Melville WK (1986) On long nonlinear internal waves over slope-shelf topography. J Fluid Mech 167: 285–308

    Article  Google Scholar 

  13. Honji H, Matsunaga N, Sugihara Y, Sakai K (1995) Experimental observation of internal symmetric solitary waves in a two-layer fluid. Fluid Dyn Res 15(2): 89–102

    Article  Google Scholar 

  14. Hsu MK, Liu AK (2000) Nonlinear internal waves in the South China Sea. Can J Remote Sens 26: 72–81

    Google Scholar 

  15. Huttemann H, Hutter K (2001) Baroclinic solitary water waves in a two-layer fluid system with diffusive interface. Exp Fluids 30(3): 317–326

    Article  CAS  Google Scholar 

  16. Kao TW, Pan FS, Renouard D (1985) Internal solitions on the pycnocline: generation, propagation, shoaling and breaking over a slope. J Fluid Mech 159: 19–53

    Article  Google Scholar 

  17. Katz EJ (1967) Effect of the propagation of internal waves in underwater sound transmission. J Acoust Soc Am 42(1): 83–87

    Article  Google Scholar 

  18. Koop CG, Butler G (1981) An investigation of internal solitary waves in a two-fluid system. J Fluid Mech 112: 225–251

    Article  Google Scholar 

  19. Liu AK, Hsu MK (2004) Internal wave study in the South China Sea using Synthetic Aperture Radar. Int J Remote Sens 25: 1261–1264

    Article  Google Scholar 

  20. Lynett PJ, Liu PLF (2002) A two-dimensional depth-integrated model for internal wave propagation over variable bathymetry. Wave Motion 36: 221–240

    Article  Google Scholar 

  21. Michallet H, Barthelemy E (1998) Experimental study of interfacial solitary waves. J Fluid Mech 366: 159–177

    Article  Google Scholar 

  22. Nagashima H (1971) Reflection and breaking of internal waves on a sloping beach. J Oceanogr Soc Jpn 27(1): 1–6

    Article  Google Scholar 

  23. Orr M, Mignerey P (2004) Internal tide and nonlinear wave behavior at the continental slope in the northern South China Sea. IEEE J Ocean Eng 29(4): 1145–1130

    Article  Google Scholar 

  24. Osborne AR, Burch TL, Scarlet TI (1978) The influence of internal waves on deepwater drilling. J Petroleum Technol 30: 1497–1504

    Google Scholar 

  25. Ramp SR, Tang TY, Duda TF, Lynch JF, Liu AK, Chiu CS, Bahr FL, Kim HR, Yang YJ (2004) Internal solitons in the northeastern South China Sea. Part 1: sources and deep water propagation. IEEE J Ocean Eng 29(4): 1157–1181

    Article  Google Scholar 

  26. Sandstrom H, Elliott JA (1984) Internal tide and solitons on the Scotian shelf: a nutrient pump at work. J Geophys Res 89(4): 6415–6426

    Article  Google Scholar 

  27. Sveen JK, Guo Y, Davies PA, Grue J (2002) On the breaking of internal solitary waves at a ridge. J Fluid Mech 469(25): 161–188

    Google Scholar 

  28. Vlasenko V, Hutter K (2002) Numerical experiments on the breaking of solitary internal waves over a slope-shelf topography. J Phys Oceanogr 32(6): 1779–1793

    Article  Google Scholar 

  29. Wessels F, Hutter K (1996) Interaction of internal waves with a topographic sill in a two-layered fluid. J Phys Oceanogr 26(1): 5–20

    Article  Google Scholar 

  30. Yang YJ, Tang TY, Chang MH, Liu AK, Hsu MK, Ramp SR (2004) Solitons northeast of Tung-Sha Island during the ASIAEX pilot studies. IEEE J Ocean Eng 29(4): 1182–1199

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Marine Environment and Engineering (and APORC), National Sun Yat-sen University, Kaohsiung, 80424, Taiwan, ROC

    Ming-Hung Cheng & John R.-C. Hsu

  2. Department of Management Information System, Yung-Ta Institute of Technology and Commerce, Lin-Luoh, PingTung County, 90941, Taiwan, ROC

    Chen-Yuan Chen

  3. Department of Logistics Management, Shu-Te University, Kaohsiung, 82445, Taiwan, ROC

    Cheng-Wu Chen

  4. School of Civil and Resource Engineering, The University of Western Australia, Perth, WA, 6009, Australia

    John R.-C. Hsu

Authors
  1. Ming-Hung Cheng
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. John R.-C. Hsu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Chen-Yuan Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Cheng-Wu Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to John R.-C. Hsu.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Cheng, MH., Hsu, J.RC., Chen, CY. et al. Modelling the propagation of an internal solitary wave across double ridges and a shelf-slope. Environ Fluid Mech 9, 321–340 (2009). https://doi.org/10.1007/s10652-008-9104-5

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10652-008-9104-5

Keywords

Search

Navigation