Cite this paper:
MA Qian, YUAN Chunxin, LIN Xiaopei, CHEN Xue'en. The investigation of internal solitary waves over a continental shelf-slope[J]. Journal of Oceanology and Limnology, 2020, 38(3): 695-706

The investigation of internal solitary waves over a continental shelf-slope

MA Qian1, YUAN Chunxin2, LIN Xiaopei1, CHEN Xue'en1
1 Physical Oceanography Laboratory/Institute for Advanced Ocean Study, Ocean University of China and Qingdao National Laboratory for Marine Science and Technology, Qingdao 266100, China;
2 School of Mathematical Sciences, Ocean University of China, Qingdao 266100, China
Abstract:
Internal solitary waves (ISWs) always happen in marginal seas, where stable stratification exists. ISWs may carry large energy when they propagate and affect marine engineering constructions such as marine drilling platforms. Previous studies, including a large number of mooring observations and laboratory experiments, show the speed of ISWs will change when they pass by shelf slopes. Korteweg-de Vries (KdV) theory explain this phenomenon. In the paper, we use a laboratory experiment and a numerical model experiment to verify this theory. In the laboratory experiment, we injected two layers of water of different densities in a tank to simulate marine stratification and make ISWs. We use a CCD camera to record the whole process. The camera can take 16 photos per second. In the numerical experiment, we input the same original conditions as the laboratory one. The results of 18 different original conditions show the dimensionless factor δ plays a key role in deciding the amplitudes and shapes of ISWs. The main conclusion also contains that small-amplitude waves match well with KdV theory while mKdV is better for largeamplitude waves. Whether the laboratory experiment or numerical experiment shows results with a high agreement. In future studies, we may use a numerical model with higher resolution to get analysis about phase speed and energy of ISWs.
Key words:    internal solitary waves|shelf-slope|laboratory experiment|numerical modeling   
Received: 2019-05-18   Revised: 2019-07-19
Tools
PDF (1886 KB) Free
Print this page
Add to favorites
Email this article to others
Authors
Articles by MA Qian
Articles by YUAN Chunxin
Articles by LIN Xiaopei
Articles by CHEN Xue'en
References:
Apel J R, Holbrook J R, Liu A K, Tsai J J. 1985. The sulu sea internal soliton experiment. Journal of Physical Oceanography, 15(12):1 625-1 651.
Ariyaratnam J. 1998. Investigation of Slope Stability Under Internal Wave Action. University of Western Australia, Australia.Benjamin T B. 1966. Internal waves of finite amplitude and permanent form. Journal of Fluid Mechanics, 25(2):241-270.
Chen C C. 2004. Experimental Study on the Propagation and Reflection of Internal Solitary Wave from a Uniform Slop.National Sun Yat-Sen University, Taiwan, China.
Gerkema T, Zimmerman J T F. 2008. An introduction to internal waves. Texel:NIOZ, 207.
Grimshaw R, Pelinovsky E, Talipova T G. 1999. Solitary wave transformation in a medium with sign-variable quadratic nonlinearity and cubic nonlinearity. Physica D:Nonlinear Phenomena, 132(1-2):40-62.
Grue J, Jensen A, Rusås P O, Sveen J K. 1999. Properties of large-amplitude internal waves. Journal of Fluid Mechanics, 380:257-278.
Grue J, Jensen A, Rusås P O, Sveen J K. 2000. Breaking and broadening of internal solitary waves. Journal of Fluid Mechanics, 413(1):181-217.
Helfrich K R. 1992. Internal solitary wave breaking and run-up on a uniform slope. Journal of Fluid Mechanics, 243(1):133-154.
Holloway P E, Pelinovsky E, Talipova T, Barnes B. 1997. A nonlinear model of internal tide transformation on the australian north west shelf. Journal of Physical Oceanography, 27(6):871-896.
Hsu J R C, Ariyaratnam J. 2000. Pressure fluctuations and a mechanism of sediment suspension in swash zone. In:Proceedings of the 27th International Conference on Coastal Engineering. ASCE, Sydney. p.610-623.
Hüttemann H, Hutter K. 2001. Baroclinic solitary water waves in a two-layer fluid system with diffusive interface.Experiments in Fluids, 30(3):317-326.
Klymak J M, Pinkel R, Liu C T, Liu A K, David L. 2006.Prototypical solitons in the South China Sea. Geophysical Research Letters, 33(11):L11607.
Marshall J, Adcroft A, Hill C, Perelman L, Heisey C. 1997. A finite-volume, incompressible Navier Stokes model for studies of the ocean on parallel computers. Journal of Geophysical Research:Oceans, 102(C3):5 753-5 766.
Michallet H, Barthélemy E. 1998. Experimental study of interfacial solitary waves. Journal of Fluid Mechanics, 366(1-2):159-177.
Michallet H, Ivey G N. 1999. Experiments on mixing due to internal solitary waves breaking on uniform slopes.Journal of Geophysical Research:Oceans, 104(C6):13 467-13 477.
Moum J N, Klymak J M, Nash J D, Perlin A, Smyth W D. 2007. Energy transport by nonlinear internal waves.Journal of Physical Oceanography, 37(7):1 968-1 988.
Nakayama K, Imberger J. 2010. Residual circulation due to internal waves shoaling on a slope. Limnology and Oceanography, 55(3):1 009-1 023.
Nakayama K, Kakinuma T, Tsuji H. 2019. Oblique reflection of large internal solitary waves in a two-layer fluid.European Journal of Mechanics-B/Fluids, 74:81-91.
Nakayama K, Shintani T, Kokubo K, Kakinuma T, Maruya Y, Komai K, Okada T. 2012. Residual currents over a uniform slope due to breaking of internal waves in a two-layer system. Journal of Geophysical Research:Oceans, 117(C10):C10002.
Nakayama K. 2006. Comparisons of CIP, compact and CIP-CSL2 schemes for reproducing internal solitary waves.International Journal for Numerical Methods in Fluids, 51(2):197-219.
Ono H. 1975. Algebraic solitary waves in stratified fluids.Journal of the Physical Society of Japan, 39(4):1 082-1 091.
Osborne A R, Burch T L. 1980. Internal solitons in the Andaman Sea. Science, 208(4443):451-460.
Rockliff N. 1984. Long nonlinear waves in stratified shear flows. Geophysical & Astrophysical Fluid Dynamics, 28(1):55-75.
Tsuji H, Oikawa M. 2007. Oblique interaction of solitons in an extended Kadomtsev-Petviashvili equation. Journal of the Physical Society of Japan, 76(8):084401.
Vallis G K. 2006. Atmospheric and Oceanic Fluid Dynamics.Cambridge University Press, Cambridge. 745p.
Vlasenko V, Hutter K. 2002. Numerical experiments on the breaking of solitary internal wavesover a slope-shelf topography. Journal of Physical Oceanography, 32(6):1 779-1 793.
Vlasenko V, Stashchuk N, Guo C, Chen X. 2010. Multimodal structure of baroclinic tides in the South China Sea.Nonlinear Processes in Geophysics, 17(5):529-543.
Vlasenko V, Stashchuk N, Hutter K. 2005. Baroclinic Tides:Theoretical Modeling and Observational Evidence, Cambridge University Press, Cambridge.
Walker S A, Martin J A, Easson W J. 1998. An experimental investigation of solitary internal waves. In:Proceedings of the 17th International Conference on Offshore Mechanics and Arctic Engineering. ASME, Lisbon.
Wallace B C, Wilkinson D L. 1988. Run-up of internal waves on a gentle slope in a two-layered system. Journal of Fluid Mechanics, 191:419-442.
Wessels F, Hutter K. 1996. Interaction of internal waves with a topographic sill in a two-layered fluid. Journal of Physical Oceanography, 26(1):5-20.
Xu Z, Yin B. 2012. Variability of internal solitary waves in the Northwest South China Sea. In:Marcelli M ed.Oceanography. InTech, Rijeka, Croatia. p.31-146.
Yuan C, Grimshaw R, Johnson E, Chen X E. 2018b. The propagation of internal solitary waves over variable topography in a horizontally two-dimensional framework.Journal of Physical Oceanography, 48(2):283-300.
Yuan C, Grimshaw R, Johnson E. 2018a. The evolution of second mode internal solitary waves over variable topography. Journal of Fluid Mechanics, 836:238-259.
Zhu H, Lin C, Wang L, Kao M, Tang H W, Williams J J R. 2018. Numerical investigation of internal solitary waves of elevation type propagating on a uniform slope. Physics of Fluids, 30(11):116602.
Zhu H, Wang L L, Avital E J, Tang H W, Williams J J R. 2017.Numerical simulation of shoaling broad-crested internal solitary waves. Journal of Hydraulic Engineering, 143(6):04017006.
Zhu H, Wang L, Avital E J, Tang H W, Williams J J R. 2016.Numerical simulation of interaction between internal solitary waves and submerged ridges. Applied Ocean Research, 58:118-134.
Copyright © Haiyang Xuebao