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In a stratified fluid tank, experiments on the propagating, shoaling and breaking of the internal solitary waves over a gentle slope similar to the topography in the northeast of the South China Sea are conducted. The qualitative analysis on the evolving characteristics of the internal solitary waves is accomplished by use of the dye-tracing technique, and their quantitative measurement is carried out by using the multi-channel conductivity-probe arrays. It is shown that due to the shoaling effect the internal solitary waves with large amplitude are restrained, but the waves with small amplitude are magnified. The shoaling effect will also lead to the decrease of the propagation velocity of the internal solitary waves. Further, the shoaling effect will bring about strong shear flow instability, and then makes the internal solitary wave broken. The breaking wave will result in the fission from one large amplitude wave into several small amplitude waves with the same polarity. By means of the Mile's stability theory, the instable happening-location of the internal solitary wave over the gentle slope can be described through the Richardson number. The experimental results accord well with the theoretical analyses.
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Keywords:
- stratified fluid /
- gentle slope /
- internal solitary wave /
- instability
[1] Cai S Q, Xie J S, He J L 2012 Surv. Geophys. 33 927
[2] Liu A K 1988 J. Geophys. Res. 93 12317
[3] Holloway P E, Pelinovasky E, Talipova T 1999 J. Geophys. Res. 104 18333
[4] Djordjevic Y D, L G Redekopp 1978 J. Phys. Oceanogr. 6 1016
[5] Cai S Q, Xie J S 2010 J. Geophys. Res. 115 1
[6] Meng J M, Zhang Z L 2001 J. Hydrodyn. 3 88
[7] Su X B, Wei G, Dai S Q 2005 Appl. Math. Mech. 26 1143
[8] Lombard P N, J J Riley 1996 Dyn. Atmos. Oceans 24 345
[9] Garrett C 2001 J. Phys. Oceanogr. 31 962
[10] Legg S, Aderoft A 2003 J. Phys. Oceanogr. 33 2224
[11] Shrira V I, Voronov V V, Sazonov I A 2000 J. Fluid Mech. 425 187
[12] Kao T W, Pan P S, Renouard D 1985 J. Fluid Mech. 195 19
[13] Helfrich K R, Melvilie W K 1984 J. Fluid Mech. 149 305
[14] Wallace B C, Wilkinson D L 1988 J. Fluid Mech. 191 419
[15] Helfrich K R 1992 J. Fluid Mech. 243 133
[16] Chen C Y, Hsu J R C, Chen H H, Kuo C F, Cheng M H 2007 Ocean Eng. 34 157
[17] Fructus D, Carr M, Grue J, Jensen A, Davies P A 2009 J. Fluid Mech. 620 1
[18] Wei G, Wu N, Xu X H, Su X B, You Y X 2011 Acta Phys. Sin 60 044704 (in Chinese) [魏岗, 吴宁, 徐小辉, 苏晓冰, 尤云祥 2011 物理学报 60 044704]
[19] Wei G, Su X B, Yang J G, Wang Q H Chinese Patent 201010103635.6 [2012-02-01]
[20] Whitham G B 1974 Linear and Nonlinear Waves (New York: John Wiely and Sons, Inc)
[21] Fang X H, Du T 2004 Fundamental of Oceanic Internal Waves and Internal Waves in the China Seas (Qingdao: China Ocean University Press) p300 (in Chinese) [方欣华, 杜涛 2004 海洋内波基础和中国海内波(青岛: 中国海洋大学出版社)第300页]
[22] Cai S Q, Gan Z J 1995 Tropic Oceanology 14 2229 (in Chinese) [蔡树群, 甘子钧 1995 热带海洋 14 2229]
[23] Miles J W 1961 J. Fluid Mech. 10 496
[24] Li Q 2008 Ph. D. Dissertation (Qingdao: China Ocean University) (in Chinese) [李群 2008 博士学位论文(青岛: 中国海洋大学)]
[25] Miles J W 1963 J. Fluid Mech. 16 209
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[1] Cai S Q, Xie J S, He J L 2012 Surv. Geophys. 33 927
[2] Liu A K 1988 J. Geophys. Res. 93 12317
[3] Holloway P E, Pelinovasky E, Talipova T 1999 J. Geophys. Res. 104 18333
[4] Djordjevic Y D, L G Redekopp 1978 J. Phys. Oceanogr. 6 1016
[5] Cai S Q, Xie J S 2010 J. Geophys. Res. 115 1
[6] Meng J M, Zhang Z L 2001 J. Hydrodyn. 3 88
[7] Su X B, Wei G, Dai S Q 2005 Appl. Math. Mech. 26 1143
[8] Lombard P N, J J Riley 1996 Dyn. Atmos. Oceans 24 345
[9] Garrett C 2001 J. Phys. Oceanogr. 31 962
[10] Legg S, Aderoft A 2003 J. Phys. Oceanogr. 33 2224
[11] Shrira V I, Voronov V V, Sazonov I A 2000 J. Fluid Mech. 425 187
[12] Kao T W, Pan P S, Renouard D 1985 J. Fluid Mech. 195 19
[13] Helfrich K R, Melvilie W K 1984 J. Fluid Mech. 149 305
[14] Wallace B C, Wilkinson D L 1988 J. Fluid Mech. 191 419
[15] Helfrich K R 1992 J. Fluid Mech. 243 133
[16] Chen C Y, Hsu J R C, Chen H H, Kuo C F, Cheng M H 2007 Ocean Eng. 34 157
[17] Fructus D, Carr M, Grue J, Jensen A, Davies P A 2009 J. Fluid Mech. 620 1
[18] Wei G, Wu N, Xu X H, Su X B, You Y X 2011 Acta Phys. Sin 60 044704 (in Chinese) [魏岗, 吴宁, 徐小辉, 苏晓冰, 尤云祥 2011 物理学报 60 044704]
[19] Wei G, Su X B, Yang J G, Wang Q H Chinese Patent 201010103635.6 [2012-02-01]
[20] Whitham G B 1974 Linear and Nonlinear Waves (New York: John Wiely and Sons, Inc)
[21] Fang X H, Du T 2004 Fundamental of Oceanic Internal Waves and Internal Waves in the China Seas (Qingdao: China Ocean University Press) p300 (in Chinese) [方欣华, 杜涛 2004 海洋内波基础和中国海内波(青岛: 中国海洋大学出版社)第300页]
[22] Cai S Q, Gan Z J 1995 Tropic Oceanology 14 2229 (in Chinese) [蔡树群, 甘子钧 1995 热带海洋 14 2229]
[23] Miles J W 1961 J. Fluid Mech. 10 496
[24] Li Q 2008 Ph. D. Dissertation (Qingdao: China Ocean University) (in Chinese) [李群 2008 博士学位论文(青岛: 中国海洋大学)]
[25] Miles J W 1963 J. Fluid Mech. 16 209
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