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A laboratory wave-making method is developed for the internal solitary wave under the condition of giving its amplitude produced by oppositely and horizontally pushing two vertical plates placed separately in the upper- and lower-layer fluids of a large-scale density stratified tank where based on the Miyata-Choi-Camassa (MCC) theoretical model, the layer-mean velocities of the upper- and lower-layer fluids induced by the internal solitary wave are used as the velocities of the two plates. On this basis, a series of experiments is conducted to explore the applicability conditions for internal solitary wave theories with stationary solutions which are Korteweg-de Vries (KdV), extended KdV (eKdV), MCC and modified KdV (mKdV) models in a two-layer fluid of finite depth respectively. It is shown that for the nonlinear parameter ε and the dispersion parameter μ defined by the total water depth, there exists a critical dispersion parameter μ0, in the case of μ μ0, the KdV model is applicable for ε ≤μ, the eKdV model is applicable for μ ε ≤√μ, as well as the MCC model is applicable for ε > √μ. However, in the case of μ ≥ μ0, the MCC model is still applicable for a wide range of ε. Furthermore, for the case where the ratio of depth between the upper- and lower-layer fluids is not close to its critical value, the mKdV model is mainly applicable for the case where the amplitude of the internal solitary wave is close to its theoretical limiting amplitude, however, the MCC model is also applicable for such a case. The investigation quantitatively characterizes the applicability conditions for four classes of internal solitary wave theories, and provides an important theoretical foundation for what kinds of theories can be chosen to model internal solitary waves in the ocean.
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Keywords:
- two-layer fluid /
- internal solitary wave /
- double-plate wave-making /
- critical dispersion parameter
[1] Wang J, Ma R L, Wang L, Meng J M 2012 Acta Phys. Sin. 61 064701 (in Chinese) [王晶, 马瑞玲, 王龙, 孟俊敏 2012 61 064701]
[2] Fang X H, Du T 2005 Fundamentals of Oceanic Internal Waves and Internal Waves in the China Seas (Qingdao:Ocean University of China Press) p101 (in Chinese) [方欣华, 杜涛 2005 海洋内波基础和中国海内波(青岛:中国海洋大学出版社, 第101页]
[3] Helfrich K R, Melville W K 2006 Ann. Rev. Fluid Mech. 38 395
[4] Shi X G, Fan Z S, Li P L 2009 Period. Ocean Univ. Chin. 39 297 (in Chinese) [石新刚, 范植松, 李培良 2009 中国海洋大学学报 39 297]
[5] Li J, Gu X F, Yu T, Hu X L, Sun Y, Guo D, Xu J P 2011 Trans. Oceanol. Limnol. 1 1 (in Chinese) [李鹃, 顾行发, 余涛, 胡新礼, 孙源, 郭丁, 徐京萍 2011 海洋湖沼通报 1 1]
[6] Chen G Y, Su F C, Wang C M, Liu C T, Tseng R S 2011 J. Oceanogr. 67 689
[7] Koop C G, Butler G 1981 J. Fluid Mech. 112 225
[8] Segur H, Hammack J L 1982 J. Fluid Mech. 118 285
[9] Helfrich K R, Melville W K 1986 J. Fluid Mech. 167 285
[10] Michallet H, Barthelemy E 1998 J. Fluid Mech. 366 159
[11] Grue J, Jensen A, Rusas P O, Seveen J K 1999 J. Fluid Mech. 380 257
[12] Sveen J K, Guo Y, Davies P A, Grue J 2002 J. Fluid Mech. 469 161
[13] Walker S A, Martin A J, EASSON W J, Evans W A B 2003 J. Waterw. Port Coastal Ocean Eng. 5 210
[14] Brandt P, Rubino A, Alpers W, Backhaus J O 1997 J. Phys. Oceanogr. 27 648
[15] Grimshaw R, Slunyaev A, Pelinovsky E 2010 Chaos 20 013102
[16] Du T, Yan X H, Timothy D 2010 Chin. J. Oceanol. Limnol. 28 658
[17] Funakoshi M, Oikawa M 1986 J. Phys. Soc. Jpn. 55 128
[18] Xu Z, Yin B S, Hou Y J 2010 Chin. J. Oceanol. Limnol. 28 1049
[19] Choi W, Camassa R 1999 J. Fluid Mech. 396 1
[20] Miyata M 1985 Mer. Tokyo 23 43
[21] Ruiz Z A, Nachbin A 2008 Commun. Math. Sci. 2 385
[22] Debsarma S, Das K P, Kirby J T 2010 J. Fluid Mech. 654 281
[23] Camassa R, Choi W, Michallet H, Rusas P O, Sveen J K 2006 J. Fluid Mech. 549 1
[24] Wessels F, Hutter K 1996 J. Phys. Oceanogr. 26 5
[25] Maderich V, Talipova T, Grimshaw R, Terletska K, Brovchenko I, Pelinovsky E, Choi B H 2010 Phys. Fluids 22 1
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[1] Wang J, Ma R L, Wang L, Meng J M 2012 Acta Phys. Sin. 61 064701 (in Chinese) [王晶, 马瑞玲, 王龙, 孟俊敏 2012 61 064701]
[2] Fang X H, Du T 2005 Fundamentals of Oceanic Internal Waves and Internal Waves in the China Seas (Qingdao:Ocean University of China Press) p101 (in Chinese) [方欣华, 杜涛 2005 海洋内波基础和中国海内波(青岛:中国海洋大学出版社, 第101页]
[3] Helfrich K R, Melville W K 2006 Ann. Rev. Fluid Mech. 38 395
[4] Shi X G, Fan Z S, Li P L 2009 Period. Ocean Univ. Chin. 39 297 (in Chinese) [石新刚, 范植松, 李培良 2009 中国海洋大学学报 39 297]
[5] Li J, Gu X F, Yu T, Hu X L, Sun Y, Guo D, Xu J P 2011 Trans. Oceanol. Limnol. 1 1 (in Chinese) [李鹃, 顾行发, 余涛, 胡新礼, 孙源, 郭丁, 徐京萍 2011 海洋湖沼通报 1 1]
[6] Chen G Y, Su F C, Wang C M, Liu C T, Tseng R S 2011 J. Oceanogr. 67 689
[7] Koop C G, Butler G 1981 J. Fluid Mech. 112 225
[8] Segur H, Hammack J L 1982 J. Fluid Mech. 118 285
[9] Helfrich K R, Melville W K 1986 J. Fluid Mech. 167 285
[10] Michallet H, Barthelemy E 1998 J. Fluid Mech. 366 159
[11] Grue J, Jensen A, Rusas P O, Seveen J K 1999 J. Fluid Mech. 380 257
[12] Sveen J K, Guo Y, Davies P A, Grue J 2002 J. Fluid Mech. 469 161
[13] Walker S A, Martin A J, EASSON W J, Evans W A B 2003 J. Waterw. Port Coastal Ocean Eng. 5 210
[14] Brandt P, Rubino A, Alpers W, Backhaus J O 1997 J. Phys. Oceanogr. 27 648
[15] Grimshaw R, Slunyaev A, Pelinovsky E 2010 Chaos 20 013102
[16] Du T, Yan X H, Timothy D 2010 Chin. J. Oceanol. Limnol. 28 658
[17] Funakoshi M, Oikawa M 1986 J. Phys. Soc. Jpn. 55 128
[18] Xu Z, Yin B S, Hou Y J 2010 Chin. J. Oceanol. Limnol. 28 1049
[19] Choi W, Camassa R 1999 J. Fluid Mech. 396 1
[20] Miyata M 1985 Mer. Tokyo 23 43
[21] Ruiz Z A, Nachbin A 2008 Commun. Math. Sci. 2 385
[22] Debsarma S, Das K P, Kirby J T 2010 J. Fluid Mech. 654 281
[23] Camassa R, Choi W, Michallet H, Rusas P O, Sveen J K 2006 J. Fluid Mech. 549 1
[24] Wessels F, Hutter K 1996 J. Phys. Oceanogr. 26 5
[25] Maderich V, Talipova T, Grimshaw R, Terletska K, Brovchenko I, Pelinovsky E, Choi B H 2010 Phys. Fluids 22 1
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