有限深两层流体中内孤立波造波实验及其理论模型

黄文昊; 尤云祥; 王旭; 胡天群

doi:10.7498/aps.62.084705

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摘要

将置于大尺度密度分层水槽上下层流体中的两块垂直板反方向平推, 以基于 Miyata-Choi-Camassa (MCC)理论解的内孤立波诱导上下层流体中的层平均水平速度作为其运动速度, 发展了一种振幅可控的双推板内孤立波实验室造波方法. 在此基础上, 针对有限深两层流体中定态内孤立波 Korteweg-de Vries (KdV), 扩展KdV (eKdV), MCC和修改的Kdv (mKdV)理论的适用性条件等问题, 开展了系列实验研究.结果表明, 对以水深为基准定义的非线性参数ε 和色散参数μ, 存在一个临界色散参数μ0, 当μ μ0 时, KdV理论适用于ε ≤μ 的情况, eKdV理论适用于μ ε ≤√μ 的情况, 而MCC理论适用于ε > √μ 的情况, 而且当μ ≥μ0 时MCC理论也是适用的.结果进一步表明, 当上下层流体深度比并不接近其临界值时, mKdV理论主要适用于内孤立波振幅接近其理论极限振幅的情况, 但这时MCC理论同样适用.本项研究定量地表征了四类内孤立波理论的适用性条件, 为采用何种理论来表征实际海洋中的内孤立波特征提供了理论依据.

关键词:

作者及机构信息

1.
上海交通大学,海洋工程国家重点实验室, 上海 200240

基金项目: 国家高技术研究发展计划(批准号:2010AA09z305) 和高等学校博士学科点专项科研基金(批准号:20110073130003) 资助的课题.

参考文献

[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 物理学报 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

施引文献

[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 物理学报 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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有限深两层流体中内孤立波造波实验及其理论模型

1. 上海交通大学,海洋工程国家重点实验室, 上海 200240

基金项目:

国家高技术研究发展计划(批准号:2010AA09z305) 和高等学校博士学科点专项科研基金(批准号:20110073130003) 资助的课题.

收稿日期: 2012-08-11

修回日期: 2012-11-05

刊出日期: 2013-04-05

摘要: 将置于大尺度密度分层水槽上下层流体中的两块垂直板反方向平推, 以基于 Miyata-Choi-Camassa (MCC)理论解的内孤立波诱导上下层流体中的层平均水平速度作为其运动速度, 发展了一种振幅可控的双推板内孤立波实验室造波方法. 在此基础上, 针对有限深两层流体中定态内孤立波 Korteweg-de Vries (KdV), 扩展KdV (eKdV), MCC和修改的Kdv (mKdV)理论的适用性条件等问题, 开展了系列实验研究.结果表明, 对以水深为基准定义的非线性参数ε 和色散参数μ, 存在一个临界色散参数μ0, 当μ μ0 时, KdV理论适用于ε ≤μ 的情况, eKdV理论适用于μ ε ≤√μ 的情况, 而MCC理论适用于ε > √μ 的情况, 而且当μ ≥μ0 时MCC理论也是适用的.结果进一步表明, 当上下层流体深度比并不接近其临界值时, mKdV理论主要适用于内孤立波振幅接近其理论极限振幅的情况, 但这时MCC理论同样适用.本项研究定量地表征了四类内孤立波理论的适用性条件, 为采用何种理论来表征实际海洋中的内孤立波特征提供了理论依据.

关键词:

Wave-making experiments and theoretical models for internal solitary waves in a two-layer fluid of finite depth

1.
State Key Laboratory of Ocean Engineering, Shanghai Jiaotong University, Shanghai 200240, China

Fund Project:

Project supported by the National High Technology Research and Development Program of China (Grant No. 2010AA09z305) and the Specialized Research Fund for the Doctoral Program of Higher Education of China (Grant No. 20110073130003).

Received Date: 11 August 2012

Accepted Date: 05 November 2012

Published Online: 05 April 2013

Abstract: 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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