Analytical Solutions of Periodic Stationary Internal Waves in Infinitely Deep Water With Exponential Vertical Density Distribution

ZOU Li; ZONG Zhi; WANG Zhen; ZHAO Yong; LIANG Hui

doi:10.3879/j.issn.1000-0887.2015.01.009

Volume 36 Issue 1

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ZOU Li, ZONG Zhi, WANG Zhen, ZHAO Yong, LIANG Hui. Analytical Solutions of Periodic Stationary Internal Waves in Infinitely Deep Water With Exponential Vertical Density Distribution[J]. Applied Mathematics and Mechanics, 2015, 36(1): 99-109. doi: 10.3879/j.issn.1000-0887.2015.01.009

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Analytical Solutions of Periodic Stationary Internal Waves in Infinitely Deep Water With Exponential Vertical Density Distribution

doi: 10.3879/j.issn.1000-0887.2015.01.009

ZOU Li^1,2,
ZONG Zhi^1,2,
WANG Zhen^3,4,
ZHAO Yong⁵,
LIANG Hui^1,2

¹State Key Laboratory of Structural Analysis for Industrial Equipment, Dalian, Liaoning 116024, P.R.China;²School of Naval Architecture, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China;³School of Mathematical Sciences, Dalian University of Technology, Dalian, Liaoning 116024, P.R.China;⁴Department of Mechanical Engineering, University College London, London WC1E 6BT, UK;⁵Transportation Equipment & Ocean Engineering College, Dalian Maritime University, Dalian, Liaoning 116026, P.R.China

Funds: The National Basic Research Program of China (973 Program)（2013CB036101）；The National Natural Science Foundation of China（51109031; 51379033; 51221961; 51309040; 51279030，51239002）

Received Date: 2014-10-14
Rev Recd Date: 2014-12-17
Publish Date: 2015-01-15

Abstract

Abstract

A train of periodic deep water stationary waves with finite amplitudes were investigated analytically with the homotopy analysis method. The vertical distribution of water density was considered as variable in a continuous exponential trend. A new form of partial differential equations were proposed as the auxiliary equations and the new-form solution expressions were obtained in order to match the level boundary condition at the bottom and the hypothetical infinitely rigid condition. The detailed recursive relation of the coefficient in the solution expression was given and the explicit expressions of the permanent stationary periodic internal waves were presented. The convergent series solutions were obtained for the global domain both in vertical and horizontal directions. The relation between the density variable and the internal wave amplitude was revealed.
- internal wave,
- deep water wave,
- nonlinearity,
- exponential density

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References(19)

References

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