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Abstract and Applied Analysis
Volume 2013 (2013), Article ID 108026, 13 pages
Research Article

Nonlinear Hydroelastic Waves beneath a Floating Ice Sheet in a Fluid of Finite Depth

1School of Mathematics and Physics, Qingdao University of Science and Technology, Qingdao 266061, China
2Shanghai Institute of Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, China
3Research Center for Complex Systems and Network Sciences, Department of Mathematics, Southeast University, Nanjing 210096, China

Received 21 May 2013; Revised 29 August 2013; Accepted 29 August 2013

Academic Editor: Rasajit Bera

Copyright © 2013 Ping Wang and Zunshui Cheng. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The nonlinear hydroelastic waves propagating beneath an infinite ice sheet floating on an inviscid fluid of finite depth are investigated analytically. The approximate series solutions for the velocity potential and the wave surface elevation are derived, respectively, by an analytic approximation technique named homotopy analysis method (HAM) and are presented for the second-order components. Also, homotopy squared residual technique is employed to guarantee the convergence of the series solutions. The present formulas, different from the perturbation solutions, are highly accurate and uniformly valid without assuming that these nonlinear partial differential equations (PDEs) have small parameters necessarily. It is noted that the effects of water depth, the ice sheet thickness, and Young’s modulus are analytically expressed in detail. We find that, in different water depths, the hydroelastic waves traveling beneath the thickest ice sheet always contain the largest wave energy. While with an increasing thickness of the sheet, the wave elevation tends to be smoothened at the crest and be sharpened at the trough. The larger Young’s modulus of the sheet also causes analogous effects. The results obtained show that the thickness and Young’s modulus of the floating ice sheet all greatly affect the wave energy and wave profile in different water depths.