Abstract and Applied Analysis

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

Ping Wang and Zunshui Cheng

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Abstract

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.

Article information

Source
Abstr. Appl. Anal., Volume 2013, Special Issue (2013), Article ID 108026, 13 pages.

Dates
First available in Project Euclid: 26 February 2014

Permanent link to this document
https://projecteuclid.org/euclid.aaa/1393450001

Digital Object Identifier
doi:10.1155/2013/108026

Mathematical Reviews number (MathSciNet)
MR3121503

Zentralblatt MATH identifier
06306027

Citation

Wang, Ping; Cheng, Zunshui. Nonlinear Hydroelastic Waves beneath a Floating Ice Sheet in a Fluid of Finite Depth. Abstr. Appl. Anal. 2013, Special Issue (2013), Article ID 108026, 13 pages. doi:10.1155/2013/108026. https://projecteuclid.org/euclid.aaa/1393450001


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