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

Ping Wang,Zunshui Cheng

doi:10.1155/2013/108026

Ping Wang, Zunshui Cheng

Open Access

https://doi.org/10.1155/2013/108026

Copy DOI

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.

Highlights

In recent decades, the ice cover in the polar region has attracted more and more attention in the field of ocean engineering and polar engineering in view of their practical importance and theoretical investigations
It should be mentioned that we study the effects of the water depth and two important physical parameters including Young’s modulus and the thickness of the ice sheet on the wave energy and its elevation in detail
In order to show the convergence of the analytical series solution to our problems by means of the homotopy analysis method (HAM), we consider the cases of k = π/5 m−1, d = 0.01 m, ρe = 900 kgm−3, ] = 0.33, E = 1010 Nm−2, h = 5 m, H = 0.1 m, and ω/ω0 = 1.01 and take these data hereinafter for computation unless otherwise stated

Summary

Introduction

The ice cover in the polar region has attracted more and more attention in the field of ocean engineering and polar engineering in view of their practical importance and theoretical investigations. One of the important problems in this field would appear to be the accurate measurement of the characteristics of waves traveling beneath a floating ice sheet. Such wave may have been generated in the ice cover itself by the wind, or it may have originated by a moving load on the ice sheets. Considerable work has been done since the first theoretical model of wave propagation in sea ice was proposed by Greenhill [1] in 1887. In addition to ice sheets, this work can apply to very large floating structures (VLFSs) such as floating airports, mobile offshore bases, offshore port facilities, offshore storage and waste disposal provisions, energy islands including some wave power configurations, and ultralarge ships, where there is an extensive complementary literature [4,5,6]

Objectives

Results

Conclusion