Proceedings of the Thirty-second (2022) International Ocean and Polar Engineering Conference
Shanghai, China, June 5–10, 2022
Copyright © 2022 by the International Society of Offshore and Polar Engineers (ISOPE)
ISBN 978-1-880653-81-4; ISSN 1098-6189

www.isope.org

Wave Motion in A Frozen Harbour Based on the Domain
Decomposition Method
Yuyun Shi, Fengzhen Wang, Zhifu Li *School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology.
Zhenjiang, Jiangsu, China

ABSTRACT

shall be considered simultaneously. Therefore, such as Hwang andTuck (1970) used the boundary integral equation both over the harbour
and coastal walls. Lee (1971) constructed a domain decomposition
method to remove the integral equation on coastal wall. Extensive work
focused on harbour boundaries were constructed (Hamanaka, 1997;
Isaacson & Qu, 1990). Kumar, Zhang, Kim, Shi, and Yuen (2015)
introduced a Chebyshev point discretization into the wave scattering ina real harbour. Shi, Li, and Wu (2018) considered a problem of anarbitrary floating body floating in harbour on three-dimensional sense,
in which highly oscillatory resonance of ship motion were discussed.

In this paper, a domain decomposition method is developed to solve theproblem of wave interaction with a frozen harbour. The linearized
velocity potential theory is adopted for fluid flow and the ice sheet ismodelized as a thin elastic plate. The domain is divided into twosubdomains. In interior harbour, the velocity potential is expanded into
series of eigenfunctions, while in exterior harbour with a free surface,
the velocity potential is solved by boundary element method through amodified Green function. An inner product is introduced to impose theimpermeable condition on the harbour wall, together with the edge
conditions on the ice sheet. Computations are carried out for arectangular harbour for validation and discussion.

The previous work on wave diffraction and ship motion in a harbour isfor a harbour with a free surface. In this paper, the harbour inside isfrozen with ice sheet. in the wave/ice sheet interaction problem has
attracted more interest in recent years, in which the wave motion offluid can be described via the linearized velocity potential theory andthe continuous ice sheet is treated as a thin elastic plate (Squire, 2007,2020). Based on the matched eigenfunction expansions and theconjugated gradient method, Fox and Squire (1990) obtained the wave
reflection for wave propagation in semi-infinite ice sheet. Wang andMeylan (2004) proposed a numerical scheme by boundary element
method for fluid flow and finite element method for ice floe witharbitrary geometry. Weber transform was used by Brocklehurst,Korobkin, and Părău (2011) on flexural-gravity wave diffraction with avertical wall of circular cross section. They solved the problem inthree-dimensional sense. Recently, Ren, Wu, and Ji (2018) considered
the problem for multiple vertical circular walls analytically. Li, Shi andWu (2021) solved the interactions of wave with ice sheet inside aharbour with matched eigenfunction expansion method.

KEY WORDS: frozen harbour; ice sheet; flexural-gravity wave;
domain decomposition method.

INTRODUCTION
Wave motion in a harbour is very complicated due to the fluid domain
is in a confined space. However, in some cold regions, the water
surface in interior harbour may be covered by ice sheet or being frozen,
while in exterior harbour away from the entrance the water surface still
remains open and free. In such a case, the ocean surface wave may
propagate into the frozen harbour, resulting a complex interaction
between ice sheet and the harbour wall.
There have been many notable works on the interactions of waves with
open and free-surface harbour. Mcnown derived an analytical solution
for a circular and a rectangular harbour with a small entrance
respectively, where the flow at the entrance is prescribed (Kravtchenko& Mcnown, 1955; Mcnown, 1952). To simulate the real flow at theentrance, the interaction of fluid flow in interior and exterior harbour*In the present paper, we first describe the mathematical model and thenumerical method with a frozen harbour of arbitrary shape. Then theverification of the proposed method and the results for ice deflection
inside the harbour are carried out. Finally, the conclusions are drawn.

Corresponding author. E-mail address: zhifu.li@hotmail.com

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