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

A Boundary Integral Equation Method for Wave Loads on A
Ship in An Ice Channel
Yuyun Shi, Naizhe Chen, Zhifu Li *School of Naval Architecture and Ocean Engineering, Jiangsu University of Science and Technology.
Zhenjiang, Jiangsu, China

ABSTRACTIn this paper, the computation of wave loads on a ship in an ice channel
is carried out through a boundary integral equation method. The icechannel is confined between two semi-infinite ice sheets. The
linearized velocity potential theory is used for the fluid flow and thethin elastic plate model is adopted for the ice sheet. A boundary
integral equation is constructed, in which the Green function satisfying
all the boundary conditions apart from that on the ship surface isadopted. Detailed results for wave loads on a barge ship are provided,
which are generally highly oscillatory due to the complex
wave/body/ice interaction.

KEY WORDS: ice sheets; wave loads; boundary integral equation
methodINTRODUCTION
The wave loads on a floating structure in restricted area is of
considerable significance in ocean engineering for its safety design andoperation. A related problem is an ice channel or a free-surface channel
confined between two semi-infinite ice sheets. Since the dispersion
equation for wave in free-surface and beneath the ice sheet are different,
the disturbed wave will be partially reflected back to the body, whichmakes the wave/body interaction in an ice channel more complex.
Notable works have been done in two-dimensional cases. Based on thelinear velocity potential theory and the thin elastic plate model, Chungand Linton (2005) solved a problem of wave propagation in the icechannel using residual calculus technique, in which the two ice sheet
are semi-infinite. Williams and Squire (2006) considered the problemof three connected ice sheets using Wiener-Hopf and residual calculus
techniques. In this work, when the ice thickness of the middle one is set
to be zero, the problem turns to be the channel one. Shi, Li, and Wu(2019) proposed an approximate method for problem of wave
scattering by multiple ice channels.
*When there is a body submerged in the fluid or floating on the water
surface confined by the ice sheet, the interaction shall be more complex.
Based on the boundary integral equation method, Sturova (2015)
considered a problem of wave radiation by a body submerged in an icechannel. For a rectangular body floating on the ice channel, Ren, Wu,and Thomas (2016) obtained an analytical solution through thematched eigenfunction expansions. Li, Shi and Wu (2018) developed ahybrid numerical method for an arbitrary shaped body floating on theice channel based on the combination of eigenfunction expansions andboundary integral equation. Through wide spacing assumption, Li, Shiand Wu (2017) provided a solution for a body in a wide ice channel.
For the three-dimensional problem, the solution becomes much morechallenging. Li, Wu and Ren (2021) derived a Green function throughapplying the Fourier transform along the ice channel and then
expanding the potential into eigenfunction series in each subdomain.
Matching was done on the interface according to the continuous
condition of pressure and velocity. In this work, a panel method isdescribed for the computation of wave loads on a ship in an ice channel,
through applying the Green’s identity to the Green function and thedisturbed velocity potential to obtained a boundary integral equation
over the body surface only. Computations of wave loads on a barge
shaped ship floating on two ice channels with different widths arecarried out, and its oscillatory behaviour against wavenumber andchannel width are analyzed.

MATHEMATICAL MODEL
The problem of computation of wave loads on a ship in an ice channelis considered. A Cartesian coordinate system O  xyz is defined. TheO  xy plane is located at the undisturbed mean free water surface.
The z axis points vertically upwards. The channel is confined by two
semi-infinite ice sheets, where the boundary of y is b respectively.
The incident wave angle is denoted by  .
The fluid is assumed to be inviscid, incompressible, homogeneous, andits motion to be irrotational. The fluid density is  w and the constantwater depth is H . When the amplitude of wave motion and bodymotion are small compared to the wavelength and the dimension of

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