Analytical Investigation Of Wave Interaction With Finite-length Ice Sheet With A Gap

Sea ice widely exists in polar region.When the wave interaction with sea ice is considered,the sea ice is usually treated as a perfect and continuous elastic plate.However,there are some imperfect ice sheets existing in the polar ocean areas.For example,behind an icebreaker,a new channel can be formed with ice pieces.These imperfect ice sheets can easily form one or more gaps,which affects not only the wave propagation,but also the hydroelastic responses of the ice sheet.Therefore,it is necessary to investigate the wave interaction with ice sheet with a gap.In the present study,we consider the sea ice as a finite elastic plate with a gap.Based on the linear potential-flow theory,the whole fluid domain is divided into 5 sub-domains.This analytical solution is solved using the eigenfunction expansion method.The implicit function image method is used to find the roots of two dispersion equations beneath the ice sheet and the open water,respectively.After matching the pressure and velocity on the interfaces of neighbor regions,a linear system of equations can be acquired by taking advantage of the orthogonality property of the vertical eigenfunctions.The corresponding unknown coefficients can be obtained by solving the linear system of equations.This paper mainly explores the effect of gap on wave propagation and the hydroelastic responses of the ice sheet,and analyzes the wave reflection and transmission coefficients and the strain and shear force on the ice sheet at different gap locations.It is found that the curves of wave reflection and transmission coefficient oscillate with frequency,and there are a series of local minima and local maxima on the curves.When the gap is located symmetrically with respect to the central point of the ice sheet,the wave transmission coefficients keep the same in the case of these two gap locations,but the hydroelastic responses of the ice sheet are different.At some specific frequencies,the wave elevation in the gap is significantly increased,the hydroelastic responses of ice sheet is also obviously increased.Both amplitudes of the strain and shear force in the head-sea ice piece are much larger than those on the lea-side piece,and these frequencies are correlate with some local maxima on the transmission coefficient curve.This paper also analyzes the effect of the structural parameters of sea ice on wave propagation and the hydroelastic responses of ice sheet.It is found that the wave transmissioncurve oscillates more obviously when the stiffness of sea ice is lower,and there are more peak points of the hydroelastic responses existing on the ice sheet.When the thickness of sea ice is small,the thickness change will not make difference on the wave reflection and transmission coefficients.The wave frequencies corresponding to the zero reflection points shift toward lower with the increase of thickness.As the length of sea ice increases,the number of zero reflection points increase,and the wave frequencies corresponding to the zero reflection points become lower.