Of ocean waves and sea-ice revisited

The linear two-dimensional problem of hydroelastic waves reflected by a vertical wall is analysed. The fluid is of finite depth and is covered by an ice sheet. The fluid is assumed incompressible and inviscid. The ice sheet is assumed thin compared with both the water depth and wavelength of the incident wave. The deflection of the ice sheet is described by linear elastic plate theory, and the fluid flow by using the potential-flow model. The ice sheet extends infinitely and is clamped to the vertical-walled structure. The incident hydroelastic wave is regular. An analytic solution is found by integral-transform methods. The ice deflection, the vertical and horizontal forces acting on the wall and the bending stresses in the ice caused by the incident wave are determined. The forces on the wall are analysed in detail, and relevant physical parameters are varied for comparison. The phase shift between the incident and reflected wave amplitudes is found as part of the complete solution. It is shown that the ice clamping condition leads to a specific effect on the ice deflection.

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Interaction of hydro-elastic waves with a vertical wall

The behavior of flexural gravity waves propagating over a semi-infinite floating ice sheet is studied under the assumptions of small amplitude linear wave theory. The vertical wall is assumed to be either fixed or harmonically oscillating with constant horizontal displacement, in which case the problem is analogous with a harmonically oscillating plane vertical wavemaker. The potential flow approach is adhered to and the higher-order mode–coupling relations are applied to determine the unknown coefficients present in the Fourier expansion formula of the potential functions. The ice sheet is modeled as a thin semi-infinite elastic beam. Three different edge conditions are applied at the finite edge of the floating ice sheet. The effects of different edge conditions, the thickness of the ice sheet and the water depth on the surface strain, the shear force along the ice sheet, the horizontal force on the vertical wall, and the flexural gravity wave profile are analyzed in detail.

Flexural gravity wave over a floating ice sheet near a vertical wall

Expansion formulae for wave structure interaction problems with applications in hydroelasticity

A new method is developed to study the problem of water wave scattering by a thin elastic plate of arbitrary width floating in deep water assuming linear theory. Using Havelock's expansion of water wave potentials, the boundary value problem describing the potentials is reduced to solving singular integral equations of Carleman type. With the introduction of some integral operators the problem is further reduced to twelve Fredholm integral equations of second kind with regular kernels, and the numerical solutions of these integral equations are used to compute the reflection and transmission coefficients. The numerical estimates for the reflection coefficient are presented in a number of figures given varying different physical parameters. It is shown that the present analysis produces known results for the reflection coefficient.

D.S. Ahluwalia

Papers

Surface water waves involving a vertical barrier in the presence of an ice-cover