Interaction of flexural-gravity waves in ice cover with vertical walls

Korobkin, A.A.; Malenica, Šime; Хабахпашева, Т. И.

doi:10.1098/rsta.2017.0347

Cited by 18 publications

(25 citation statements)

References 14 publications

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“…. In the present analysis we follow the procedure from [8] and we restrict ourselves to the roots 2 1 0 , , ,…”

Section: Solution Methodologymentioning

confidence: 99%

“…Interaction of gravity waves with different obstacles received much attention in the past both in the context of water waves [1,2,3] as well as in the context of flexural gravity waves [4,5,6,7,8,9,10,11,12,13,14]. Both the linear [1,6,7,8,11,13] and higher order interactions [2,3,15,16] were of concern. The problem of flexural gravity waves is relevant in the context of the ice structure interactions (both for the floating bodies as well as for the cracks which might occur in the ice sheets) and in the context of the elastic floating structures such as floating airports or the elastic plates lying at the water surface.…”

Section: Introductionmentioning

confidence: 99%

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An Alternative Solution for Interaction of Flexural Gravity Waves With Bottom Mounted Circular Cylinder

Malenica¹

2019

brod

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The problem of interaction of the flexural gravity waves with the bottom mounted circular cylinder is discussed. Both the linear and second order problems are considered and they are solved by using the eigenfunction expansion principles together with the Boundary Integral Equation technique. The linear solution, which was proposed in the litterature by different authors in the past, is explicitely recovered. For the second order problem, a new original solution strategy is proposed and it was shown that, in the case of water waves, a well known semi-analytical solution is also recovered, proving the generality of the proposed approach.

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“…. In the present analysis we follow the procedure from [8] and we restrict ourselves to the roots 2 1 0 , , ,…”

Section: Solution Methodologymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

An Alternative Solution for Interaction of Flexural Gravity Waves With Bottom Mounted Circular Cylinder

Malenica¹

2019

brod

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“…The present analysis is inspired by the approach suggested in [2], where two-dimensional problems of flexural-gravity waves interacting with a vertical wall were studied by the vertical mode method. The approach of [2] was generalised in [3] to the three-dimensional problems. In this generalised approach, the vertical coordinate is separated in the solution reducing the original three-dimensional problem to a set of two-dimensional radiation and diffraction problems.…”

Section: Introductionmentioning

confidence: 99%

“…The resulting two-dimensional problems are similar to radiation problems of acoustics. They are formulated for the two-dimensional Helmholtz equations with the wavenumbers equal to the roots of the dispersion relation of the hydroelastic waves, see [3]. The equations should be solved outside the cross section of the vertical cylinder with corresponding far-field conditions.…”

Section: Introductionmentioning

confidence: 99%

The vertical mode method in the problems of flexural-gravity waves diffracted by a vertical cylinder

Korobkin

Malenica

Хабахпашева

2019

Applied Ocean Research

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The linear three-dimensional problem of ice loads acting on a vertical circular cylinder frozen in an ice cover of infinite extent is studied. The loads are caused by an uni-directional hydroelastic wave propagating in the ice cover towards the cylinder mounted to the see bottom in water of constant depth. There are no open water surfaces in this problem. The deflection of the ice cover is described by the Bernoulli-Euler equation of a thin elastic plate of constant thickness. At the contact line between the ice cover and the surface of the cylinder, some edge conditions are imposed. In this study, the edge of the ice plate is either clamped to the cylinder or has no contact with the cylinder surface, with the plate edge being free of stresses and shear forces. The water is of finite constant depth, inviscid and incompressible. The problem is solved by both the vertical mode method and using the Weber integral transform in the radial coordinate. Each vertical mode corresponds to a root of the dispersion relation for flexural-gravity waves. It is proved that these two solutions are identical for the clamped edge conditions. This result is non-trivial because the vertical modes are non-orthogonal in a standard sense, they are linearly dependent, the roots of the dispersion relation can be double and even triple, and the set of the modes could be incomplete. A general solution of the wave-cylinder interaction problem is derived by the method of vertical modes and applied to different edge conditions on the contact line. There are three conditions of solvability in this problem. It is shown that these conditions are satisfied for any parameters of the problem.

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“…Results for the deflection and strain of the ice sheet, the horizontal wave forces as well as the vertical shear forces due to the clamped edge were provided. Recently, Korobkin et al [34] further considered hydroelastic waves scattering by a vertical cylinder of an arbitrary cross section using a vertical mode method.…”

Section: Introductionmentioning

confidence: 99%

Diffraction of hydroelastic waves by multiple vertical circular cylinders

Ren

2018

J Eng Math

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The diffraction problem of hydroelastic waves beneath an ice sheet by multiple bottom-mounted circular cylinders is considered. The elastic thin-plate theory is adopted to model the ice sheet, while the linearized velocity potential theory adopted for the fluid flow. The velocity potential corresponding to each cylinder is expanded into a series of eigenfunctions, and the total potential is expressed as a summation of these expansions over the entire NC number of cylinders. For each cylinder, the Green's second identity is used outside its domain to obtain a set of linear equations. For each different cylinder, the domain used is different. NC cylinders give NC sets of coupled linear equations. Investigations are made for different arrangements of cylinders, piercing through ice sheets. Results for the wave forces on the cylinders with clamped and free conditions of the ice edge are obtained. Physical phenomena corresponding to cylinders arranged in square, in an array, in a double-array and in a staggered double array are discussed.

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Interaction of flexural-gravity waves in ice cover with vertical walls

Cited by 18 publications

References 14 publications

An Alternative Solution for Interaction of Flexural Gravity Waves With Bottom Mounted Circular Cylinder

An Alternative Solution for Interaction of Flexural Gravity Waves With Bottom Mounted Circular Cylinder

The vertical mode method in the problems of flexural-gravity waves diffracted by a vertical cylinder

Diffraction of hydroelastic waves by multiple vertical circular cylinders

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