Hydroelastic waves and their interaction with structures

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Description:	Korobkin, A Tuesday 7th November 2017 - 13:30 to 14:30


Created:	2017-11-08 13:54
Collection:	Mathematics of sea ice phenomena
Publisher:	Isaac Newton Institute
Copyright:	Korobkin, A
Language:	eng (English)


Abstract:	Co-author: S. Malenica (BV), T. Khabakhpasheva (Lavrentyev Institute of Hydrodynamics) Linear problems of hydroelastic wave diffraction by structures with vertical walls are studied for a circular cylinder frozen in ice cover of constant thickness and infinite extent. The water depth is constant. The ice plate is modelled by a thin elastic plate clamped to the surface of the cylinder. The cylinder is mounted at the sea bottom. One-dimensional incident hydroelastic wave of small amplitude propagates towards the cylinder and is diffracted on the cylinder. Deflection of the ice plate and the bending stresses in it are determined by two methods: (a) using the integral Weber transform in radial direction, (b) using the vertical modes for the fluid of constant depth with the rigid bottom and elastic upper boundary. The solution by the second method is straightforward but we cannot prove that the solution is complete because the properties of the vertical modes are not known. The solution by the Weber transform is more complicated but this solution is unique. We will show that these two solutions are identical. This result justifies the method of the vertical modes in the hydroelastic wave diffraction problems. For a circular cylinder the vertical-mode solution can be also justified by substitution. Different conditions at the contact line between the cylinder and the ice sheet are considered. The wave diffraction problem for broken ice is also considered. It is shown how the problem can be generalised to non-circular cylinders and interaction of several cylinders in ice.

Abstract:

Co-author: S. Malenica (BV), T. Khabakhpasheva (Lavrentyev Institute of Hydrodynamics)

Linear problems of hydroelastic wave diffraction by structures with vertical walls are studied for a circular cylinder frozen in ice cover of constant thickness and infinite extent. The water depth is constant. The ice plate is modelled by a thin elastic plate clamped to the surface of the cylinder. The cylinder is mounted at the sea bottom. One-dimensional incident hydroelastic wave of small amplitude propagates towards the cylinder and is diffracted on the cylinder. Deflection of the ice plate and the bending stresses in it are determined by two methods: (a) using the integral Weber transform in radial direction, (b) using the vertical modes for the fluid of constant depth with the rigid bottom and elastic upper boundary. The solution by the second method is straightforward but we cannot prove that the solution is complete because the properties of the vertical modes are not known. The solution by the Weber transform is more complicated but this solution is unique. We will show that these two solutions are identical. This result justifies the method of the vertical modes in the hydroelastic wave diffraction problems. For a circular cylinder the vertical-mode solution can be also justified by substitution. Different conditions at the contact line between the cylinder and the ice sheet are considered. The wave diffraction problem for broken ice is also considered. It is shown how the problem can be generalised to non-circular cylinders and interaction of several cylinders in ice.

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