Diffraction of flexural-gravity waves by a vertical cylinder of non-circular cross section

Abstract

The linear three-dimensional problem of flexural-gravity wave (hydro-elastic wave) diffraction by a vertical cylinder of an arbitrary smooth cross section is studied using an asymptotic approach combined with the vertical mode method for water of finite depth. The surface of the water is covered by an infinite, continuous elastic ice plate. The rigid cylinder extends from the sea bottom to the ice surface. The ice plate is frozen to the cylinder. The ice deflection is described by the equation of a thin elastic plate of constant thickness with clamped edge conditions at the cylinder. The flow under the ice is described by the linear theory of potential flows. The coupled problem of wave diffraction is solved in two steps. First, the problem is solved without evanescent waves similar to the problem of water waves diffracted by a vertical cylinder. This solution does not satisfy the edge conditions. Second, a radiation problem with a prescribed motion of the ice plate edge is solved by the vertical mode method. The sum of these two solutions solve the original problem. Both solutions are obtained by an asymptotic method with a small parameter quantifying a small deviation of the cylinder cross section from a circular one. Third-order asymptotic solutions are obtained by solving a set of two-dimensional boundary problems for Helmholtz equations in the exterior of a circle. Strains along the edge, where the ice plate is frozen to the cylinder, are investigated for nearly square and elliptic cross sections of the vertical cylinders depending on the characteristics of ice and incident wave. The strains are shown to be highest in the places of high curvatures of the cross sections. The derived asymptotic formulae can be used in design of vertical columns in ice. They directly relate the strains in ice plate to the shape of the column.

Hydroelastic wave diffraction by a vertical circular cylinder standing in a channel with an ice cover

“…For three-dimensional surface-piercing bodies, Brocklehurst, Korobkin & Părău (2011) studied the problem of hydroelastic waves scattered by a vertical circular cylinder using the Weber transform, where the cylinder was assumed to be clamped into the ice sheet, and detailed analyses were made on the hydrodynamic forces and vertical shear forces on the cylinder, as well as the principal strain and deflection of the ice sheet. Dişibüyük, Korobkin & Yılmaz (2020) studied a similar topic but for a vertical cylinder of non-circular cross-section. In their work, the impermeable condition on the body surface was satisfied on the mean position by applying the perturbation theory, and then the velocity potential was derived by the method of eigenfunction expansion.…”

Three-dimensional interaction between uniform current and a submerged horizontal cylinder in an ice-covered channel

“…For wave interaction with structures piercing the ice plate or water surface, Brocklehurst, Korobkin & Părău (2011) investigated the diffraction problem of a hydroelastic wave beneath an ice sheet by a single bottom-mounted circular cylinder based on the Weber transform. Later, Dişibüyük, Korobkin & Yılmaz (2020) further extended it to a vertical cylinder of non-circular cross-section by applying the perturbation method at the mean position of the section. Hydroelastic wave diffraction problems by multiple vertical cylinders are solved by Ren, Wu & Ji (2018 a ).…”