Hydroelastic Waves in a Frozen Channel with Non-Uniform Thickness of Ice

Abstract

The periodic flexural-gravity waves propagating along a frozen channel are investigated. The channel has a rectangular cross section. The fluid in the channel is inviscid, incompressible and covered with ice. The ice is modeled by a thin elastic plate whose thickness varies linearly. Two cases have been considered: the ice thickness varies symmetrically across the channel, being the smallest at the center of the channel and the largest at the channel walls; the ice thickness varies from the smallest value at the one wall to the largest value at another wall. The periodic 2D problem is reduced to the problem of the wave profiles across the channel. The solution of the last problem is obtained by the normal mode method of an elastic beam with linear thickness. The behavior of flexural-gravity waves depending on the inclination parameter of the ice thickness has been studied and the results have been compared with those for a constant-thickness plate. Dispersion relations, profiles of flexural-gravity waves across the channel and distributions of strain in the ice cover have been determined. In the asymmetric case, it is shown that for long waves, the most probable plate failure corresponds to transverse strains at the thin edge of the plate, which can lead to detachment of the ice from the corresponding bank. For short waves, the longitudinal stresses within the plate, localized closer to the thick edge, become maximum. This can lead to cracking of the plate in transverse direction. In the symmetric case, the maximum strains are achieved inside the plate — close to the center, but not necessarily in the midpoint.

Steady-State Motion of a Load on an Ice Cover with Linearly Variable Thickness in a Channel

“…The results for a plate with constant thickness can be calculated by the method described in [26]. Convergence of characteristics of periodic hydroelastic waves propagating along a frozen channel was investigated in [30].…”

“…The spectral functions ψ n (y) are called normal modes of oscillations of a beam with linear thickness. They were calculated in [30] for consideration in this article for the case of the shape of ice thickness. The functions ψ n (y) are solutions of the spectral problem…”

“…In [30], the case of flexural-gravity waves propagation when ice thickness varies linearly across the channel was considered. The problem was solved by the normal mode method, where modes of plates with linear thickness were present analytically by functions found in [31].…”

Dipole Oscillations along Principal Coordinates in a Frozen Channel in the Context of Symmetric Linear Thickness of Porous Ice

“…The fluid pressure, as well as the kinematic condition, for a dipole with a small radius a and a small inclination angle α dimm , can be written in a linearized form. See the corresponding discussions in [39,49]. The fluid pressure p(x, y, 0, t) at the ice/liquid interface is described by the linearized Bernoulli integral…”

“…In many studies, cases of uniform ice with constant thickness are considered. However, in natural conditions, the ice cover is not homogeneous, making it important to study models where the ice thickness varies [38,39]. The challenges associated with wave generation in a liquid, whether covered by ice or not, represent significant theoretical and practical interest.…”