Waves propagating along a channel with ice cover

Linear progressive waves in a channel covered with ice sheet are studied. The channel is of rectangular cross section. The ice sheet is clamped to the walls of the channel. The thickness of the ice plate is constant. Deflections of the ice sheet are described by the linear elastic plate equation. The hydroelastic waves in the channel are combinations of waves propagating along the channel and sloshing waves. The problem is formulated with respect to the wave profiles across the channel. The problem is solved by the normal mode method for a channel of finite depth and by using the shallow water approximation for a channel of small depth. The dispersion relations of the hydroelastic waves and the characteristics of these waves are determined. It is shown that the shallow water approximation predicts well the dispersion relations for long waves. The dispersion relation for the wave, which does not oscillate across the channel, is well approximated by the corresponding dispersion relation of one-dimensional hydroelastic waves in an unbounded ice sheet. The wave profiles across the channel and the distributions of strains in the ice sheet are investigated. It is shown that the strains are maximum at the walls for long waves and at the centreline of the channel for short waves. The bending stresses across the channel are higher than the stresses along the channel for the conditions of the present study.