Ship waves on an elastic floating ice plate

We study a wave wake produced by a finite-size source uniformly moving on an ice plate overlying deep water. We describe the kinematic characteristics of source-generated flexural-gravity waves in terms of isophase patterns scaled by the minimum phase speed and show that the wave picture is determined by ad hoc defined Mach and Bond numbers. Then, we show that several bifurcations occur in the wave wake when the source speed increases. In particular, cusps appear in the wake patterns at certain speeds due to the merging at specific points of two or three wave characteristics (wave rays) which correspond to longitudinal (divergent), transverse, and fan waves. To describe the distribution of wave amplitudes in the wake accounting for the source size and shape, we use the reference solution approach. This approach agrees with the stationary phase method in the far-field zone and reproduces also specific wave dynamics at short and intermediate distances from the source. The effect of a source shape on the wave wake pattern is graphically illustrated for the elliptic source as the dependence on the dimensionless Bond number and the source length-to-beam ratio. The illustrations of the source speed and shape effects are given for low-speed regimes when wave patterns are conformed by single-ray solutions. Ways of the generalization of the suggested approach are outlined.