Wave scattering at the sea-ice/ice-shelf transition with other applications

We present a mathematical model that describes how ice-coupled (flexural-gravity) waves traveling beneath a uniform, floating sea-ice sheet, defined over (-infinity, 0), propagate into a second ice sheet (l, infinity) of different thickness by way of an arbitrarily defined transition region of finite width (0, l). Each ice sheet is represented as an Euler-Bernoulli thin plate with a prescribed thickness and material properties, either or both of which vary across the transition. The most familiar application of this geometry is to sea-ice abutting an ice-shelf-a common occurrence found in the waters around Antarctica and parts of the Arctic or to sea-ice skirting sikussak-the band of extremely thick coastal fast ice that can form when local ice is sheltered from destructive storms. Another application is to breakwaters, and this is also discussed. By using Green's theorem two coupled integral equations are derived: one defined over (0, l) and the second of the Wiener-Hopf type, defined over (l, infinity). The latter is solved analytically, allowing the integral equations to be decoupled and the first equation to be solved numerically. Results are presented for the geophysical and engineering examples referred to above.