Oblique waves are propagated across a crack in an infinite homogeneous ice sheet that is modelled as an Euler-Bernoulli thin plate. The water beneath is taken to be infinitely deep and of constant density, and the flow is assumed to be inviscid and irrotational. An integral representation of the appropriate Green's function is found, from which analytical formulae for the reflection and transmission coefficients are deduced. The paper extends the work of Squire and Dixon (2000), which is concerned with waves at normal incidence.
Deep into the Arctic Ocean, many hundreds of kilometres from the nearest ice edge, the sea-ice cover is known to exhibit small oscillatory motions that arise due to the presence of ice-coupled waves. These waves, recorded by both tiltmeters and strain gauges, originate as surface gravity waves in the open sea to the South. As they impinge on the ice edge, the surface gravity waves are partially transmitted as ice-coupled waves, in a way that favours the propagation of longer periods at the expense of short period waves because of the impedance change at the ice margin. Within the heterogeneous ice veneer the ice-coupled waves encounter many flaws, such as pressure ridges and cracks, which affect their passage. These imperfections also discourage short waves (Squire and Dixon, 2000), as does hysteresis in the ice sheet itself that results from the inherent inelasticity of sea-ice. Squire and Dixon (2000) model how ice-coupled waves are affected by an open crack met at normal incidence. While this problem has been studied in the past (Barrett and Squire, 1996), it is shown by Squire and Dixon that simple algebraic formulae emerge for the reflection and transmission coefficients and that the numerical solution developed in the 1996 paper is unnecessary.