The effect of submergence on wave scattering across a transition between two floating flexible plates

• Published in: Wave motion 2008, Vol.45 (3), p.361-379
• Main Authors: Williams, T.D., Squire, V.A.
• Format: Article
• Language: English
• Subjects: Exact sciences and technology; Finite draft; Fluid dynamics; Fundamental areas of phenomenology (including applications); General theory; Green’s function method; Mathematical methods in physics; Numerical approximation and analysis; Ordinary and partial differential equations, boundary value problems; Physics; Sea-ice; Solid mechanics; Structural and continuum mechanics; Vibration, mechanical wave, dynamic stability (aeroelasticity, vibration control...); Wave–ice interaction
• ISSN: 0165-2125; 1878-433X
• DOI: 10.1016/j.wavemoti.2007.07.003

The reflection and transmission of flexural-gravity waves at a sudden change of properties of finite extent, e.g., an irregularity such as an entrapped iceberg, in an otherwise uniform sea-ice sheet is considered theoretically. Although similar in purpose to Squire and Dixon [V.A. Squire, T.W. Dixon, On modelling an iceberg embedded in shore fast sea ice, J. Eng. Math. 40 (3) (2001) 211–236], the current paper correctly incorporates changes of Archimedean draft, i.e., submergence, between the three adjoining plates and thereby allows the approximations in that work to be examined and quantified. This is unusual, as the bulk of the published work concerned with wave propagation beneath floating ice sheets ignores the effects of submergence on the basis that the wavelengths involved significantly exceed the ice thickness and hence the draft of the sheet. After validation, results are presented showing how the reflection coefficient depends on the geometry of the arrangement being modelled, including both isolated floes in the open sea, which may surge, and ice floes and bergs surrounded by a contiguous uninterrupted ice sheet. The effect of draft is investigated and a wide spacing approximation is also developed that allows the scattering coefficients for the boundary between two floating semi-infinite sheets to be deduced when submergence is included. This also enables us to approximate the scattering by a lead.