Of ocean waves and sea-ice revisited

The interaction of waves with obstacles is an everyday phenomenon in science and engineering, arising for example in acoustics, electromagnetism, seismology and hydrodynamics. The mathematical theory and technology needed to understand the phenomenon is known as multiple scattering, and this book is the first devoted to the subject. The author covers a variety of techniques, describing first the single-obstacle methods and then extending them to the multiple-obstacle case. A key ingredient in many of these extensions is an appropriate addition theorem: a coherent, thorough exposition of these theorems is given, and computational and numerical issues around them are explored. The application of these methods to different types of problems is also explained; in particular, sound waves, electromagnetic radiation, waves in solids and water waves. A comprehensive bibliography of some 1400 items rounds off the book, which will be an essential reference on the topic for applied mathematicians, physicists and engineers.

Multiple Scattering: Interaction of Time-Harmonic Waves with N Obstacles

This article reviews Multiple Scattering, Interaction of Time-Harmonic Waves with N Obstacles by P. A. Martin , 2006. 450 pp. Price: $140.00 (hardcover). ISBN: 0-521-86554-9

Multiple Scattering, Interaction of Time-Harmonic Waves with N Obstacles

[1] We present a model for wave attenuation in the marginal ice zone (MIZ) based on a two-dimensional (one horizontal and one vertical dimension) multiple floating elastic plate solution in the frequency domain, which is solved exactly using a matched eigenfunction expansion. The only physical parameters that enter the model are length, mass, and elastic stiffness (of which, the latter two depend primarily on thickness) of the ice floes. The model neglects all nonlinear effects as well as floe collisions or ice creep and is therefore most applicable to floes which are large compared to the thickness and to wave conditions which are not extreme. The solution for a given arrangement of floes is fully coherent, and the results are therefore dependent on the exact geometry. We firstly show that this dependence can be removed by averaging over a distribution of floe lengths (we choose the Rayleigh distribution). We then show that after this averaging, the attenuation coefficient is a function of floe number and independent of floe length, provided the floe lengths are sufficiently large. The model predicts an exponential decay of energy, just as is shown experimentally. This enables us to provide explicit values for the attenuation coefficient, as a function of the average floe thickness and wave period. We compare our theoretical predictions of the wave attenuation with measured data and other scattering models. The limited data allows us to conclude that our model is applicable to large floes for short to medium wave periods (6 to 15 seconds). We also derive a floe breaking model, based on our wave attenuation model, which indicates that we are under-predicting the attenuation coefficients at long periods.

https://agupubs.onlinelibrary.wiley.com/doi/pdf/10.1029/2007JC004434

An elastic plate model for wave attenuation and ice floe breaking in the marginal ice zone

We present a solution to the water-wave interaction with a submerged elastic plate of negligible thickness by the eigenfunction-matching method. The eigenfunction expansion depends on the solution of a special dispersion equation for a submerged elastic plate and this is discussed in detail. We show how the solution can be calculated for the case of normal incidence on a semi-infinite plate in two spatial dimensions and then extend this solution to obliquely incident waves, to a plate of finite length and to a circular finite plate in three dimensions. Numerical calculations showing various properties of the solutions are presented and a near-orthogonality relation for the eigenfunctions is used to derive an energy-balance relation.

/pdf/water-wave-scattering-by-submerged-elastic-plates-4fa8ngrvut.pdf

D. Brossard

Papers

Linear water wave propagation through multiple floating elastic plates of variable properties