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Wave scattering by a periodic line array of axisymmetric ice floes
by
Luke Bennetts
Uni of Otago
Coauthors: Vernon Squire
The case of a periodic array of identical circular ice floes that are equispaced along an infinite straight line is considered under linear and time-harmonic conditions.
In this model the floes possess the new features of a realistic non-zero draught and the ability to vary in thickness axisymmetrically via both their upper and lower surfaces. Moreover, our model is designed in such a manner that we may easily solve for geometrical configurations consisting of an arbitrary number of these straight lines of circular floes and may dictate either free-surface or ice-covered conditions away from the floes. Such extensions could be used as a model of the MIZ for example, or pancake ice appearing within a lead.
The geometry is divided into channels that contain a single floe. By applying phase change conditions on the sides of the channel we may reduce the problem posed by the infinite line array to that of a single channel only. The channel problem is simplified by invoking an approximation of the vertical dependence of the fluid motion. Green's functions are then used to convert the resulting equations into a integral system over the ice-covered disc, which may be solved numerically.
Date received: October 15, 2007
An Elastic Plate Model for Wave Scattering in the Marginal Ice Zone
by
Alison Kohout
University of Auckland
Coauthors: Mike Meylan
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 which 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 non-linear 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 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, exactly 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 prediction 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. This also allows us to conclude that we are under prediction the attenuation at long periods.
Date received: October 10, 2007
Simulation of near-trapping time-dependent water wave problem.
by
Michael Meylan
University of Auckland
This paper discusses the problem of near trapping by water waves and their simulation in the time domain. In particular, I focus on the problem scattering by cylinders, which is particularly simple to compute in the frequency domain. The methods consists of the following steps. The solution in the time-domain is written as a generalised eigenfunction expansion. Then the single frequency solution is extended to the complex plane where singularities are found close to the real axis. We then approximate the time domain solution as a sum over the contribution from these singularities.
Date received: October 9, 2007
Time-dependent water waves incident on a vertical elastic plate
by
Malte A. Peter
University of Auckland
A time-dependent water-wave scattering problem in two spatial dimensions is considered in a semi-infinite domain: the water is of finite depth and infinite extent in one horizontal direction. It is bounded by a vertical elastic plate in the other horizontal direction. The plate is fixed at the sea bed and either fixed or pinned somewhere above the free water surface. The problem is solved by Fourier transform making use of solutions of the corresponding time-harmonic problem. Near-resonance and trapping are investigated making use of an abstract operator calculus.
Date received: October 29, 2007
Scattering and damping of ice coupled waves
by
Gareth L. Vaughan
Otago university
Coauthors: Vernon A. Squire
Ice-coupled waves propagating beneath solid ice sheets experience attenuation that arises due to both scattering and damping effects, where the latter occurs because of hysteresis in the ice, i.e. its inherent inelasticity, and because of energy loss in the water column. Ice floe collisions, which occur during ridge building events, can also potentially cause waves to be attenuated, particularly where the ice sheet is at its most dynamic due to wind, waves and currents. Both scattering and damping have been examined in isolation but rarely together. Real waves experience both mechanisms and, accordingly, both must be included if a model is to describe physical reality accurately.
I will describe a model that simulates both scattering and damping in two dimensional ice sheets of variable thickness. The damping is accommodated using a linear Kelvin-Voigt beam equation, the most basic viscoelastic model that reproduces the behaviour of ice when it is subjected to stress-strain tests in a laboratory, and the solution is found by means of Green's functions.
Results from examples of simulations are presented that illustrate the most important marine geophysical outcomes that emerge.
Date received: October 14, 2007