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

Abstract

[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.Citation: Kohout, A. L., and M. H. Meylan (2008), An elastic plate model for wave attenuation and ice floe breaking in the marginal ice zone,

Size distribution and shape properties of relatively small sea-ice floes in the Antarctic marginal ice zone in late winter

“…However, it should also be kept in mind that most of the models that examine the wave-ice interaction (e.g. Fox and Squire, 1991;Kohout and Meylan, 2008) assume one directional wave propagation into long ice plate.…”

“…Due to a lack of ice thickness data, the mechanism for 5 the floe size distribution has been unknown. From theoretical studies based on a solution for wave propagation under floating elastic plates, it is shown that ice thickness is by far the most important factor for determining the scattering and break-up of ice (Meylan, 2002;Kohout and Meylan, 2008).…”

Past, present and impendent hydroelastic challenges in the polar and subpolar seas

“…This is essentially a two-dimensional MIZ, as an open lead surrounded by ice is the same as two ice floes separating a stretch of open water, once waves local to the edges have dissipated. Exploiting an eigenfunction expansion under each ice floe and matching the expansions at the plate boundaries where free-edge conditions (2.7) must hold, Kohout & Meylan [28] used an equivalent approach. On also comparing with some field data, they concluded that their model, even though two dimensional, is applicable to large floes for short-to medium-wave periods in the 6-15 s range.…”

Measurements of wave damping by a grease ice slick in Svalbard using off-the-shelf sensors and open-source electronics

“…Neither of these models predict wave attenuation, which needs to be described by separate mechanisms. Such mechanisms can be of two kinds: wave scattering, which is especially important in the case of the marginal ice zone (Kohout and Meylan, 2008); and the introduction of an effective viscosity in either the water or the ice layer (Weber, 1987;Keller, 1998;Carolis and Desiderio, 2002). The introduction of viscosity was initially proposed by Weber (1987) and refined by several authors later on (Keller, 1998;Carolis and Desiderio, 2002;Wang and Shen, 2010b).…”