Modelling wave propagation through broken ice

The Marginal Ice Zone (MIZ) is located in polar regions between the open ocean and the shore-fast sea ice and develops when seasonally-formed sea ice begins to break up. The MIZ can extend away from its edge with the open sea for hundreds of kilometres and consists of a variety of ice structures from large solid floating ice to grease ice and pancake ice. Because sea ice is relatively thin (typically 0.5m to 2m thick) ice sheets are able to support flexural waves which allow wave energy from the ocean to propagate into regions of unbroken ice where it can assist further break up. The dynamic process of ice break up is an important component in the climate system since it enhances melting which drives ocean circulation as well as reducing the albino effect of the polar regions. In recent years considerable effort has been placed on developing a better understanding of wave propagation through the MIZ through field measurements, laboratory experiments and by employing physical models. This PhD project is aimed at developing models which describe some of the main features of wave propagation in the MIZ. Specifically, the work will focus on 1) developing new "effective medium" equations for distributions of floating broken ice and 2) developing simulations of wave scattering through random ice floe/crack configurations. The ulimate challenge, and goal of this work, is to see if our models can be used to predict the trends see in experimental data of wave attenuation (e.g. Doble et al (2016), "Dissipation of wind waves by pancake and frazil ice in the autumn Beaufort Sea," J. Geophys. Res. Oceans). This challenge is particularly difficult because there is no evidence for or scientific agreement on the physical processes that lead to wave attenuation. Of the many possible mechanisms, two stand out. The first is that there are losses associated with local ocean/ice interactions (these could be mechanical of viscous losses). The second is that multiple wave scattering effects in random configurations give rise to attenuation (similar to Anderson localisation). We plan to investigate both using a variety of technical mathematical methods such as effective medium modelling, but will place a larger emphasis on the second idea. In particular we plan to apply ideas in the work of Stanke and Kino (1984, "A unified theory for elastic wave propagation in polycrystalline materials", J Acoust Soc Am) to regions of broken ice. Especially promising in this regard is the variation of wave attentuation rates with frequency reported by Stanke and Kino for elastic waves propagating into a crystalline material are similar to experimental data for Doble et al. (2016) for ice. The work will involve applied mathematical, statistical and computational methods.