Modelling wave propagation through broken ice

边缘冰带（MIZ）位于开阔海洋和滨临海冰之间的极地地区，是季节性形成的海冰开始破裂时形成的。MIZ可以从其边缘延伸到公海数百公里，由各种冰结构组成，从大型固体浮冰到油脂冰和煎饼冰。由于海冰相对较薄（通常为0.5米至2米厚），冰盖能够支撑弯曲波，从而使来自海洋的波浪能量传播到未破碎的冰区，从而有助于进一步破碎。冰破碎的动态过程是气候系统中的一个重要组成部分，因为它促进了融化，从而驱动海洋环流并减少极地地区的白化效应。近年来，通过实地测量、实验室实验和采用物理模型，已经作出了相当大的努力，以便更好地了解通过MIZ的波传播。这个博士项目的目的是开发模型来描述MIZ中波传播的一些主要特征。具体来说，这项工作将集中在1)为浮冰的分布建立新的“有效介质”方程和2)通过随机浮冰/裂缝配置进行波散射模拟。这项工作的终极挑战和目标是，看看我们的模型是否可以用来预测波衰减实验数据中看到的趋势(例如Doble等人（2016），“秋季波弗特海的煎饼和冰的风波耗散，”J. Geophys。海洋》)。这一挑战尤其困难，因为没有证据表明导致波衰减的物理过程，也没有科学共识。在许多可能的机制中，有两种机制引人注目。首先，存在与当地海洋/冰相互作用相关的损失（这些可能是机械的粘性损失）。其次，随机配置中的多波散射效应会产生衰减（类似于安德森局域化）。我们计划使用各种技术数学方法（如有效介质建模）来研究这两种方法，但将重点放在第二个想法上。特别是，我们计划将斯坦克和基诺（1984年，“多晶材料中弹性波传播的统一理论”，J Acoust Soc Am）的工作思想应用于碎冰区域。在这方面特别有希望的是，Stanke和Kino报道的弹性波传播到晶体材料中的波衰减率随频率的变化与Doble等人（2016）对冰的实验数据相似。这项工作将涉及应用数学、统计和计算方法。

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.