Interactions between steady and oscillatory convection in mushy layers

预测多组分材料（如金属铸件）凝固的挑战之一是描述糊状层的演变：固相和液相共存的部分凝固区域。这种系统表现出在单相系统中所没有的不同寻常的特性。一个例子是通过热量和溶质的对流改变晶体结构，使流动问题非线性，并导致在固体基质中形成无固体溶解通道或“烟囱”。在最近的实验室实验中，发现了一种极其复杂的烟囱对流模式：一种新的对流“呼吸模式”，在这种模式中，烟囱都周期性地出现和消失。该项目旨在利用数学技术理解观察到的行为。特别地，定常和驻波振荡对流模式之间的非线性相互作用将被阐明，稳定流型及其参数灵敏度将被量化。还将进行进一步的实验室实验，以提供有关这一新发现现象的更详细信息。

One of the challenges in predicting the solidification of multicomponentmaterials such as metallic castings is to describe the evolution of mushy layers: partially solidifiedregions in which solid and liquid phases coexist. Such systems exhibitunusual properties not seen in single-phase systems. One example is thealteration of the crystalline structure by convection of heat and solute making theflow problem nonlinear and leading to the formation of solid-free dissolution channels,or 'chimneys', in the solid matrix. A strikingly complex pattern ofchimney convection has been observed in recent laboratory experiments: a new'breathing mode' of convection has been found, in which chimneys allperiodically appeared and disappeared in phase. This project aims at anunderstanding of the observed behaviour using mathematical techniques. In particular, the nonlinear interactions between steady andstanding-wave oscillatory convection modes will be elucidated, and stableflow regimes and their parametric sensitivity quantified. Further laboratory experiments will also be conducted to provide more detailed information about this newly discovered phenomenon.