Investigation Of Sea-Ice Growth By Multi-phase-Field Approach

Due to global warming which leads to significant climate changes and more and more frequently occurring severe weather disasters,such study seems more important than ever,since sea ice has begun to melt and this makes sea level arise considerably so that some islandish countries may vanish.In this dissertation we shall employ phase-field approach to model the growth of sea ice,this approach,though it has been developed since 1980 s thus is very young,is now a very powerful tool for both theoretical and numerical studies in many fields.To our knowledge,the application presented in this thesis,of a multi-phase-field model to the investigation of sea-ice growth is the first one in phase-field modeling for sea-ice evolution.This thesis consists of two parts.The first,which includes Chapters 2,3and 4,is concerned with the formulation of a new multi-phase-field model,the existence,regularity and large-time behavior of weak solutions to the new model.The second,i.e.,Chapter 5,is for a new proof of the existence of weak solutions to a model proposed by Alber and Zhu.This model may be applied for describing structural phase transitions between different states of sea ice.In Chapter 2,we first present a brief derivation of the new multi-phase-field model.Since the original multi-phase model is very complex,we then reduce this model in Chapter3 into a two-phase one.With the help of the Banach fixed-point theorem we prove the existence of weak solutions,and study regularity of weak solutions for the slightly simplified model.Also we study the existence of a global attractor for this simplified model and investigate the large time behavior of weak solutions.Finally,we perform numerical simulations for the one-dimensional model.The existence of local solutions to the multi-phase-field model is proved in the fourth chapter,again by making use of the Banach fixed-point theorem.Sea ice possesses different microstructures,so it is classified into several kinds,say,Ice IV,Ice V,etc.Sea ice may change from one kind to another,and this transformation is a kind of solid-solid phase transitions driven by configuration forces,therefore we use in Chapter 5,a phase-field model by Alber and Zhu to describe the evolution of interfaces between the different kinds of sea ice,the dynamic behavior of the sea-ice growth is thus more profoundly understood.We contribute mathematically to this field by giving a new proof of the existence of weak solutions to that model.Chapter 6 is a summary of the results obtained in this thesis,and discussions and perspective of investigations related to the topics of this thesis.