海啸生成、传播、爬高与淹没过程,以及海啸预警方法是海啸动力学研究的重要内容.近十年来国内外学者在该领域开展了大量的研究工作.本文总结了海啸数学模型研究进展,重点介绍了高阶Boussinesq水波模型及其在海啸研究中的应用,包括海啸在沿海大陆架上传播、演化与爬高特征和实际海啸过程的数值模拟.针对南中国海马尼拉海沟断裂带潜在的海啸风险,建立了该海域的基于多浮标观测反演和数值模拟的海啸预警方法,并提出了一种新的快速预警策略.探讨了海啸波导致地磁场异常的理论预报模型,并针对实际海啸过程给出了地磁场异常的时空分布. The process of tsunami generation, propagation, climb and submergence, and the method of early warning of tsunamis are the important contents of the research on the dynamics of tsunamis.Many scholars at home and abroad have carried out a great deal of research work in this field in recent ten years.This paper summarizes the research progress of mathematical model of tsunami, The high order Boussinesq wave model and its application in tsunami research are introduced, including the tsunami propagation, evolution and climbing characteristics along the coastal shelf and the numerical simulation of the actual tsunami process.Aiming at the potential tsunami risk of the Manila trench in the South China Sea, A tsunami early warning method based on multi-buoy observation inversion and numerical simulation is established and a new rapid warning strategy is proposed.The theoretical prediction model of geomagnetic anomalies caused by tsunami waves is discussed and given for the actual tsunami process The spatial and temporal distribution of the abnormal magnetic field.