水波动力学研究进展

ADVANCES IN WATER WAVE MECHANICS

水波动力学，历史悠久，内容丰富，此文仅进行简要的历史回顾，以阐明其进展的思想、智慧、途径以及这门学科对其它学科进展的贡献和影响．随后，引进一个新理论，能模拟三维、非定常、有完全非线性和频散（或色散）性的重力毛细波，在深度任变的水中传播和演化的现象．此外，对二维水波在海滩上之涨落问题，提供一个Ｌａｇｒａｎｇｅ－Ｅｕｌｅｒ观点相结合的精确计算方法，以供读者推广和应用，此外，对外力作用下的水波系统共振现象，作些补充论述．

This article first gives a brief review on the history of various approaches of modeling water waves based on differing emphases on the main physical parameters involved. It presents a unified theory for modeling unsteady, three-dimensional, fully nonlinear and fully dispersive gravity-capillary waves in water of variable depth. Also presented is a Lagrangian-Eulerian hybrid numerical method for evaluating run-ups of nonlinear waves on sloping beach. Applications of these methods are illustrated with several problems of fundamental significance.