Mathematical Sciences: Geophysical Fluid Dynamics

这一建议涉及围绕波-波和波-固体相互作用这一中心概念的海浪流体动力学中的一些重要主题。具体地说，作者将研究倾斜海滩上的波浪反射、参数激发的边缘波、轴对称横波、共振相互作用和Wilton波纹，以及关于表面和内部潮汐耦合的拉普拉斯潮汐方程。对海浪的研究有着悠久的历史，今天它仍然是一个极其重要的研究领域，包括船舶在水中的运动、日潮汐运动和结构。这项提议将涉及研究这些现象的基本数学和物理；从这项研究中获得的理解将具有真正的技术意义。

This proposal concerns a number of important topics in the fluid dynamics of ocean waves revolving around the central concept of wave-wave and wave-solid interactions. Specifically the proposer will study wave reflection on a sloping beach, parametrically excited edge waves, axisymmetric cross-waves, resonant interactions and Wilton's ripples, and the tidal equations of Laplace with regard to the coupling between surface and internal tides. The study of ocean waves has a long and venerable history, and it remains today a vitally important area of research that includes the motion of ships through water, the diurnal tidal motions, and structures. This proposal will involve looking into the underlying mathematics and physics of these phenomena; the understanding gained from this research will have genuine technological significance.