Waves in fluids and solids

微扰和数值技术的结合将用于研究各种实际感兴趣的波传播问题。从海洋沉积物的液化，到高压声波振荡，以及沿海含水层的流动。液化会造成海洋结构的破坏，如海底失去支撑力，造成稳定性问题。一个目标是通过建立不同土壤情况的模型来探索渐进液化的机制。了解沙质海滩的地下水动力学对侵蚀和盐水入侵具有重要意义。建议考虑土壤分层对地下水位波动的影响。湖泊和尾矿库底部流体泥浆层中物质的再悬浮具有重要的实际意义。一种机制是由于表面波运动在流体泥浆和上覆水之间的界面上产生波浪。需要研究的主题是非线性和粘性状态下的相互作用，以及波浪破碎引起的质量扩散。当水从分层水库中抽出时，低流量的水流被限制在靠近水池的一个狭窄的层内。这种现象被称为选择性取水，它被用作一种管理技术，以供应具有所需质量的水。地形特征，如收缩或静止会影响流出物的质量。目标是量化地形对提取层厚度和密度的影响。最近，人们对在特殊形状的容器中产生高压无冲击振荡的气体产生了兴趣。在没有冲击的情况下，同样的能量输入会产生更高的压力。在解释这种现象时，挑战在于理解几何与非线性的相互作用。目的是将这些概念扩展到球面几何问题中，例如考虑球壳中非均匀气体的振荡。

A combination of perturbation and numerical techniques will be used to investigate a variety of wave propagation problems of practical interest. These range from liquefaction in marine sediments, to high-pressure acoustic oscillations, and flows in coastal aquifers. Liquefaction can cause the failure of marine structures, such as the loss of supporting power of the seabed, causing stability problems. One objective is to explore the mechanism of progressive liquefaction by developing models for different soil situations. Knowledge of groundwater dynamics in sandy beaches is important for erosion and saltwater intrusion. It is proposed to consider the effects of soil stratification on water table fluctuations. Re-suspension of material from the layers of fluid mud at the bottom of lakes and mine-tailings ponds can be of practical importance. One mechanism is the generation of waves at the interface between the fluid mud and the overlying water due to surface wave motion. Topics that need examination are the interaction in the nonlinear and viscous regimes, and mass diffusion due to wave breaking. When water is withdrawn from a stratified reservoir, the flow at low discharges is confined to a narrow layer adjacent to the sink. This phenomenon, known as selective withdrawal, is used as a management technique for the supply of water with desired qualities. Topographic features such as a contraction or a sill affect the outflow quality. A goal is to quantify the effects of topography on the thickness and density of the withdrawal layer. There has been interest recently in producing high-pressure shockless oscillations of gasses in specially shaped containers. With no shocks, higher pressures result for the same energy input. In explaining this phenomenon, the challenge is to understand the interaction of the geometry with the nonlinearity. The intent is to extend these concepts to problems with spherical geometry, for example considering oscillations of an inhomogeneous gas in a spherical shell.