Waves in fluids and solids

我们将结合摄动和数值技术来研究各种有实际意义的波传播问题。其范围从海洋沉积物中的液化，到高压声波振荡，以及沿海含水层中的流动。液化可导致海洋结构物失效，如失去海床的支撑力，造成稳定性问题。一个目标是通过为不同的土壤情况建立模型来探索渐进液化的机制。沙质海滩地下水动力学知识对侵蚀和咸水入侵很重要。建议考虑土壤层化对地下水位波动的影响。从湖泊和尾矿库底部的悬浮泥层中重新悬浮物质可能具有实际意义。一种机制是由于表面波运动，在浮泥和上覆水之间的界面上产生波。需要研究的课题是非线性和粘性区域中的相互作用，以及由于波浪破碎而产生的质量扩散。当水从分层水库抽出时，低流量时的水流被限制在水槽附近的窄层内。这种现象被称为选择性退出，被用作一种管理技术，用于提供所需质量的水。地形特征，如收缩或基床，会影响流出水质。一个目标是量化地形对退出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震动气体振荡很感兴趣。在没有冲击的情况下，相同的能量输入会产生更高的压力。要解释这一现象，挑战在于理解几何与非线性之间的相互作用。其目的是将这些概念扩展到球面几何问题，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 When water is withdrawn from a stratified reservoir, the flow at low discharges is confined to a narrow layer adjacent to the sink.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.