Waves in fluids and solids

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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 When water is withdrawn from a stratified reservoir, the flow at low discharges is confined to a narrow layer adjacent to the sink.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.