Disturbances in stratified fluids and solids

点击翻译按钮获取中文摘要

Predicting the movement of a disturbance in a fluid or solid whose properties vary rapidly poses considerably more of a challenge than the equivalent problem in homogeneous materials. The inhomogeneities can arise through changes in geometry or of material properties. A combination of perturbation and numerical techniques will be used to investigate a variety of propagation problems in strongly stratified materials. These include high-pressure acoustic oscillations, flows in coastal aquifers, disturbances in functionally graded materials, and the evolution of Kelvin-Helmholtz (KH) instabilities. 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 geometry, stratification and nonlinearity. The intent is to extend these concepts to problems with different geometries and boundary conditions. Coastal aquifers have a dynamic seaward boundary at the coastline that is influenced by oceanic water level fluctuations. The dynamics of these groundwater flows are important for erosion and saltwater intrusion. Natural variations in properties such as hydraulic conductivity and soil porosity mean that the full equations describing flows in aquifers contain variable coefficients. This will be the first systematic attempt to understand the effects of large inhomogeneities on tidal propagation in coastal aquifers. Materials with continuously varying spatial properties are termed functionally graded materials. Our investigation will consider the effects of material inhomogeneities on diffusion and wave-like problems. For wave problems the effect of nonlinearity has the potential to produce shocks. The effects of the stratification and whether different forms of strong stratification can inhibit shocks formation can then be examined. The evolution of KH instabilities at different stages of their life cycle will be examined for Prandtl and Reynolds numbers varying over three decades. Simulation of KH instabilities with Prandtl numbers representing the salinity stratification in the ocean will be considered for the first time.