Disturbances in stratified fluids and solids

预测性质变化迅速的流体或固体中的扰动运动比均匀材料中的等效问题更具挑战性。不均匀性可以通过几何形状或材料性质的变化而产生。微扰和数值技术的结合将被用来调查各种传播问题在强分层材料。这些包括高压声振荡，在沿海含水层的流动，功能梯度材料的扰动，和开尔文-亥姆霍兹（KH）不稳定性的演变。 最近人们对在特殊形状的容器中产生高压无冲击气体振荡很感兴趣。在没有冲击的情况下，对于相同的能量输入，会产生更高的压力。在解释这一现象时，面临的挑战是理解几何、分层和非线性之间的相互作用。其目的是将这些概念扩展到具有不同几何形状和边界条件的问题。 沿海含水层在海岸线有一个动态的向海边界，受海洋水位波动的影响。这些地下水流的动态对侵蚀和盐水入侵很重要。水力传导率和土壤孔隙度等性质的自然变化意味着描述含水层流动的完整方程包含可变系数。这将是第一次系统地尝试了解沿海含水层中大的不均匀性对潮汐传播的影响。 具有连续变化的空间特性的材料被称为功能梯度材料。我们的研究将考虑材料的不均匀性对扩散和波动问题的影响。对于波动问题，非线性效应有可能产生冲击。然后可以检验分层的影响以及不同形式的强分层是否能够抑制冲击的形成。 KH不稳定性在其生命周期的不同阶段的演变将检查普朗特和雷诺数变化超过三十年。模拟KH不稳定性与普朗特数代表在海洋中的盐度分层将被认为是第一次。

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.