Effects of Spatial Inhomogeneity on Nonlinear Pattern Forming Systems

本文研究了热驱动对流和泰勒涡流(TVF)中空间不均匀的影响。研究将同时考虑多孔介质对流(PMC)和瑞利-贝纳德对流(RBC)。PMC上的实验将继续探索介质空间结构对模式选择和稳定性的影响-以及随之而来的对热量和杂质传输的影响，通常是很大的。这项工作将把模式选择与孔结构联系起来，对于纯流体和二元混合物。关于红细胞，实验将涉及层厚度和温度分布的水平变化。相关实验将解决泰勒涡流(TVF)中的类似效应，其中内、外圆柱之间的径向间隙(Delta)R是变化的。这种流动的优点是，第一个图案形成不稳定性(仅当内筒旋转时)是沿圆柱轴对齐的滚动-因此，消除了方向退化的复杂情况。可以预见，对不同的水动力系统进行实验，以不同的方式控制空间变化，将对空间变化对这种流动的影响产生更广泛的洞察。在过去，已经有一些工作集中在参数的缓慢空间变化或周期变化上，但对宽带随机空间变化的影响的研究很少，而宽带随机空间变化是PMC的一个特别重要的问题。这项工作有许多重要的应用，包括热传递装置、绝缘和当存在温度或浓度梯度时地下水中污染物的流动。在大多数涉及热流和质流的实际应用中，系统与通常研究的理想化相去甚远，并且需要更多关于不完美系统的信息。最近发展起来的实验技术将使实验人员能够在PMC中非侵入性地成像图案，从而对介质结构对图案选择的影响产生重要的新的见解。粒子成像测速技术(PIV)将用于TVF的研究。

This is an investigation of the effects of spatial inhomogeneities in both thermally driven convection and Taylor vortex flow (TVF). The investigation will consider both porous media convection (PMC) and Rayleigh-Benard convection (RBC). The experiments on PMC will be a continued exploration of the effects of media spatial structure on both pattern selection and stability-and the consequent, often large, effects on heat and impurity transport. This work will relate pattern selection to pore structure, for both pure fluids and binary mixtures. Regarding RBC, the experiments will involve horizontal variations in both the layer thickness and in the temperature profile. Related experiments will address similar effects in Taylor vortex flow (TVF) where the radial gap, (delta)R, between the inner and outer cylinder varies. The advantage of this flow is that the first pattern-forming instability (when only the inner cylinder rotates) is to rolls aligned along the cylinder axis-therefore, the complications of directional degeneracy are removed. It is envisioned that experiments on different hydrodynamic systems with control over spatial variations in different ways, will yield broad insight into the effects of spatial variations on such flows. In the past, there has been some work focusing on slow spatial variations of parameters or periodic variation of parameters, but very little on the effects of broad-band random spatial variations, a particularly important issue for PMC. There are a number of important applications for this work including heat transfer devices, insulation, and the flow of contaminants in ground water when there are temperature or concentration gradients. In most practical applications involving heat and mass flows, the systems are far from the usually studied idealizations, and the need for more information on imperfect systems is considerable. Recently developed experimental techniques will allow experimenters to non-invasively image patterns in PMC, leading to im portant new insights into the effects of the medium structure on pattern selection. Particle imaging velocimetry (PIV) will be used to study TVF.