Collaborative Research: Statistical Mechanics of Turbulence

非技术性考虑湍流流体，如通过内壁粗糙的管道泵送的石油，在不规则的河岸之间流动的河流，或穿越山区的天气锋面。出于经济原因、风暴预报和公共安全，了解湍流摩擦如何将部分流动能量转化为热量是很重要的。本项目旨在了解这一现象。湍流也是理解混沌行为的肥沃土壤。混沌定律支配着流体流动的波动、股市的波动以及心脏和大脑的不规则性。在一组拟议的实验中，研究了湍流中的混沌和无序。该项目具有很强的教育性。相当多的本科生在暑期在实验室工作时接受流体力学的讲授。这也证明了将混沌的概念引入匹兹堡学校系统是可能的。技术流体流经光滑或粗糙的管道时会对墙上的墙壁施加压力。由此产生的摩擦损失是雷诺数(Re)和管道粗糙度的非单调函数。奈杰尔·戈登菲尔德从临界现象和定标的观点出发，证明了所有已知的测量结果都可以映射到一条曲线上。戈登菲尔德的方法将被用于二维系统的实验测试，即肥皂膜在两条平行的、粗糙的垂直导线之间的流动。还测量了漂浮在强烈湍动的水箱上的颗粒的运动。这些漂浮物对表面的底层水流进行采样。人们可以将浮子的速度发散与熵S联系在一起，或者更确切地说，它的速率DS/dt。这个速率是一个随机变量，不像整体一样等于零。结果将与计算机模拟和“涨落定理”进行比较，“涨落定理”是涨落-耗散定理的扩展，仅适用于接近热平衡的系统。这些实验为本科生和研究生提供了一个很好的训练场地。

Non-technicalConsider a turbulent fluid such as oil pumped through a pipeline with a rough interior wall, a river flowing between its irregular banks, or a weather front crossing mountainous terrain. For economic reasons, for storm prediction, and for public safety it is important to understand how turbulent friction converts some of the flow energy into heat. This project is aimed at understanding this phenomenon. Turbulence is also a fertile ground of understanding chaotic behavior. The laws of chaos govern fluctuations in fluid flow, stock market gyrations, and irregularities of the heart and the brain. In one set of proposed experiments, chaos and disorder are investigated in turbulent flows. The project has a strong educational element. A sizeable group of undergraduates receive lectures in fluid dynamics as they work in the laboratory during the summer. It has also proved possible to introduce ideas of chaos into the Pittsburgh school system.TechnicalFluid flowing through smooth or roughened pipes exert stress on the on the wall. The resulting frictional loss is a non-monotonic function of the Reynolds number (Re) and the pipe roughness. Drawing on ideas from critical phenomena and scaling, Nigel Goldenfeld has shown that all known measurements can be mapped into a single curve. Goldenfeld's approach will be put to an experimental test for a two-dimensional system, namely the flow of a soap film between two parallel, roughened vertical wires. Measurements are also made of the motion of particles that float on a strongly turbulent tank of water. These floaters sample the underlying flow at the surface. One can relate the velocity divergence of the floaters to the entropy S, or rather its rate dS/dt. This rate is a random variable and not identically zero as in the bulk. The results will be compared with computer simulations and with the "fluctuation theorem", which is an extension of the fluctuation-dissipation theorem, applicable only to systems near thermal equilibrium. The experiments provide a good training ground for both undergraduates and graduate students.