Collaborative Research: Statistical Mechanics of Turbulence

非技术性考虑湍流流体，例如通过内壁粗糙的管道泵送的石油，在其不规则两岸之间流动的河流，或穿越山区地形的天气锋面。 出于经济原因，风暴预测和公共安全，重要的是要了解湍流摩擦如何将一些流动能量转化为热量。本项目旨在了解这一现象。湍流也是理解混沌行为的沃土。混沌法则支配着流体流动的波动、股票市场的波动以及心脏和大脑的不规则性。 在一组拟议的实验中，混沌和无序的湍流进行了研究。该项目具有很强的教育性。一个相当大的本科生群体在夏天在实验室工作时接受流体动力学的讲座。 事实证明，将混乱的思想引入匹兹堡的学校系统也是可能的。流体流过光滑或粗糙的管道时，会对管壁产生应力. 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。 从临界现象和尺度中汲取灵感，奈杰尔·戈登菲尔德证明了所有已知的测量都可以映射到一条曲线上。 Goldenfeld的方法将用于二维系统的实验测试，即两个平行的，粗糙的垂直金属丝之间的肥皂膜流动。还测量了漂浮在强烈湍流的水箱上的颗粒的运动。 这些浮式仪器在水面采集底层水流的样本。 我们可以把漂浮物的速度发散与熵S联系起来，或者更确切地说，与熵S的速率dS/dt联系起来。这个比率是一个随机变量，并不像在整体中一样为零。 结果将与计算机模拟和“波动定理”，这是一个扩展的波动耗散定理，只适用于系统接近热平衡进行比较。实验为本科生和研究生提供了一个良好的训练平台。

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.