Mathematical Sciences: Dynamo Theory Methods for Vorticity Generation in Viscous Fluids

主要研究者将研究稳定性问题， 在非常大的雷诺数（小雷诺数）的限制下的粘性流 粘度）使用来自发电机理论的技术。 特别是， 他将应用WKB-马斯洛夫型的渐近方法， 涡度生成的问题。 这些方法已经证明 在研究与“快”有关的类似问题时很有用 发电机效应 基本思想是计算拉格朗日量 轨道负责涡产生的大部分 就像计算李雅普诺夫指数一样 用于在导电材料中产生磁场 流体. 科学中经常使用的一种技术可以称为 “类比推理”。 在这个项目中，校长 研究人员将使用旋涡性质之间的类比， 粘性流体中的线和电介质中的磁力线 传导流体来研究快速的 在轻微粘性流体的旋涡，利用的想法， 发电机（磁场产生）理论。 这项研究 与地球内部发生的现象有关， 大气层和外层空间。

The principal investigator will study stability problems for viscous flows in the limit of very large Reynolds numbers (small viscosities) using techniques from dynamo theory. In particular, he will apply asymptotic methods of the WKB-Maslov type to problems in vorticity generation. Such methods have proved useful in studying analogous problems related to the "fast" dynamo effect. The basic idea is to calculate the Lagrangian trajectories responsible for the vorticity generation in much the same way that one calculates the Lyapunov exponents responsible for the generation of magnetic fields in electrically conducting fluids. A technique that is used often in science may be called "reasoning by analogy". In this project the principal investigator will use analogies between the properties of vortex lines in viscous fluids and magnetic lines in electrically conducting fluids to study the generation and propagation of fast vortices in slightly viscous fluids by making use of ideas from dynamo (magnetic field generation) theory. The research has relevance to phenomena that occur inside the earth, in the atmosphere and in outer space.