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

主要研究人员将使用发电机理论中的技术来研究在非常大的雷诺数(小粘度)范围内粘性流动的稳定性问题。特别是，他将应用WKB-Maslov类型的渐近方法来解决涡度产生的问题。事实证明，这些方法在研究与“快速”发电机效应有关的类似问题时是有用的。其基本思想是计算导致涡量产生的拉格朗日轨迹，其方法与计算导电流体中产生磁场的李雅普诺夫指数大致相同。在科学上经常使用的一种技术可称为“类比推理”。在这个项目中，主要研究人员将利用粘性流体中涡旋线和导电流体中磁力线的性质之间的类比，利用发电机(磁场产生)理论的思想来研究弱粘性流体中快速涡旋的产生和传播。这项研究与地球内部、大气层和外层空间发生的现象有关。

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.