Mathematical Sciences: Comparative Study of Waves in Fluids and Plasmas

首席研究员将研究均衡 流体和等离子体中的结构、不稳定性和波动。 特别是，他将重点关注已知的流体结构， 如具有漩涡的涡环和它们的等离子体对应物， 等离子体环 这样的平衡构型来自于 变分原理，首席研究员将采用 研究稳定性的古老的几何光学方法 这些平衡态的性质。 为了准确地研究内部流体的行为， 地球的核心，人们必须认识到， 在许多情况下，核心内的流体 像等离子体（电离流体）比普通的气体和液体。 在这个项目中，首席研究员将首先做一个 平衡结构及其稳定性的比较研究 在流体和等离子体中。 然后，他将这些结果应用于 描述小振幅扰动的长期演变 到稳定的涡环和等离子体环面的类型中发现的 地球的核心。

The principal investigator will study equilibrium configurations, instabilities and waves in fluids and plasmas. In particular, he will focus attention on fluid structures known as vortex rings with swirl and their plasma counterparts known as plasma tori. Such equilibrium configurations are derived from a variational principle, and the principal investigator will employ the venerable method of geometric optics to study the stability properties of these equilibrium states. In order to study accurately the behavior of fluids within the core of the earth one must appreciate the fact that under many sets of circumstances the fluids within the core act more like plasmas (ionized fluids) than ordinary gases and liquids. In this project the principal investigator will first make a comparative study of equilibrium structures and their stability in both fluids and plasmas. Then he will apply these results to describe the long-term evolution of small-amplitude perturbations to stable vortex rings and plasma tori of the type found in the earth's core.