Mathematical Sciences: Topics in Hydrodynamics and Magnetohydrodynamics

研究人员与M. M.维希克 芝加哥大学，将继续调查的主题， 流体动力学 她使用逆散射技术来获得 欧拉方程的解决方案，管理流动的一个 不可压缩无粘性流体 这项工作遵循一个宽松的 对公式的欧拉方程推导的 调查员和维希克 她还建议将发电机 理论技术，以扩大适用性的不稳定性 她和Vishik最近获得的标准， 线性化流体方程 调查员将继续她的 检查，通过使用汉密尔顿技术， 三维轴对称稳定性/不稳定性 磁流体动力学平衡 本研究的主要主题涉及以下标准 不稳定性的存在（即，当一个小的变化， 稳定构型随时间变得越来越大。 流体 不稳定性是决定 许多重要的物理系统。 例如，所谓的 斜压不稳定控制着大尺度环流， 大气;对流不稳定性在 海气相互作用及其对可能的全球气候的影响 变暖;磁流体动力学不稳定性的基础 等离子体聚变现象;地球和 太阳磁场取决于发电机的不稳定性。 的 研究者对流体方程的数学分析 运动导致了具体标准的存在， 某些类型的不稳定性和她提出的研究将 继续推进我们对行为的理解 地球物理和天体物理流体。

The investigator, in collaboration with Dr. M. M. Vishik of University of Chicago, will continue to investigate topics in fluid dynamics. She uses inverse scattering techniques to obtain solutions to the Euler equations that govern the flow of an incompressible, inviscid fluid. This work follows from a Lax pair formulation for the Euler equations derived by the investigator and Vishik. She also proposes to apply dynamo theory techniques to extend the applicability of the instability criteria that she and Vishik have recently obtained for the linearized fluid equations. The investigator will continue her examination, via the use of Hamiltonian techniques, of the stability/instability of three dimensional axisymmetric magnetohydrodynamic equilibria. The primary subject of this research concerns criteria for the existence of instabilities (i.e., when a small change in a steady configuration becomes larger and larger with time.) Fluid instabilities are crucial factors in determining the behavior of many important physical systems. For example, the so called baroclinic instability governs the large scale circulation of the atmosphere; convective instabilities play an important role in air-sea interaction with implications for possible global warming; magnetohydrodynamic instabilities underlie the phenomenon of plasma fusion; the existence of terrestrial and solar magnetic fields is dependent on dynamo instabilities. The investigator's mathematical analysis of the equations of fluid motion has led to specific criteria governing the existence of certain types of instabilities and her proposed research will continue to advance our understanding of the behavior of geophysical and astrophysical fluids.