Stochastic Analysis of Vortex Filaments

BessaihDMS-0608494 研究人员研究随机涡丝及其与湍流的关系。 她开发了一个严格的随机描述的细丝结构，研究conventientdynamics，并检查平均场限制相互作用vortexfilaments和它们的关系，欧拉方程。 布朗半鞅是在其它随机涡丝研究中受到较多关注的随机过程，本文考虑了具有多重分形结构或不连续性特征的随机过程的推广。湍流的根本问题是根本性的。 学生们参与了这个项目。 随机涡丝--粗略地说，在随机过程的影响下运动的流体的涡管--是流体运动的模型，可以揭示流体流动中湍流的发展和演变。 研究人员研究随机涡丝，考虑他们的结构，他们的动力学，行为的大集合ofvortex丝，和他们的关系，欧拉方程，一个著名的流体流动模型。 学生们参与了这个项目。 更好的流体湍流数学模型将有助于更好地理解湍流的机理。 这反过来将提高我们对大气和海洋环流的理解，可能对天气预报产生影响，以及工程应用中的流体流动，例如设计更快，更经济的船舶，飞机和车辆。

BessaihDMS-0608494 The investigator studies random vortex filaments and theirrelationship to turbulent flows. She develops a rigorousstochastic description of filament structures, studies filamentdynamics, and examines mean field limits for interacting vortexfilaments and their relation to the Euler equations. WhileBrownian semimartingales are the stochastic processes that havereceived more attention in other studies of random vortexfilaments, here extension to stochastic processes withmultifractal structure or intermittency features is considered. The underlying problem of turbulence is fundamental. Studentsare involved in the project. Random vortex filaments -- roughly speaking, vortical tubesof fluid moving under the influence of a random process -- are amodel for the motion of fluids that could shed some light on thedevelopment and evolution of turbulence in fluid flows. Theinvestigator studies random vortex filaments, considering theirstructure, their dynamics, the behavior of large collections ofvortex filaments, and their relationship to the Euler equations,a well-known model of fluid flows. Students are involved in theproject. Better mathematical models of turbulence in fluid flowscould lead to a better understanding of the mechanisms ofturbulence. This in turn would improve our understanding ofatmosphere and ocean circulation, with possible consequences forweather prediction, and of fluid flows in engineeringapplications, such as the design of faster and more economicallyoperated ships, planes, and vehicles.