Theoretical Modeling of Inertial Phenomena in Chaotic Advection Dynamics

本项目致力于发现和模拟开放(大规模)流体流动中惯性粒子输运的基本性质，使用一种新的方法，将非线性动力学和混沌理论的先进方法与拉格朗日流体动力学相结合。大尺度惯性现象是涉及小刚性粒子平流的广泛物理过程的重要问题，由于粒子的大小和密度有限，其运动轨迹可能偏离流体元件的运动轨迹。这项研究将：1)描述惯性效应对单粒子和系综动力学的影响，包括吸引子和空洞的可能形成；2)确定可能导致PI最近发现的粒子和流体参数--二维开放流体流动中重惯性粒子的流体动力学捕获和聚集；3)探索这些结果在涉及惯性粒子的分离、混合和反应过程的情况下的应用。预期的结果包括对惯性现象的系统描述，并将对基础理论和许多应用产生革命性的影响。拟议的研究将有助于促进对降雨形成和行星形成等自然过程潜在机制的理解，以及从化学到环境工程的各种应用。计划的研究活动将涉及一名研究生和本科生，包括来自代表性不足群体的学生。预计该项目还将影响PI关于非线性动力学和混沌的课程，以及他在当地一所公立高中的外联活动。

This project focusses on discovering and modeling fundamental properties of inertial particle transport in open (large-scale) fluid flows, using a novel approach that combines advanced methods from nonlinear dynamics and chaos theory with Lagrangian fluid dynamics. Large-scale inertial phenomena are of significant interest to a wide range of physical processes involving the advection of small rigid particles, whose trajectories may deviate from the trajectories of the fluid elements due to particle finite-size and density. The research will: 1) characterize the impact of inertial effects on single-particle and ensemble dynamics, including the possible formation of attractors and voids; 2) determine the particle and fluid parameters that can lead to the PI's recently discovered fluid-dynamic trapping and clustering of heavy inertial particles in two-dimensional open fluid flows; 3) explore applications of these results to situations involving segregation, mixing, and reactive processes with inertial particles. The expected results include the systematic characterization of inertial phenomena and would be transformative both to the basic theory and the many applications. The proposed research will help advance the understanding of mechanisms underlying natural processes such as rain formation and planet formation, and of applications ranging from chemical to environmental engineering. The planned research activities will involve a graduate student and undergraduate students, including students from underrepresented groups. The project is also expected to impact the PI's course on nonlinear dynamics and chaos and his outreach activities at a local public high school.