Theoretical Modeling of Inertial Phenomena in Chaotic Advection Dynamics

本项目主要研究开放（大尺度）流体流动中惯性粒子输运的基本特性，采用一种新颖的方法，将非线性动力学和混沌理论与拉格朗日流体动力学相结合。大尺度惯性现象对于涉及小刚性颗粒平流的广泛物理过程具有重要意义，由于颗粒的大小和密度有限，这些小刚性颗粒的轨迹可能偏离流体元件的轨迹。研究将：1)描述惯性效应对单粒子和系综动力学的影响，包括可能形成的吸引子和空洞；2)确定可能导致PI最近发现的二维开放流体流动中重惯性粒子的流体动力学捕获和聚类的粒子和流体参数；3)探索这些结果在涉及分离、混合和惯性粒子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表征，对基础理论和许多应用都将是革命性的。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的机制的理解，以及从化学到环境工程的应用。计划中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。该项目还有望影响PI的非线性动力学和混沌课程，以及他在当地一所公立高中的推广活动。

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.