Off-campus UMass Amherst users: To download dissertations, please use the following link to log into our proxy server with your UMass Amherst user name and password.
Non-UMass Amherst users, please click the view more button below to purchase a copy of this dissertation from Proquest.
(Some titles may also be available free of charge in our Open Access Dissertation Collection, so please check there first.)
Topics in chaotic flows: Mixing, transition, and aggregation
Abstract
This work focuses on the role of chaotic advection in promoting mixing, transition, and aggregation. We examine the perturbed Kelvin-Stuart cat eye flow as a motivation for introducing a number of different techniques from dynamical systems theory. We then apply these techniques to the analysis of mixing in the vortex pairing flow that develops as a secondary instability. The presence of time-periodicity plays a key role in the enhancement of mixing in both flows. Flow separation plays an essential role in generating chaotic motion of fluids near solid walls. We examine the relationship between flow structure and the dynamic stability of two- and three-dimensional separated flows which are asymptotic approximations of the Navier-Stokes equations. When the Reynolds number reaches a critical value, the field undergoes a time-periodic instability, resulting in chaotic advection. Chaotic advection significantly enhances the mixing and transport characteristics of the flow, and also appears to play a role in the transition to chaos in the velocity field itself. In order to study aggregation in a chaotic flow, a simple model is developed. The presence of chaos is shown to be a necessary condition for widespread aggregation to occur, while the presence of regular regions inhibits aggregation. The fractal dimension of the aggregates formed is shown to depend strongly on the nature of the flow.
Subject Area
Chemical engineering
Recommended Citation
Danielson, Thomas John, "Topics in chaotic flows: Mixing, transition, and aggregation" (1991). Doctoral Dissertations Available from Proquest. AAI9207382.
https://scholarworks.umass.edu/dissertations/AAI9207382