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PART I - VISCOUS EVOLUTION OF POINT VORTEX EQUILIBRIA
PART II - EFFECTS OF BODY ELASTICITY ON STABILITY OF FISH
MOTION
by
Fangxu Jing
A Dissertation Presented to the
FACULTY OF THE USC GRADUATE SCHOOL
UNIVERSITY OF SOUTHERN CALIFORNIA
In Partial Ful llment of the
Requirements of the Degree
DOCTOR OF PHILOSOPHY
(AEROSPACE ENGINEERING)
August 2011
Copyright 2011 Fangxu Jing
Object Description
| Title | Part I: Viscous evolution of point vortex equilibria; Part II: Effects of body elasticity on stability of fish motion |
| Author | Jing, Fangxu |
| Author email | fjing@usc.edu;jingfangxu@gmail.com |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Aerospace Engineering |
| School | Viterbi School of Engineering |
| Date defended/completed | 2011-08-09 |
| Date submitted | 2011-08-08 |
| Date approved | 2011-08-08 |
| Restricted until | 2011-08-08 |
| Date published | 2011-08-08 |
| Advisor (committee chair) | Kanso, Eva |
| Advisor (committee member) |
Newton, Paul K. Flashner, Hendryk Friedlander, Susan Redekopp, Larry |
| Abstract | Vortex dynamics and solid-fluid interactions are two of the most important and most studied topics in fluid dynamics for their relevance to a wide range of applications from geophysical flows to locomotion in moving fluids. In this work, we investigate two problems in two parts: Part I studies the viscous evolution of point vortex equilibria; Part II studies the effects of body elasticity on the passive stability of submerged bodies. ❧ In Part I, we describe the viscous evolution of point vortex configurations that, in the absence of viscosity, are in a state of fixed or relative equilibrium. In particular, we examine four cases, three of them correspond to relative equilibria in the inviscid point vortex model and one corresponds to a fixed equilibrium. Our goal is to elucidate the dominant transient dynamical features of the flow. A multi- Gaussian “core growing” type of model is typically used in high fidelity numerical simulations, but we propose to implement it as a low-order model for the flow field. We show that all four configurations immediately begin to rotate unsteadily. We then examine in detail the qualitative and quantitative evolution of the structures as they evolve, and for each case show the sequence of topological bifurcations that occur both in a fixed reference frame, and in an appropriately chosen rotating reference frame. Comparisons between the cases help to reveal different features of the viscous evolution for short and intermediate time scales of vortex structures. We examine the dynamical evolution of passive particles in the viscously evolving flows and interpret it in relation to the evolving streamline patterns. Although the low-order multi-Gaussian model does not exactly coincide with the Navier-Stokes solution, the two results show remarkable resemblances in many aspects. ❧ In Part II, we examine the effects of body geometry and elasticity on the passive stability of motion in a perfect fluid. Our main motivation is to understand the role of body elasticity on the stability of fish swimming. The fish is modeled as an articulated body made of N links (assumed to be identical ellipses in 2D or identical ellipsoids in 3D) interconnected by hinge joints. It can undergo shape changes by varying the relative angles between the links. Body elasticity is accounted for via the torsional springs at the joints. The unsteadiness of the flow is modeled using the added mass effect. Equations of motion for the body-fluid system are derived using Newtonian and Lagrangian approaches for both hydrodynamically decoupled and coupled models in 2D and 3D. We specifically examine the stability associated with a relative equilibrium of the equations, traditionally referred to as the “coast motion” (proved to be unstable for a rigid elongated body model), and found that body elasticity does stabilize the system. Stable regions are identified based on linear stability analysis in the parameter space spanned by aspect ratio (body geometry) and spring constants (muscle stiffness), and the findings based on the linear analysis are verified by direct numerical simulations of the nonlinear system. Our result shows that even in the absence of fin movement and vortex interaction, shape change and muscle elasticity allow stable conditions of the coast motion. |
| Keyword | vortex dynamics; fish stability |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m |
| Rights | Jing, Fangxu |
| Access conditions | The author retains rights to his/her dissertation, thesis or other graduate work according to U.S. copyright law. Electronic access is being provided by the USC Libraries in agreement with the author, as the original true and official version of the work, but does not grant the reader permission to use the work if the desired use is covered by copyright. It is the author, as rights holder, who must provide use permission if such use is covered by copyright. The original signature page accompanying the original submission of the work to the USC Libraries is retained by the USC Libraries and a copy of it may be obtained by authorized requesters contacting the repository e-mail address given. |
| Repository name | University of Southern California Digital Library |
| Repository address | USC Digital Library, University of Southern California, University Park Campus MC 7002, 106 University Village, Los Angeles, California 90089-7002, USA |
| Repository email | cisadmin@usc.edu |
| Archival file | uscthesesreloadpub_Volume71/etd-JingFangxu-258.pdf |
Description
| Title | Page 1 |
| Full text | PART I - VISCOUS EVOLUTION OF POINT VORTEX EQUILIBRIA PART II - EFFECTS OF BODY ELASTICITY ON STABILITY OF FISH MOTION by Fangxu Jing A Dissertation Presented to the FACULTY OF THE USC GRADUATE SCHOOL UNIVERSITY OF SOUTHERN CALIFORNIA In Partial Ful llment of the Requirements of the Degree DOCTOR OF PHILOSOPHY (AEROSPACE ENGINEERING) August 2011 Copyright 2011 Fangxu Jing |
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