Citation
Hill, David J. (1998) Part I. Vortex dynamics in wake models. Part II. Wave generation. Dissertation (Ph.D.), California Institute of Technology. http://resolver.caltech.edu/CaltechETD:etd04052007141032
Abstract
In Part I, steady wakes in inviscid fluid are constructed and investigated using the techniques of vortex dynamics. As a generalization of Foppl's flow past a circular cylinder [5], a steady solution is given for flow past an elliptical cylinder of arbitrary aspect ratio (perpendicular or parallel to the flow at infinity) with a bound wake of two symmetric recirculating eddies in the form of a point vortex pair. Linear stability analysis predicts an asymmetric instability and the symmetric nonlinear evolution is discussed in terms of a KirchhoffRouth path function. The wake behind a sphere is represented by a thin cored vortex ring of arbitrary internal structure. Steady configurations are obtained and longwavelength perturbations to the ring centerline identify a tilting instability. A generalization of the Kirchhoff Routh function to an axisymmetric flow consisting of vortex rings and a body is presented. Using conformal maps and point vortices, translating symmetric twodimensional bubbles with a vortex pair wake are constructed. An instability in which the bubble and vortex pair tilt away from each other is found as well as a symmetric oscillatory instability. The crosssection of a trailing vortex pair immersed in a cross stream shear is represented by two counterrotating vortex patches. Numerical and analytical analyses are provided. The method of Schwarz functions as introduced by Meiron, Saffman and Schatzman [13] is used in the computation and stability analysis of steady patch shapes. Excellent agreement is obtained using an elliptical patch model. An instability essentially isolated to a single patch is identified, the nonlinear evolution of the elliptical patch model suggests that the patch whose fluid elements rotate against the shear will be destroyed.
Part II examines a possible mechanism for the generation of water waves which arises from the instability of an initially planar free surface in the presence of a parallel, sheared, inviscid flow. A twodimensional steady flow comprised of exponential profiles representing both wind and a drift layer in the water is infinitesimally perturbed. The resulting Rayleigh equation is analytically solved by mean of Hypergeometric functions and the dispersion relation is implicitly defined as solutions of a transcendental equation; stability boundaries are determined and growth rates are calculated. Comparisons are made with the simpler model of Caponi et al. [2] which uses piecewise linear profiles.
Item Type:  Thesis (Dissertation (Ph.D.)) 

Degree Grantor:  California Institute of Technology 
Division:  Engineering and Applied Science 
Major Option:  Applied And Computational Mathematics 
Thesis Availability:  Public (worldwide access) 
Research Advisor(s): 

Thesis Committee: 

Defense Date:  20 May 1998 
Record Number:  CaltechETD:etd04052007141032 
Persistent URL:  http://resolver.caltech.edu/CaltechETD:etd04052007141032 
Default Usage Policy:  No commercial reproduction, distribution, display or performance rights in this work are provided. 
ID Code:  1274 
Collection:  CaltechTHESIS 
Deposited By:  Imported from ETDdb 
Deposited On:  05 Apr 2007 
Last Modified:  26 Dec 2012 02:36 
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