Date of Award

8-9-2006

Degree Type

Dissertation

Degree Name

Ph.D.

Degree Program

Engineering and Applied Science

Department

Physics

Major Professor

Eschenazi, Elia; Ioup, Elias

Second Advisor

Saxton, Ralph

Third Advisor

Ioup, Juliette

Fourth Advisor

Falzarano, Jeffrey

Abstract

Transport rates for the Kelvin-Stuart Cat Eyes driven flow are calculated using the lobe transport theory of Rom-Kedar and Wiggins through application of the Topological Approximation Method (TAM) developed by Rom-Kedar. Numerical studies by Ottino (1989) and Tsega, Michaelides, and Eschenazi (2001) of the driven or perturbed flow indicated frequency dependence of the transport. One goal of the present research is to derive an analytical expression for the transport and to study its dependence upon the perturbation frequency ù. The Kelvin-Stuart Cat Eyes dynamical system consists of an infinite string of equivalent vortices exhibiting a 2ð spatial periodicity in x with an unperturbed streamfunction of H(x, y) = ln(cosh y + A cos x) – ln(1+A). The driven flow has perturbation terms of å sin(ùt) in both the x and y directions. Lobe dynamics transport theory states that transport occurs through the transfer of turnstile lobes, and that transport rates are equal to the area of the lobes transferred. Lobes may intersect, necessitating the calculation and removal of lobe intersection areas. The TAM requires the use of a Melnikov integral function, the zeroes of which locate the lobes, and a Whisker map (Chirikov 1979), which locates lobe intersection points. An analytical expression for the Melnikov integral function is derived for the Kelvin-Stuart Cat Eyes driven flow. Using the derived analytical Melnikov integral function, derived expressions for the periods of internal and external orbits as functions of H, and the Whisker map, the Topological Approximation Method is applied to the Kelvin-Stuart driven flow to calculate transport rates for a range of frequencies from ù = 1.21971 to ù = 3.27532 as the structure index L is varied from L = 2 to L = 10. Transport rates per iteration, and cumulative transport per iteration, are calculated for 100 iterations for both internal and external lobes. The transport rates exhibit strong frequency dependence in the frequency range investigated, decreasing rapidly with increase in frequency.

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The University of New Orleans and its agents retain the non-exclusive license to archive and make accessible this dissertation or thesis in whole or in part in all forms of media, now or hereafter known. The author retains all other ownership rights to the copyright of the thesis or dissertation.

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