Dynamics of a class of vortex rings
Abstract
The contour dynamics method is extended to vortex rings with vorticity varying linearly from the symmetry axis. An elliptic core model is also developed to explain some of the basic physics. Passage and collisions of two identical rings are studied focusing on core deformation, sound generation and stirring of fluid elements. With respect to core deformation, not only the strain rate but how rapidly it varies is important and accounts for greater susceptibility to vortex tearing than in two dimensions. For slow strain, as a passage interaction is completed and the strain relaxes, the cores return to their original shape while permanent deformations remain for rapidly varying strain. For collisions, if the strain changes slowly the core shapes migrate through a known family of two-dimensional steady vortex pairs up to the limiting member of the family. Thereafter energy conservation does not allow the cores to maintain a constant shape. For rapidly varying strain, core deformation is severe and a head-tail structure in good agreement with experiments is formed. With respect to sound generation, good agreement with the measured acoustic signal for colliding rings is obtained and a feature previously thought to be due to viscous effects is shown to be an effect of inviscid core deformation alone. For passage interactions, a component of high frequency is present. Evidence for the importance of this noise source in jet noise spectra is provided. Finally, processes of fluid engulfment and rejection for an unsteady vortex ring are studied using the stable and unstable manifolds. The unstable manifold shows excellent agreement with flow visualization experiments for leapfrogging rings suggesting that it may be a good tool for numerical flow visualization in other time periodic flows.
Additional Information
Apart from minor modifications, this work is a doctoral thesis submitted to Stanford University. I wish to express here my gratitude to my advisors and colleagues. A thesis rarely embodies the work and ideas of a single individual and during writing I fondly recalled how a colleague helped me through a difficult point, corrected my faulty reasoning, suggested a fresh interpretation or struggled for me through a derivation. For their help I would like to thank Tanios Honein, Drs. Moon Joo Lee, Sanjiva Lele, Yen Liu, Nagi Mansour, Robert Moser, Eugene Pak, Ugo Piomelli, Bart Singer and Philippe Spalart. My understanding of dynamical systems theory benefited greatly from a study group with Marouhn Aboudi and Tanios Honein. Without the friendship and encouragement of Dr. Sharon Stanaway and Gary Coleman, completion of the manuscript would not have been possible. I am extremely fortunate to have had two advisors. I am grateful to Prof. Joel Ferziger for his guidance in keeping this work focussed, for his encouragement during the wanderings and dry periods and for his careful editing of the manuscript. Prof. Anthony Leonard had the knack for taking my vague and confused ideas and sharpening them but still making it seem that I had known the answer all along. That encouragement really helped. I appreciate the unsung effort of Prof. Brian Cantwell in serving on my reading committee. Dr. Philippe Spalart not only launched the work in the direction that it took (see §1.5) but provided several ideas and critically reviewed the manuscript. For its tonal quality and style, this work owes a lot to the work of Prof. Norman Zabusky. In addition, during his stay he provided several interpretations of the results, new diagnostics and tests which then led to further insight. I am indebted to Dr. Vered Rom-Kedar, Profs. Steve Wiggins and Anthony Leonard whose results and methods provided the inspiration for the work in Chapter 6. Profs. T. Matsui, Y. Oshima, B. Sturtevant and H. Yamada kindly sent me their experimental photographs whenever I requested them, many of them unpublished, or allowed their reproduction. Financial support, computer and other resources were provided by NASA Ames Research Center under grant NCA 2-OR745-313 and the Co-op Program enabled completion of coursework requirements. Partial support during my Masters year was provided by the Aga Khan Foundation. I would like to dedicate this work to my parents Rajab and Nür, to their love and sacrifice, to my father's love of learning and eclecticism and to my mother's hard work yet tender nurturance. Thornton Wilder has said that "the impulses of love return to the love that made them." Let this work be a token of that return. K.S.Files
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2006-08-07Created from EPrint's datestamp field
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2019-10-02Created from EPrint's last_modified field
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