Acknowledgements

It is my pleasure to acknowledge my teachers and fellow students for their contribution to this work and their friendship over the past years.

It is my privilege to thank my advisor Prof. Van Dommelen for his excellent guidance in bringing this work to its present form. I also thank him for contributing subsections 8.2.7 and 8.2.8.

My sincere thanks to him and to Prof. Lourenco for providing the financial support through a grant provided by the Air Force Office of Scientific Research (AFOSR).

I appreciate Prof. Tam's continued interest in my progress. I also appreciate his guidance during my early years as a graduate student in the mathematics department.

Prof. Shih provided me an opportunity to work with him in experimental fluid mechanics. I appreciate his guidance and friendship.

I thank Prof. Hollis for graciously accepting to serve on my committee.

It is a pleasure to thank Prof. Krothapalli for his constant support in many ways and for his lively friendship during all these years.

Zhong Ding provided the experimental data in figure 8.20(a) obtained at our Fluid Mechanics Research Laboratory (FMRL). He also cheerfully let me use his computer facilities at any time.

Many people from other universities graciously shared with me their computational data: Prof. Paul Fischer and Jerry Kruse (Center for Fluid Mechanics, Brown University) provided their data in figure 8.21(a). Dr. Petros Koumoutsakos (NASA Ames and Center for Turbulence Research at Stanford University) provided the figure 8.22(a). Doug Shiels (Caltech) continued some of the earlier computations of Dr. Koumoutsakos and shared with me many of his computational results, in addition to that in figure 8.35. Dr. X.-H. Wu (Caltech) provided the data in figures 8.15 and 8.28.

The Supercomputer Computations Research Institute (SCRI) at the Florida State University (FSU) was instrumental in providing the computer time and many other facilities that made this work possible. I also thank the SCRI personnel for their help; in particular, Eric Pepke helped me with the SciAn software used to create the color figures in this work.

I appreciate the administrative assistance given to me by all of our personnel at the Mechanical Engineering department and FMRL.

Many thanks to all the sleuths at our FSU interlibrary loan department for their excellent job in tracking down all my requests over these years.

Thank you all !.