iii To my family iv Acknowledgements I would like to first express my deepest gratitude to my advisor, Professor Dale Pullin, who provided a chance to work on exciting and fulfilling research projects. I sincerely appreciate his incredible patience in teaching me the fundamental process of research in the computational fluid dynamics of turbulence. I am also grateful for his understanding my pursuing a minor in Applied & Compu-tational Mathematics, which helped me expand my intellectual horizon. Being honored to be one of his students, I could not have asked for a better advisor. I also gratefully acknowledge the help-ful comments and suggestions on my thesis from the members of my thesis committee, Professors Beverley McKeon, Tim Colon...