Swimming without a Spine: Hydrodynamics and Swimming Performance of some Marine Invertebrates By Zhuoyu Zhou A dissertation submitted to Johns Hopkins University in conformity with the requirements for the degree of Doctor of Philosophy Baltimore, Maryland January, 2018 © 2018 Zhuoyu Zhou All Rights Reserved ABSTRACT The primary focus of the present study is to employ computational modeling to investigate the hydrodynamics of free-swimming marine invertebrates. A high-fidelity computational tool based on a sharp interface immersed boundary method (ViCar3D), is developed, and this solver incorporates a non-inertial reference frame treatment in order to significantly reduce the computational cost of these simulations. The analysis includes the details of the wake characteristics and correlation with thrust generation mechanisms, as well as the swimming performance evaluated by coefficient variety of metrics. Simulations of free-swimming of three distinct marine invertebrates - the Spanish Dancer, Aplysia and the marine Flatworm, are performed. These animals are known to be active and effective swimmers and exhibit swimming gaits including body/mantle undulation and/or body bending, which are generally representative of a wide range of soft-bodied swimmers. Simulation show that despite a somewhat ungainly swimming motion, the swimming speed and propulsive efficiency of the Spanish Dancer are quite comparable to other more proficient swimmers. For the Spanish Dancer, a body planform with a wider caudal region has better swimming performance and this might explain the planform shape typically found for these animals. This importance of body-bending become apparent when examining free-swimming in marine Flatworms with two kinematic models- pure lateral flapping (LF) and combined lateral flapping and body pitching (CFP). While the body pitch magnitude is quite small (with maximum deflection angle of 15°), this small addition results in a significantly larger swimming speed (with increments ranging from 16% to 121% depending on the phase differences between lateral flaps and body pitch) and a higher Froude efficiency with increases ranging up to 43%. ii For the Aplysia, it is found that animals swimming with kinematics that match field videos have high propulsive efficiency and a relatively high swimming speed. By examining the Froude efficiency and power coefficient for various body planforms and kinematics, it is found that animals that employ the LF gait fall into one group, whereas other animals that employ the CFP gait fall into another, regardless their body shape. In general, the CFP gait is found to be more effective for swimming than the LF gait. Wake characteristics of the free-swimming of these animals are also analyzed. A bifurcated train of vortex rings is identified within the wake of the Spanish Dancer, and these vortex rings are found responsible for thrust generation. Other vortices in the wake are found to be drag producing. In the wake of the Aplysia, three distinct trains of vortex rings are identified in addition to other spanwise vortex structures resembling the Karman vortex street. For some models of Flatworms, the addition of a small body pitch was found to significantly change the wake topology, and a well- organized wake with distinct vortex rings is found to be associated with improved swimming performance. The current study provides a first-of-its-kind view of swimming in invertebrates and the comparative analysis performed here could provide insights into how these animals have adapted for life under water. The current research could also provide data and insights for the design of bioinspired soft swimming robots. Advisor: Rajat Mittal Reader: Jung-Hee Seo Cynthia Moss iii ACKNOWLEDGEMENTS Now, as I write down this very last part of the thesis, I realized that my student-life has come to an end. Memories of the pleasures and vexations over the years have come alive. I can’t be more grateful to those loving, kind people that have helped me through the difficult and confusing times. First and foremost, I would like to express my utmost gratitude to my advisor Prof. Rajat Mittal for his continuous support over the years, this piece of work would not have been possible without his insightful guidance, vast patience, and constant encouragement. He has set an example of excellence as both a scientist and a mentor. As a scientist, an expert in computational fluid dynamics, Prof. Mittal has not only a very detailed know-how of the mathematical formulas and CFD algorithms but also a profound understanding of the fundamental physics. As a mentor, he always puts the interests and growths of students in the first place. He cares about the future of his students. He taught me the importance of working with a can-do attitude. I simply could not imagine a better advisor. Second, I would also like to thank Dr. Jung-Hee Seo at the Flow Simulations and Analysis Group, who also served as my thesis reader, and Dr. Kourosh Shoele, for many invaluable, thought-provoking discussions throughout my doctoral research. I am also thankful to Dr. Chao Zhang for walking me through the code when I first joined the FSAG. Thanks also go to other fellow graduate students, colleagues in the group and department, as well as our collaborators at Georgia Tech. In addition, I would like to thank Drs. Jung-Hee Seo and Cynthia Moss for providing valuable comments on the thesis. iv Third, I would like to thank Mr. Kuan Xing who always replied promptly to my requests for the sketches of the animals presented in this work, Mr. Harry Blalock for allowing us to use his video of the Spanish Dancer, Mr. Simone Carletti, Mr. George Skeparnias, and Dr. Matteo Charlie Ichino for their videos of the Aplysia. Finally, special thanks are given to my family for their unconditional love through my life. They have always been supportive of my decisions and encouraged me to pursue a higher education. This work was supported by NSF Grant PLR-1246317. The flow solver developed here benefited from support from NSF CBET-1511200 and IIS-1344772, and the JHU Provost Discovery Award. v TABLE OF CONTENTS ABSTRACT ............................................................................................................................ II ACKNOWLEDGEMENTS ................................................................................................. IV TABLE OF CONTENTS ..................................................................................................... VI LIST OF TABLES ................................................................................................................ IX LIST OF FIGURES .............................................................................................................. XI CHAPTER 1. INTRODUCTION ....................................................................................... 1 CHAPTER 2. NUMERICAL METHOD ......................................................................... 14 2.1. GOVERNING EQUATIONS AND DISCRETIZATION SCHEME........................................... 14 2.2. IMMERSED BOUNDARY TREATMENT .......................................................................... 17 2.3. FLOW-INDUCED MOTION ........................................................................................... 20 2.4. VALIDATIONS OF THE NUMERICAL METHOD IN NON-INERTIAL REFERENCE FRAME . 22 2.4.1. Inline oscillations of a circular cylinder............................................................ 23 2.4.2. Freely falling sphere under gravity ................................................................... 26 CHAPTER 3. METRICS FOR SWIMMING PERFORMANCE ................................. 31 CHAPTER 4. SWIMMING HYDRODYNAMICS OF THE SPANISH DANCER .... 35 4.1. INTRODUCTION .......................................................................................................... 35 4.2. METHODOLOGY ......................................................................................................... 36 4.2.1. Kinematic Model .............................................................................................. 36 vi 4.2.2. Pitching Moment Balance Study ...................................................................... 44 4.2.3. Simulation Setup ............................................................................................... 47 4.2.4. Grid Convergence ............................................................................................. 48 4.3. RESULTS .................................................................................................................... 50 4.3.1. Effect of Stokes Number on Swimming Performance ...................................... 50 4.3.2. Wake Topology ................................................................................................. 54 4.3.3. Implications of Planform Shape on Propulsion ................................................ 59 4.4. SUMMARY .................................................................................................................. 63 CHAPTER 5. THE WAKE TOPOLOGY AND SWIMMING PERFORMANCE OF THE SEA HARE (APLYSIA)..................................................................................................... 64 5.1. INTRODUCTION .......................................................................................................... 64 5.2. METHODS .................................................................................................................. 67 5.2.1. Body Geometry and