Computational study of 2D jellyfish with the immersed boundary method

Jellyfish have evolved the most energy-efficient method of propulsion of any animal on Earth, despite having an extremely simple physical and neural structure. For this reason, they are a very popular model organism for biologists and have been the subject of numerous experimental and computational studies. But despite the many attempts to comprehend their swimming dynamics and performance, there still remains a great deal to discover about jellyfish. This thesis employs numerical simulations using the immersed boundary method to investigate the fluid-structure interaction between a 2D model for a swimming jellyfish with the surrounding fluid. Various jellyfish species employ a variety of swimming ``gaits'' to generate forward motion, and we will focus on jet-like swimming occurring mostly in prolate jellies that contract their bell muscles periodically to expel water from their interior. We first study the scaling properties of jellyfish in terms of two dimensionless parameters -- the Reynolds number and swimming number -- to show that a power-law dependence derived for undulatory swimmers (such as fish and eels) extends naturally to jellyfish that use a jetting mode of propulsion. We next investigate the feeding technique used by jetting swimmers, in which trailing vortices generated by bell contractions are exploited to redirect into their bell interior the mostly passive prey such as algae and plankton that they feed on. Our numerical simulations are used to quantify and visualize the effect of changes in prey distribution and jellyfish size and shape with a degree of detail that is typically not possible in experiments. Finally, we present a preliminary study of pair-wise interactions between jellyfish in which nearby swimmers generate repulsion forces and initiate turning responses when they come into close proximity. The overall aim of this research is to lay the groundwork for future computational simulations of swimming and feeding dynamics in swarms of interacting jellyfish.