Document Type
Dissertation
Date of Award
8-31-2025
Degree Name
Doctor of Philosophy in Mathematical Sciences - (Ph.D.)
Department
Mathematical Sciences
First Advisor
Michael Siegel
Second Advisor
Anand Uttam Oza
Third Advisor
Michael R. Booty
Fourth Advisor
Brooke Elizabeth Flammang-Lockyer
Fifth Advisor
Monika Nitsche
Abstract
Fish schools exhibit a collective behavior and self-organization that is mediated by hydrodynamic interactions between individual fish. However, the long-time evolution of hydrodynamically interacting collectives is challenging to investigate due to the persistent influence of long-lived vortical structures, and the high-resolution requirements of direct numerical simulation at large Reynolds numbers. Reduced-order models have therefore played an important role in theoretical investigations of collectives of swimming bodies. The main results detailed herein are several new reduced-order models of swimmers that self-propel by flapping, i.e., by executing a prescribed periodic rigid body motion. The models are extensions of a discrete-time dynamical system developed previously in the literature in which flapping swimmers interact through periodically shed vortices. The extensions include allowing a variable separation distance between swimmers, and more faithful treatment of wing-wing interactions by modeling neighboring wings as point vortices. The models are used to investigate conditions under which hydrodynamic interactions lead to stable swimming configurations. Analytical results include closed form expressions for the velocity potential and total forces on the wings for an arbitrary number of swimmers. Numerical results illustrate steady state solution branches and their stability. Taken together, the analytical and numerical results exhibit favorable agreement with laboratory experiments on flapping wings in a water tank, and elucidate how hydrodynamic interactions can influence the structure and stability of collectives of flapping bodies.
Recommended Citation
Pabon, Jose, "Reduced order models of hydrodynamically interacting flapping wings" (2025). Dissertations. 1855.
https://digitalcommons.njit.edu/dissertations/1855
