Abstract
The grace and efficiency of fish locomotion have long inspired scientists and engineers. Unlike conventional underwater vehicles, fish have evolved flexible body morphologies and undulatory gaits that enable efficient propulsion and maneuverability in water. Within schools, their collective motion confers additional hydrodynamic benefits, as each fish interacts with vortices and pressure fields generated by its neighbors. The dense water thus becomes a dynamic carrier of mechanical information and energy exchange. This dissertation investigates the schooling interactions mediated by vortex and body-generated pressure fields through a series of high-fidelity computational studies of body-caudal-fin (BCF) propulsion.
As a fish undulates, a traveling wave of body deformation propagates from head to tail, pushing and pulling on the surrounding flow to generate unsteady pressure gradients. The motion of the fins and the shedding of vorticity create a rich wake containing both momentum and pressure fluctuations. The pressure-mediated (body-body) and vortex-mediated (body-vortex) interactions differ in range and latency, and would require different kinematic adjustments. To examine these two modes of hydrodynamic coupling, this work employs direct numerical simulation (DNS) with biologically informed kinematics and carefully controlled variations in morphology, phase, and spacing.
The first part of the study focuses on vortex-mediated interactions within a solitary trout, specifically between the anal and caudal fins. Using a three-dimensional digital trout model with realistic traveling-wave motion, simulations comparing models with and without the anal fin reveal that capturing anal-fin vortices increases caudal-fin thrust by 8\% and reduces body drag by 18\%. Systematic variation of fin spacing and height identifies competing thrust enhancement and drag mitigation mechanisms, with optimal performance occurring near the natural fin configuration.
The second part examines interactions between a fish and a fish-like vortex wake, reconstructed from flume experiments with a flapping hydrofoil. The simulations show that the fish’s undulation is phase-locked to oncoming vortices, allowing them to roll smoothly over the body while minimizing disturbance. This synchronization reduces power expenditure by 11\% compared to uniform flow. The undulatory wavelength is identified as a distinctive feature of the phase-locking locomotion. Extending from the reconstructed kinematics, a method of modeling and controlling body deformation in untethered flow simulations was developed and demonstrated in the foil-fish setup in 2D. By minute adjustments of the deformation traveling wave, the fish maintains stable station-holding over many cycles. The wavelength variation showed a trade-off between propulsion and energy extraction, with the optimal balance struck nearest to the foil's wake wavelength.
The final part investigates pressure-mediated interactions in side-by-side (phalanx) swimming, where vortical coupling is suppressed. In three-dimensional simulations of tethered swimmers, anti-phase undulation between neighbors enhances propulsive efficiency by over 20\%, while in-phase motion yields moderate power savings. Extending the phalanx to a non-planar configuration with vertically stacked swimmers shows that this anti-phase benefit persists. The mechanism arises from constructive interference of body-generated pressure waves, which amplify thrust and merge the downstream jets of individual fish.
Together, these studies provide a mechanistic understanding of how fish exploit unsteady flow structures for propulsion and energy conservation. By linking body deformation, flow physics, and control, this work offers new insight into the energetics of fish schooling and informs the design of bio-inspired underwater vehicles capable of coordinated, efficient swimming in complex flow environments.
