Abstract
Schooling is a striking collective behavior adopted by many fish species. The tight groupings of fish generate an energetic flow environment that is widely hypothesized to provide hydrodynamic advantages by augmenting force production or reducing power consumption for individual swimmers. However, important three-dimensional (3D) facets remain unresolved, including the hydrodynamic impacts of median fin structures, and the effects of vertical and fully volumetric schooling formations on the flow experienced by neighbors. The research presented in this dissertation uses high-fidelity direct numerical simulations to investigate flow interactions in 3D fish schooling. The complexity of the formations is increased gradually throughout the dissertation, systematically varying the presence of certain features, such as median fins or groups of fish, to identify their contribution to the 3D flow environment and hydrodynamic performance.
First, using in-line formations, the median fin presence is varied to separate self-induced median fin effects from neighbor-induced median fin effects on the follower. Across the simulated spacings, phase differences, Reynolds numbers, and fin heights, a full-finned leader consistently alters the wake around the follower, reducing the follower’s drag relative to being behind a finless leader. These changes are linked to modified pressure and velocity fields behind the leader which originate from the leader's median fins strengthening its leading-edge vortex and re-orienting the shed wake structures.
Next, the three-fish vertical stagger and four-fish vertical diamond formations are analyzed to understand the hydrodynamic interactions within vertical schools. The results show that the region between vertical neighbors experiences high flow speed and suction pressure. This concentrates the drag reduction to the downstream fish while penalizing the upstream fish. In vertical diamonds, varying the streamwise and vertical spacing reveals different avenues for interaction in dense vertical planar schooling. In vertically-dense diamonds, the leader and follower both enhance the stacked top and bottom fish through their wake and body-generated pressure fields, respectively. The follower itself obtains a large net force improvement by leveraging its location within the vertically compressed wakes of the top and bottom neighbors to extract wake-body and wake-fin interactions. In contrast, in streamwise-dense vertical diamonds, the top and bottom fish contribute to the follower’s large force improvement by lowering the inter-fish pressure through a vertical channel effect. The vertical interactions depend strongly on the flapping phase of the top and bottom fish in the vertically-dense diamonds, and less so for the streamwise-dense diamond. The performance enhancements and body force distribution for the two different diamond formations are found to be consistent across a range of varied Reynolds number, too.
Finally, the performance and wake environment in volumetric schools is analyzed by comparing a fully 3D volumetric diamond school to its isolated planar subsets. The presence of both vertical and lateral neighbors forms a volumetric channel with reduced inter-fish pressure inside the school, boosting the follower’s net force production, while other fish in the school experience degraded net force as a result. The school length is increased by appending additional diamond units, and the volumetric channel is again identified to contribute to a force improvement for the follower fish. Unique to the longer schools is the presence of middle fish, which also exhibit drag reduction. However, this benefit is attributed primarily to lateral-neighbor interactions, and the influence of the volumetric channel is more nuanced than for the follower because middle fish are immersed within a lowered-pressure corridor that extends both upstream and downstream. As a result, lower pressure flow interacts with the anterior body favorably, while lower pressure behind the fish partially offsets the benefit.
This dissertation contributes a mechanistic understanding of hydrodynamic interactions in 3D fish schools. Detailed analysis of the flow physics reveals how median fins, vertical formations, and fully volumetric schools generate specific wake enhancements and interactions that reshape the flow experienced by neighbors, and as a result, the hydrodynamic performance. The work both refines our physical understanding of schooling locomotion and suggests strategies for arranging bio-robotic swimmers in formations for enhanced hydrodynamic performance.
