Here Fishy Fishy: Resolvent Analysis of the Boundary Layer a Swimming Foil*

This study uses resolvent analysis to explore the dynamics and coherent structures in the boundary layer of a foil that swims via a travelling wave undulation. A modified NACA foil shape with undulatory kinematics is used to represent fish-like bodies at realistic Reynolds numbers (Re = 10,000 and Re = 100,000) in both thrust and drag producing propulsion regimes. We introduce a novel coordinate transformation that enables us to use data-driven resolvent analysis to investigate the stability of the boundary layer of the swimming foil. This is the first study to use resolvent analysis on deforming bodies with non-zero thickness and at realistic swimming Reynolds numbers. The analysis shows that swimming kinematics drives the system's physics. In drag-producing regimes, it reveals breakdown mechanisms of the propulsive wave, while thrust-producing regimes show uniform wave amplification across the foil's back half. The key thrust and drag mechanisms scale with boundary-layer thickness, implying geometric self-similarity in this Re regime. Additionally, we identify a mechanism less strongly coupled to body motion. We compare this to a rough foil that reduces the amplification of this mechanism, demonstrating how roughness can control the amplification of key mechanisms in the flow. These results provide valuable insights into the dynamics of swimming bodies and suggest ways to develop opposition control strategies.