Resolvent analysis of a swimming foil

This study employs 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 is used together with undulatory kinematics to represent fish-like bodies at realistic Reynolds numbers ($ \mathit{Re} = 10,000 $ and $ \mathit{Re} = 100,000 $) in both thrust- and drag-producing propulsion regimes. We introduce a novel coordinate transformation that enables the implementation of the data-driven resolvent analysis \citep{herrmann_data-driven_2021} to dissect the stability of the boundary layer of the swimming foil. This is the first study to implement resolvent analysis on deforming bodies with non-zero thickness and at realistic swimming Reynolds numbers. The analysis reinforces the notion that swimming kinematics drive the system's physics. In drag-producing regimes, it reveals breakdown mechanisms of the propulsive wave, while thrust-producing regimes show a uniform wave amplification across the foil's back half. The key thrust and drag mechanisms scale with the boundary-layer thickness, implying geometric self-similarity in this $\mathit{Re}$ regime. In addition, we identify a mechanism that is less strongly coupled to the body motion. We offer a comparison to a rough foil that reduces the amplification of this mechanism, demonstrating the potential of roughness to control the amplification of key mechanisms in the flow. The results provide valuable insights into the dynamics of swimming bodies and highlight avenues for developing opposition control strategies.