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Abstract Several fishes swim by undulating a thin and elongated median fin while the body is mostly kept straight, allowing them to perform forward and directional maneuvers. We used a robotic vessel with similar fin propulsion to determine the thrust scaling and efficiency. Using precise force and swimming kinematics measurements with the robotic vessel, the thrust generated by the undulating fin was found to scale with the square of the relative velocity between the free streaming flow and the wave speed. A hydrodynamic efficiency is presented based on propulsive force measurements and modelling of the power required to oscillate the fin laterally. It was found that the propulsive efficiency has a broadly high performance versus swimming speed, with a maximum efficiency of 75%. An expression to calculate the swimming speed over wave speed was found to depend on two parameters: A p / A e (ratio between body frontal area to fin swept area) and C D / C x (ratio of body drag to fin thrust coefficient). The models used to calculate propulsive force and free-swimming speed were compared with experimental results. The broader impacts of these results are discussed in relation to morphology and the function of undulating fin swimmers. In particular, we suggest that the ratio of fin and body height found in natural swimmers could be due to a trade-off between swimming efficiency and swimming speed. 

Abstract Mangrove swamps are extremely productive ecosystems providing many ecological services in coastal regions. The hydrodynamic interactions of mangrove roots and water flow have been proposed as a key element to mitigate erosion. Several studies reveal that precise prediction of the morphological evolution of coastal areas, in the face of global warming and the consequent sea-level rise, requires an understanding of interactions between root porosity (the fraction of the volume of void space over the total volume), water flows, and sediment transport. Water flows around the mangrove prop roots create a complex energetic process that mixes up sediments and generates a depositional region posterior to the roots. In this work, we investigated the boundary layer behind permeable arrays of cylinders (patch) that represent the mangrove roots to explore the impact of patch porosity on the onset of sediment transport. The flow measurements were performed in a vertical plane along the water depth downstream of the mangrove root models. A high-resolution Particle Image Velocimetry (PIV) was used in a flume to observe the impact of porosity on the mean flow, velocity derivatives, skin friction coefficient, and production of turbulent kinetic energy for Reynolds number of 2500 (based on patch diameter length-scale). Here, we proposed a predictive model for critical velocity for incipient motion that takes into account the mangrove roots porosity and the near-bed turbulence effect. It is found that the patch with the $$\phi =47\%$$ ϕ = 47 % porosity, has the maximum critical velocity over which the sediment transport initiates. We found the optimum porosity has the minimum sediment erosion and creates negative vorticity sources near the bed that increases the critical velocity. This signifies an optimum porosity for the onset of sediment transport consistent with the porosity of mangroves in nature. The phenomenological model is elucidated based on an analysis of the vorticity evolution equation for viscous incompressible flows. For the optimum porous patch, a sink of vorticity was formed which yielded to lower the near-bed turbulence and vorticity. The minimum velocity fluctuations were sufficient to initiate the boundary layer transition, however, the viscous dissipation dominated the turbulence production to obstruct the sediment transport. This work identified the pivotal role of mangrove root porosity in sediment transport in terms of velocity and its derivatives in wall-bounded flows. Our work also provides insight into the sediment transport and erosion processes that govern the evolution of the shapes of shorelines.