Free surface-induced ground effect for flapping swimmers

Numerous flying and swimming creatures use the ground effect to boost their propulsive performance, with the ``ground" referring to either a solid boundary or a free surface. While our knowledge of how a solid boundary affects biolocomotion is relatively comprehensive, little is understood about the effect of a free surface. To address this limitation, we conduct a numerical investigation on the propulsion performance of a flapping plate under a free surface, subject to a range of control parameters. When the Froude number is very low (i.e., little surface deformation), the effects of a free surface are similar to those of a solid boundary, with enhanced thrust and input power but little change in efficiency. However, as the Froude number increases (i.e., more surface deformation), our results reveal an optimal Froude number of approximately 0.6, where the free surface induces a more streamlined flow around the flapping plate, effectively reducing the added mass. This results in a significant decrease in input power and greatly enhanced efficiency. Our simulation results are supported by measurement data of fish Froude numbers from the literature.