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, the ground effect of a free surface is not fully understood. 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 ($Fr$) 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 $Fr$ increases (i.e. more surface deformation), our results reveal an optimal $Fr$ 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.