Ground Effect on Undulation and Pumping Near Surfaces

Locomotion and fluid pumping near surfaces are ubiquitous in nature, ranging from the slow crawling of snails to the rapid flight of bats. This study categorizes these behaviors based on the undulation number (Un) and Reynolds number ($Re$). We contrast low $Re$ undulatory propulsion ($\text{Un} \gt 1$), exemplified by freshwater snails, with high $Re$ flapping propulsion ($\text{Un} \lt 1$), seen in bats and bees. For snails, we derive lubrication models showing that pumping and swimming speeds scale with $(a/h_0)^2$, a result validated by robotic experiments which also reveal the detrimental effects of surface deformation (high capillary/Bond ratio). Conversely, for high $Re$ fliers, we examine the ground effect's role in lift enhancement. Biological data from bats (Hipposideros pratti and Rhinolophus ferrumequinum) reveal a 2.5-fold increase in lift coefficient during surface-skimming drinking flights, attributed to aerodynamic squeezing effects. Finally, we analyze honeybee fanning, demonstrating how a "jet-vortex" mechanism utilizes ground effect to transport pheromones efficiently against diffusion. These findings provide a unified framework for understanding fluid-structure interactions near boundaries in biological systems.