The three-dimensional hydrodynamics of tadpole model’s solitary swimming and parallel schooling

Tadpole swimming, including a solitary tadpole swimming and schooling side-by-side in an in-phase mode, is investigated numerically in the present paper. The three-dimensional Navier-Stokes equations for the unsteady incompressible viscous flow are solved. A dynamic mesh fitting the tadpole’s deforming body surface is adopted. The results showed that for a solitary tadpole swimming, two vortex rings are shed in each undulating period. However, as the resultant force on the tadpole is drag, the vortex rings are obviously asymmetric, shaped like “C”. When the resultant force in the swimming direction approaches zero, the axes of the vortex rings are nearly vertical to the swimming direction. Distorted vortex rings are found when the resultant force on the tadpole is thrust. When the tadpole model obtains the optimum propulsive efficiency, its swimming speed and undulating frequency are close to the values observed in nature. For tadpoles swimming side-by-side in an in-phase mode, the vortex structures in the wake may merge, split and recombine. Compared with a solitary tadpole swimming, only a small hydrodynamic advantage occur with schooling in parallel, which may be one of the reasons why tadpoles rarely, if ever swim, side by side for any amount of time or distance in nature. The effect of the undulating frequency on the tadpoles schooling is similar to that on a solitary tadpole. In addition, with an increase in the Reynolds number, the thrust force and the propulsive efficiency both increase, while the power consumption decreases. We also found that the tadpole benefits from the vortex pair shedding from its blunt snout, which can strengthen the vortex intensity in the wake and improve the pressure distribution.