Intermittent swimming of two self-propelled flexible fins with laterally constrained heaving motions in a side-by-side configuration

Inspired by the intermittent locomotion of fish schools, numerical simulations are performed with two self-propelled flexible fins in a side-by-side configuration with anti-phase oscillation actuated by laterally constrained heaving motions. For an intermittent swimming gait, one type of the half-tail-beating mode (HT mode) and two types of multiple-tail-beating modes coasting at the smallest (MTS mode) and largest (MTL mode) lateral gap distances are applied. Similar to the continuous-tail-beating mode (CT mode), equilibrium lateral gap distances between two fins with HT and MTL modes exist, whereas two fins with MTS mode do not maintain a lateral equilibrium state. Although the cycle-averaged lateral force acting on two fins with CT and MTL modes is mostly determined by an outward deflected jet and enhanced positive pressure between two fins, an added-mass lateral force related to an asymmetric flapping kinematics by passive flexibility also plays an important role in MTL mode to achieve a stable state with a lateral gap distance smaller than that in CT mode. When the cruising speed or the cycle-averaged input power is identical in a stable state, the cost of transport (COT) for two fins with MTL mode is smaller than that with CT mode due to not only a benefit from the intermittent swimming gait but also an enhanced schooling benefit with a small equilibrium lateral gap distance. The COT for two fins with CT mode is reduced further when the bending rigidity increases, whereas it is opposite with MTL mode.