Mechanism of maximum thrust generation by oscillating compliant caudal-fin model in a quiescent fluid

A certain level of flexibility of moving appendage like a fin enhances its hydrodynamic performance (e.g., thrust generation). However, little efforts have been spent to characterize the condition in which the beneficial impact of compliance is maximized. Recent report (Park \emph{et al}. 2012, TRO) has shown that a sinusoidally oscillating caudal-fin model generates the maximum thrust when its compliance creates a phase difference ($\xi$) of $\pi/2$ between the oscillating and fin-bending angles, irrespective of its planform shape. To establish the underlying mechanism, we have analyzed the time-averaged and instantaneous flow fields around nine (9) oscillating caudal-fin models with varying their compliance. A series of particle image velocimetry measurements were performed in a quiescent water tank. When $\xi < \pi/2$, a strong interaction between the separated trailing-edge vortex (TEV) and the TEV forming at next stroke directs the flow in a transverse way, thereby enhancing the decay of thrust-generating jet velocity. At $\xi = \pi/2$, this interaction is weak such that the fast jet velocity is retained along the streamwise direction. On the other hand, when $\xi > \pi/2$, the trailing-edge is moving opposite to the oscillation reducing the rotational circulation of TEV.