Asymmetries in passive propulsion of a flexible foil under water waves

Fish swimming close to water wave surfaces can extract wave energy to produce thrust and save their energy expenditure. To understand this passive propulsion mechanism, we investigated the unsteady motions of a two-dimensional flexible foil in an incident wave. The fluid-structure interaction problem was simulated using a diffused immersed boundary (IB) method, together with a coupled level set and volume-of-fluid (CLSVOF) method to capture the wave surfaces. After reaching a periodic steady state, the passive propulsion performances are asymmetrical in up- and downstroke, including the thrust force and wave energy extraction. Detail kinematics studies show that the passive flapping motion is asymmetric in the upstroke and downstroke, with an increased trailing edge amplitude and a higher vertical speed during the upstroke when the foil approaches the wave surface. These asymmetries are attributed to the passing-over leading-edge vortex (PO-LEV), where a vortex pair, formed at the leading edge of the downside of the foil at the beginning of the upstroke, circumnavigates or passes over the leading edge and rotates to the upside of the foil, and continues to shed into the wake during the rest of the upstroke. The potential impact of the asymmetries on the performance of the passive propulsion will also be investigated.