The present work numerically investigates the dynamics of inclined thin flexible plates in oscillatory flows to assess the effects of bending stiffness, wave orbital excursion and inclination angle on plate deflection, reconfiguration, drag force and energy conversion. Four distinct structural response modes are identified, together with their transition conditions. An analytical expression for the lift coefficient of inclined rigid plates in the oscillatory flow is derived. By combining the drag and lift coefficients, we propose a modified Cauchy number, which quantitatively reveals the inclination effect from both geometric and mechanical perspectives. The dynamic behaviours of the plate deflection can be separated into two states. In the fully reconfigured state, a balance is achieved between elastic restoring force and hydrodynamics-driven force. Based on moment and energy balance, we derive a scaling law incorporating the modified Cauchy number, which accurately predicts the variation of tip deflection. In the passive movement state, the flexible plate moves passively along the flow, and its tip deflection saturates to the order of wave orbital excursions. A pronounced drag reduction is induced by the plate reconfiguration, following a -1 scaling law with a combined parameter, which is explained by the model of effective plate length. The energy conversion from fluid kinetic energy to structural elastic strain energy first increases and then decreases with increasing flexibility, yielding an optimal energy conversion efficiency. The modified Cauchy-number-based scaling law accurately predicts the averaged elastic energy growth and critical conditions for optimal energy conversion through a time scale competition mechanism.
Zhang et al. (2026) studied this question.