Lift reversal from vortex-surface phase coupling in a heaving foil near a free surface

Classical descriptions of flapping propulsion near a free surface emphasize the energetic penalties of wave generation, treating the interface primarily as an energy sink. Here, we show that the same deformable boundary can also act as a phase-dependent kinematic constraint on vertical force generation. Using force measurements, particle image velocimetry and potential-flow simulations, we characterize how a free surface reorganizes vortex shedding for a heaving hydrofoil at moderate Reynolds number (O(10^4)). For moderate to deep submergence, the cycle-averaged lift undergoes a systematic transition from repulsion to suction as the unsteady number increases. The reversal occurs within a narrow band of unsteady numbers, where the phase-shifted surface motion generates vertical advection that alters the pairing of trailing-edge vortices and redirects the wake momentum flux. A force decomposition shows that the reversal arises from a coordinated change in quasi-steady pressure loading and wake-induced force. These results identify the phase of the free-surface response, organized by unsteady number, as a key parameter governing near-surface lift and illustrate how deformable boundaries can reconfigure unsteady loading through vortex-surface phase coupling.