Dynamics and propulsive performance of a flexible oscillating foil in a wavy flow

Swimming and flying animals demonstrate remarkable adaptations to diverse flow conditions in their environments. In this study, we aim to advance the understanding of the interaction between flexible bodies and heterogeneous flow conditions, providing insights into the propulsive capabilities of swimming and flying animals in their natural habitats.

We have investigated the dynamics and propulsive performance of a thin foil, which serves as a simplified model for swimming or flying organisms. The foil is driven by a periodic heaving motion while being exposed to a wavy freestream. Flexibility is modelled via a torsional spring at the leading edge, and the pitching motion is passive. We employ a linearized thin airfoil model to capture the flow physics.

The kinematic response under applied heaving and wavy forcing is analyzed separately, revealing the dominance of wavy forcing at lower frequencies. The foil exhibits thrust generation despite purely passive kinematics in a wavy stream. The interactions between various time scales in the problem, including convective, elastic, and wave, give rise to unexpected results. Notably, when the freestream and wave speeds coincide, non-circulatory forces vanish, diminishing the expected elastic resonance.