Quasi-Steady and Wake-Induced Forces Balance to Generate Equilibrium Altitudes in Near-Ground Swimming

Neutrally-buoyant near ground swimmers experience alterations in their added mass, quasi-steady, and wake-induced forces compared to swimming far from a ground plane. In fact, using a simple freely-swimming pitching hydrofoil as a model near-ground swimmer it has been shown that a hydrofoil will be attracted to a stable equilibrium altitude due to competing hydrodynamic forces. Here, a potential flow decomposition method using the unsteady Bernoulli equation is presented and applied to understand the competing forces that give rise to equilibria. It is shown that many previous hypotheses do not hold and that equilibria are a balance between negative time-averaged quasi-steady lift and positive time-averaged wake-induced lift, while the time-averaged added mass lift is nearly zero across all ground proximities. Results that run counter to previous hypotheses are examined in detail.