  "Ground effect" refers to the enhanced performance enjoyed by fliers or
swimmers operating close to the ground. We derive a number of exact solutions
for this phenomenon, thereby elucidating the underlying physical mechanisms
involved in ground effect. Unlike previous analytic studies, our solutions are
not restricted to particular parameter regimes such as "weak" or "extreme"
ground effect, and do not even require thin aerofoil theory. Moreover, the
solutions are valid for a hitherto intractable range of flow phenomena
including point vortices, uniform and straining flows, unsteady motions of the
wing, and the Kutta condition. We model the ground effect as the potential flow
past a wing inclined above a flat wall. The solution of the model requires two
steps: firstly, a coordinate transformation between the physical domain and a
concentric annulus, and secondly, the solution of the potential flow problem
inside the annulus. We show that both steps can be solved by introducing a new
special function which is straightforward to compute. Moreover, the ensuing
solutions are simple to express and offer new insight into the mathematical
structure of ground effect. In order to identify the missing physics in our
potential flow model, we compare our solutions against new experimental data.
The experiments show that boundary layer separation on the wing and wall occurs
at small angles of attack, and we suggest ways in which our model could be
extended to account for these effects.
