# Compressible Flow Past a Wing in the Extreme Ground Effect

It is practical to extend the analysis of the aerodynamics of a wing in the ground effect to account for the dynamic compressibility of the air. In fact, the cruise speed of ground-effect vehicles can amount to half or more of the speed of sound. At the same time, it is known that the problem of unsteady subsonic flow is one of the most challenging in lifting surface theory; see Belotserkovsky et al. [139]. The complexity of the problem partly stems from the fact that in a compressible fluid the perturbations propagate with finite speeds.

The problem of compressible flow past a wing in the extreme ground effect can be treated on the basis of the approach, similarly to that applied in section 2 for an incompressible fluid. Here one adopts the same assumption as previously, stating that both deviations and slopes of the surfaces of the wing, vortex wake, and the ground should be small, i. e., of the order of the relative ground clearance; see (2.1). In this case, it becomes possible to linearize the flows above the wing and the wake and introduce linearizing simplifications into formulations for edge flows. As earlier, with an asymptotic error of the order of О (h-o), channel flow can be shown to retain almost a two-dimensional nature and incorporate nonlinearity. In what follows, the derivation of the solution will be confined to the leading order of 0(1) and the case of constant speed U(t) = 1. Then, some examples are considered, including linearized steady and unsteady compressible flows past a rectangular wing and the nonlinear flow problem for a two-dimensional foil in the extreme ground effect.