Flow around an unsteady thin wing close to curved ground

Abstract

The method of matched asymptotic expansions is applied to the flow analysis of a three-dimensional thin wing, moving uniformly in very close proximity to a curved ground surface. Four flow regions, i.e. exterior, bow, gap, and wake, are analysed and matched in an appropriate sequence. The solutions in expansions up to third order are given both in nonlinear and linear cases. It is shown that the flow above the wing is reduced to a direct problem, and the flow beneath it appears to be a two-dimensional channel flow. The wake assumes a vortex-sheet structure close to the curved ground, undulating with the amplitude of the ground curvature, and the flow beneath it is also two-dimensional channel flow. As a consequence, an equivalence is found between the extreme curved-ground effect and the corresponding flat-ground effect, which can be treated by the image method.