Problem Formulation for the Flow Past a Lifting Surface in Proximity to a Solid Boundary

Consider a wing of small thickness and curvature, performing an unsteady motion above a solid nonplanar underlying surface in an ideal incompressible fluid1 (see Fig. 2.1). Assume that motion of the wing is the result of superposition of the main translational motion with variable speed U(t) and small vertical motions due to heave, pitch, and possible deformations of the lifting surface. Introduce a moving coordinate system in which the axes x and z are located upon an unperturbed position of the underlying boundary (the ground). Axis x is directed forward in the plane of symmetry of the wing, and axis y is directed upward and passes through the trailing edge of the root chord.