A higher order theory for the potential flow about thin hydrofoils

The potential flow about a two dimensional hydrofoil moving with constant velocity at a fixed depth beneath a free surface (air-water interface) is investigated. The presence of the free surface adds kinematic and kinetic boundary conditions not found in the related airfoil problem. Disturbances generated by the hydrofoil propagate downstream along the free surface in the form of waves. A higher order method is developed that approximates body and free surface boundary conditions in a consistent manner for thin hydrofoils near the free surface. The thickness-to-chord ratio of the hydrofoil is assumed to be small and disturbances to the undisturbed stream are assumed to be small. Free surface and boundary conditions are transferred to the undisturbed free surface location and chord respectively using Taylor series expansions. Dependent variables are expanded in powers of a small expansion parameter.