Abstract

This talk discusses, in the limit of large Froude number, a closed-form, analytical solutionfor steady, two-dimensional, inviscid, free-surface attached flow over a submerged planarhydrofoil for arbitrary angles of attack and depths of submergence. The doubly connectedflow domain is conformally mapped to a concentric annulus in an auxiliary plane.The complex flow potential and its derivative, the complex velocity, are obtained inthe auxiliary plane by considering their form at known special points in the flow, andthe required conformal mapping is determined by explicit integration. The four realsolution parameters are determined as the simultaneous roots of four real nonlinearalgebraic equations arising from the flow normalisation. The explicit form allows accurateevaluation of various flow quantities, including the lift on the foil, and these are related tothe large-Froude-number results in recent numerical solutions.  J.S. Marshall and E.R. Johnson