Motion of a Yawed Supercavitating Wedge Beneath a Free Surface

The problem that is studied concerns a yawed wedge under a free surface, moving at a uniform speed. The model involves a trailing cavity whose boundary is a dividing streamline through the vertex of the wedge. The cavity closure mechanism is described according to the Tulin– Terent’ev single-spiral-vortex model. A closed-form solution to the governing nonlinear boundaryvalue problem is found by the method of conformal mappings. The doubly connected flow domain is treated as the image by this map of the exterior of two slits in a parametric plane. The mapping function is constructed through the solution to two boundary-value problems of the theory of analytic functions, the Hilbert problem for two slits in a plane, and the Riemann–Hilbert problem on an elliptic surface. Numerical results for the shape of the cavity and the free surface, the yaw angle, the drag and lift coefficients, and the circulation are reported.