Similarity solution for oblique water entry of an expanding paraboloid

Similarity solutions based on velocity potential theory are found to be possible in the case of an expanding paraboloid entering water when gravity is ignored. Numerical solutions are obtained based on the boundary element method. Iteration is used for the nonlinear boundary conditions on the unknown free surface, together with regular remeshing. Results are obtained for paraboloids with different slenderness (or bluntness). Flow features and pressure distributions are discussed along with the physical implications. It is also concluded that similarity solutions may be possible in more general cases.