Higher-Order Thin-Ship Theory by Means of the Method of Matched Asymptotic Expansions

Abstract

A new approach to the higher-order thin_ship theory is developed by means of the method of matched asymptotic expansions. The result which is obtained here is not new, but the approach is entirely different from others. The source distributions are determined by the process of matching of the far_field solution to the near_field solution. So the expression for the higher-order thin_ship theory is valid in the far field. &&The near field is a combination of thin_ship and slender_ship near field. The slender_ship near field is necessary to take care of the free-surface condition, which is satisfied on the free surface instead of the z = O plane. A combination thin_ship and slender-ship approach makes it possible to construct higher-order potentials. &&In the far field, the potential is composed of three types of potentials. They are the thin-ship potential, the slender_ship potential, and the pressure-distribution potential, all of which satisfy linearized free_surface conditions at the z = O plane. Among them, the slender_ship potential has the most interesting features.