A singular perturbation theory for nonlinear free surface flow problems

Article type: Research Article

Authors: Wu, T. Yao-Tsu

Affiliations: California Institute of Technology, Pasadena, California

Abstract: The method of matched singular perturbation expansions is applied to calculate the asymptotic solution of a steady two-dimensional free surface flow past a body of an arbitrary form for large values of the Froude number. The expansion parameter is β=gℓ/U2 (ℓ being the body dimension, U the free stream velocity, g the gravity constant) which is assumed small. The zeroth order inner solution near the body is based on the free streamline theory with no gravity effect; and the higher order terms give rise to the gravitational correction. The outer solution contains in the order β-term a train of gravity waves on the downstream side, the nonlinear correction appears in the terms of order higher than β. The two expansions are matched to obtain a solution uniformly valid throughout the flow field.

DOI: 10.3233/ISP-1967-1415101

Journal: International Shipbuilding Progress, vol. 14, no. 151, pp. 88-97, 1967