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 (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.
A singular perturbation theory for nonlinear free surface flow problems
International Shipbuilding Progress ; 14 , 151 ; 88-97
1967-03-01
10 pages
Article (Journal)
Electronic Resource
English
Singular perturbation problems in ship hydrodynamics
TIBKAT | 1970
|Problems in Sonic Boom Theory Studied as Issues of Singular Perturbation
British Library Conference Proceedings | 1996
|Singular Perturbation Technique for Nonlinear Aeroelastic Analysis
British Library Conference Proceedings | 1999
|