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 / U 2 (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.


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    Title :

    A singular perturbation theory for nonlinear free surface flow problems


    Contributors:

    Published in:

    Publication date :

    1967-03-01


    Size :

    10 pages




    Type of media :

    Article (Journal)


    Type of material :

    Electronic Resource


    Language :

    English




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