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Gravity effects in the initial value problems of water wave theory

Published online by Cambridge University Press:  09 April 2009

A. H. Low
A. H. Low
Affiliation:
Department of Applied MathematicsThe University of Sydney
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The theory described in this paper is directed towards obtaining a general expression for the development of the free surface of a fluid, subsequent to a given initial state and prescribed boundary conditions, as a power series in g, the gravitational acceleration. In an earlier paper [4], a result, applicable to the particular case of the entry of a thin wedge into an incompressible fluid, was obtained and gave the shape of the free surface as such a power series. This series was valid for values of the ratio ut/x < 1, where u, was the (constant) velocity of entyr of the wedge; x the horizontal distance from the vertex of the wedge; and t the times elapsed after entry. This particular problem was first investigated by Mackie [6] who derived an asymptotic solution.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 8 , Issue 2 , May 1968 , pp. 269 - 274
Copyright
Copyright © Australian Mathematical Society 1968

References

[1]Erdélyi, A. (ed), (a) Higher transcendental functions, Vol. I; (b) Higher transcendental functions, Vol. II (McGraw-Hill, New York, 1953).Google Scholar
[2]Erdélyi, A. (ed.), Tables of integral transforms, Volume I (McGraw-Hill, New York, 1954).Google Scholar
[3]Lamb, H., Hydrodynamics (Cambridge University Press, 6th ed. 1932).Google Scholar
[4]Low, A. H., ‘The gravity terms in the water entry problem’, J. and Proc. Roy. Soc. N.S.W. 100 (1966), 29–32.Google Scholar
[5]Mackie, A. G., ‘Initial value problems in water wave theory’, J. Aust. Math. Soc. 3 (1963), 340–350.CrossRefGoogle Scholar
[6]Mackie, A. G., ‘Gravity effects in the water entry problem’, J. Aust. Math. Soc. 5 (1965), 427–433.CrossRefGoogle Scholar