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The application of uniform-slender-body theory to the motion of two ships in shallow water

Published online by Cambridge University Press:  20 April 2006

A. M. J. Davis  and
J. F. Geer
A. M. J. Davis
Affiliation:
Department of Mathematics, University College London, Gower Street, London WC1E 6BT, U.K.
J. F. Geer
Affiliation:
Department of Systems Science, State University of New York at Binghamton, N.Y. 13901, U.S.A.
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Abstract

The techniques of uniform-slender-body theory are employed to investigate the hydrodynamic forces and moments acting on a moving ship in shallow water and the interaction forces between two such ships on parallel courses. Of particular interest is the verification by these methods of the validity of the solutions by matched asymptotic expansions constructed by previous authors. The free surface is assumed rigid and each ship is modelled as a slender body of revolution located midway between two closely spaced parallel planes. The velocity potential due to the presence of a single ship is represented as the potential due to singularities distributed along a portion of the axis inside the body, together with appropriate image singularities outside the body. The boundary condition on the body leads to a linear integral equation for the density of singularities, which is solved using the asymptotic analysis discussed by Geer (1975). The sinkage force and trimming moment on the vessel are computed. When two ships are moving on parallel courses, appropriate interaction potentials are introduced in a manner similar to that for a single ship and the integral equations resulting from the application of the boundary condition are solved asymptotically. The interaction forces and moments between the ships are computed and compared with some experimental and other theoretical results.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 114 , January 1982 , pp. 419 - 441
Copyright
© 1972 Cambridge University Press

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