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A slender ship moving at a near-critical speed in a shallow channel

Published online by Cambridge University Press:  26 April 2006

Xue-Nong Chen  and
Som Deo Sharma
Xue-Nong Chen
Affiliation:
Department of Marine Technology, Mercator University, Duisburg, Germany Present address: University of Stuttgart, Math. Inst. A, D-70569 Stuttgart, Germany.
Som Deo Sharma
Affiliation:
Department of Marine Technology, Mercator University, Duisburg, Germany
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Abstract

The problem solved concerns a slender ship moving at a near-critical steady speed in a shallow channel, not necessarily in symmetric configuration, involving the special phenomenon of generation of solitary waves. By using the technique of matched asymptotic expansions along with nonlinear shallow-water wave theory, the problem is reduced to a Kadomtsev–Petviashvili equation in the far field, matched with a nearfield solution obtained by an improved slender-body theory, taking the local wave elevation and longitudinal disturbance velocity into account. The ship can be either fixed or free to squat. Besides wave pattern and wave resistance, the hydrodynamic lift force and trim moment are calculated by pressure integration in the fixed-hull case; running sinkage and trim, by condition of hydrodynamic equilibrium in the free-hull case. The numerical procedure for solving the KP equation consists of a finite-difference method, namely, fractional step algorithm with Crank–Nicolson-like schemes in each half step. Calculated results are compared with several published shipmodel experiments and other theoretical predictions; satisfactory agreement is demonstrated.

Type
Research Article
Information
Journal of Fluid Mechanics , Volume 291 , 25 May 1995 , pp. 263 - 285
Copyright
© 1995 Cambridge University Press

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