The purpose of this paper is to provide a mathematical tool to improve the optimal design of ship forms. It is common practice that hull forms are designed such that they have minimal wave resistance in calm wter. In this paper a theory is described by which the effect of short waves may be incorporated. The basic tool we use is the ray theory. First, the appropriate free-surface condition is shown. Then, the standard ray method, well-known in geometric optics, is formulated in the fluid region and a the free surface. After an elimination process the eiconal equation and the transport equation are obtained. The characteristic equations for the nonlinear eiconal equations are derived, keeping in mind that the charcteristics (rays) are not perpendicular to the wavefronts, due to the influence of the double-body potential generated by the slow forward speed of the ship, which is assumed to be a good approximation for the steady potential. Numerical integration of the ray equations lead to the ray pattern. After some manipulations the amplitude may be computed just as well. Finally, the second order mean force or added resistance is calculated.
The diffraction of short free surface water waves, a uniform expansion
Die Brechung von kurzen Wellen von freiem Oberflächenwasser, eine gleichförmige Erweiterung
1992
23 Seiten, 11 Bilder, 17 Quellen
Report
Englisch
Second-Order Diffraction in Short Waves
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