Twenty-First Symposium on Naval Hydrodynamics (1997) / Chapter Skim
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On Ships at Supercritical Speeds
On Ships at Supercritical Speeds
Pages 715-726
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From page 715... ...
* ~ smallness parameter for wave = A-/ (h-4Eg h- ~ depth-averaged potential ~ = ~ /~£h ~ free surface elevation INTRODUCTION This paper deals with the problem of wave pattern and wave resistance of a slender ship moving steadily at supercritical speeds in shallow water.
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From page 716... ...
It is probably less well-known that the favorable effect of wave interference between twin hulls of a catamaran in shallow water, which diminishes total wave resistance, is more significant in the supercritical speed range than in the subcritical speed range (and, of course, in deep water)
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From page 717... ...
For a ship in horizontally unbounded shallow water moving at supercntical speed, we reduce the ship wavemaking problem from the boundary value problem of the extended KP equation to an initial value problem of the KdY equation without loss of precision. The slowly varying transverse variable Y plays the same role as slowly varying time In the standard KdV equation.
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From page 718... ...
(1) is the stationary extended KP equation that holds for a wide speed range and is precise to We came order as the Boussinesq equations.
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From page 719... ...
This is why we usually see dispersive undulating waves instead of a soliton in the wake. We conclude Cat as a ship moves at supercriiical speed In horizontally unbounded shallow water its forebody can generate oblique solitary waves which extend to infinity along their characteristic lines while its afterbody generates an undulating wave Win which disperses into 5, < 0.
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From page 720... ...
This may be due to the Act that one usually does not deal with the term ~' By We further note that F and G are riot necessarily single soliton solutions, they can also be multiple solitons or even undulating dispersive wave solutions of the KdV equation. We leave the task of solving for the N-soliton interaction to the next section and show here only the simplest example, namely, the two single soliton interaction.
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From page 721... ...
0 5 10 IS x Fig. 2 The superconductive results of wave pattern and ship hullform as E = 0.08, x1 = 7 and w = 10 .
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From page 722... ...
A reasonable method to determine which model is better in its linear part would be to compare the exact stationary dispersion relation in hnite-depth water with the approximate dispersion relations of various linearized shallow-water wave equations. One can also heuristically introduce sp0dependent coefficients into the equation and obtain an even better model of which the dispersion relation is almost identical to the exact one.
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From page 723... ...
,1~1 ,'1' // 0.2 0.4 0.6 0.8 1 1.2 1.4 Fig. 5 Companson of dispersion relations at U=1.5, where the exact one is represented by a solid line, KP's by a dashed line md Boussinesq's by a dot~hed line.
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From page 724... ...
We believe that equation (17) will yield better results, specially less distorted wave patterns, than other shallow-water wave models.
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From page 725... ...
and Cho, I.-lI. 1990 "Nonlinear free surface waves due to a ship moving near the critical speed in a shallow water," Proceedings of 18~ Symposium on Naval Hydrodynamics, Ann Arbor, pp.173-189.
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From page 726... ...
, we compared the specific resistance of our catamaran with that of a monohull identical to orate of the component hulls so that the displacement of the catamaran was twice that of the monohull. In this case, as the depth Froude number and, hence, the effective separation tends to infinity, the specific wave resistance of the catamaran should asymptotically equal exactly that of the monohull, even in nonlinear theory since He interference effects disappear.
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