Twenty-First Symposium on Naval Hydrodynamics (1997) / Chapter Skim
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Divergent Bow Waves
Divergent Bow Waves
Pages 661-679
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From page 661... ...
Froude numbers, Dagan and Tulin(1973~; exact two-dimensional calculations of the "smooth" flow before the bow, vanden Broeck and Tuck(19771; an asymptotic analytical theory of blunt bow flow before three dimensional shallow water ships, Fernandez(19811; studies of the necklace vortex and of viscous free surface stability, Mori(19851; exact unsteady free surface calculations of evolving bow waves, Grosenbough and Yeung(1989) , Yeung(1991~; and through exact analytical modeling of jet flows at the bow, Dias and vanden Broeck(19931; and others.
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From page 662... ...
A set of nested divergent waves appeared, Figure 4. Since that time, actual divergent bow waves have with little exception been linked with the Kelvin wave pattern, and simply considered part of it.
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From page 663... ...
3.The wedge flow The free surface flow about the inclined wedge, for which a length scale is absent, offers an important opportunity for understanding the morphology of bow waves produced by fine ships. Its consideration leads immediately to understanding of the inner flow (side splash)
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From page 664... ...
The Water Entry and Wavemaker Analysis The wedge flow corresponds to the vertical water entry of a two dimensional wedge in a vertical cross section. In the 2D+T view, the fine bow corresponds to an expanding section in the vertical plane, more like a wavemaker action.
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From page 665... ...
. For fine bows, however, the stagnation point is weak, and does not exist on the free surface.
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From page 666... ...
Since we believe that divergent bow waves are produced, at least in part, by the bow splash, it could be a test of 3-D codes to reproduce the flow at the bow of this frigate in reasonable detail. Non-linear Effects vs.
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From page 667... ...
6. The narrow divergent wave spectrum Since the bow divergent waves seem to arise from the relaxation of the bow splash, the spectral wave number content of the free waves in the divergent system must be found in a transverse cut through the splash at its maximum.
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From page 668... ...
6. The divergent bow waves have their origin in the bow splash which appears on either side of the bow and the spectral content of the waves originates in the spectral content in the splash cross section taken where the splash reaches its maximum height.
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From page 669... ...
P and Wu, M 1994 Bow waves on fine ships - nonlinear numerical studies.
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From page 670... ...
__.' i ,,~////~////,/~i>~//////~///~//~/~////~/.~i T~~ _# WAKE ( C ) U_ SEPARATING BOW EDDY MODEL Figure 1: Models of Blunt Bow Flow(Tulin)
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From page 671... ...
TV I I - Figure 4: Kelvin Kinematical Wave Pattern Figure 5: Large Wake (Black) Originating m Breaking Divergent Waves Alluminum Powder V~sualizaton, From Inui(1980)
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From page 672... ...
__~ 1 · - 1~ 1 X me, 6 ~ 7 . B Figure 8: Wave Profile on Wigley Hull, FL=0.25 (Simulation Shifted by Kx=O.
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From page 675... ...
B 0.4 0.2 '/L L/B=S, L/d=10, FL—0-30 I.o O.B o.e of 0.2 0.2 0.. L/B= 10, L/d= 10, FL=0.46 figure 11: Wave Pattern of Wigley Hull at different L/d, L/B, FL 675 0.8 O.B of 0 2 _O.O.= _0.O 0.2 °~4 ,/L L/13=10, L/d=10, FL=0 30 0.8 O.B of 0.2 —o.o - .0 0.2 0..
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From page 676... ...
o ~/ll o to a' ~ c2 o o.
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From page 677... ...
Figure 13: 2D+T Simulated Bow Wave by Frigate Hull, FL=0 5 (top) Photo (bottom)
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From page 678... ...
3/L=0. 11, d/L=0.072 0.16 -0.0 0.2 0.4 -0.0 0.2 0.4 -0.0 0.2 0.4 7/L ,/L ,/L L/B=20, L/d=10, FL=0 30 L/~=10, L/d=10, FL=0.23 L/B=20, L/d=1, FL=0-30 Figure 14: Comparison Between Calculated Bow Wave on Wigley Hulls linear (ldichell)
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From page 679... ...
1/2 = 1 03 0.02 0.01 0.00 -0.0 1 X/L=0.206 -- - -- -- , -- -: -- -- : -- -- : -- - 1 0.05 0.10 0.15 y/L (b) Figure 16: Bow Wave Crest Cut at xiL=0.206 for Parent Wigley Hull at F~,=0.30 679
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