Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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Near-Field Nonlinearities and Short Far-Field Ship Waves
Near-Field Nonlinearities and Short Far-Field Ship Waves
Pages 465-476
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From page 465... ...
More precisely, the far-field wave spectrum is determined in a simple and practical manner by means of a waterlineintegral approximation obtained from a modified Neumann-Kelvin integral representation; and the nonlinear near-field flow along the ship waterline is determined via a nonlinear correction defined by a simple analytical expression. Numerical calculations for the Wigley hull predict short divergent waves too steep to exist in reality within a significant sector in the vicinity of the ship track.
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From page 466... ...
Reliable predictions of the short waves in a ship wave spectrum are quite difficult to obtain because of the significant numerical difficulties mentioned in the foregoing, as well as for yet another reason. This second source of difficulties stems from the fact that short far-field ship waves are closely related to the velocity distribution along the ship mean waterline, especially the fluid velocity at the ship bow and stern, as is shown further on in this study.
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From page 467... ...
Approximate forms of these expressions valid in the short-wave limit are now given. THE WAVE SPECTRUM: APPROXIMATE INTEGRAL REPRESENTATION The expression for the slender-ship approximation Ko defined by (30)
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From page 468... ...
. These equations provide a simple and practical basis for numerically evaluating the short divergent waves in the steady wave spectrum of a ship, given the value of the fluid velocity components as and of at the waterline, by dividing the waterline w into a large number of straight segments within which the amplitude functions A+ are assumed to vary linearly.
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From page 469... ...
which shows that the very short divergent waves in the steady wave spectrum of a ship primarily stem from the central (midship) portion of the ship 469
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From page 470... ...
However, it was already noted that existing nearfield-flow calculation methods, including the socalled nonlinear methods, cannot provide accurate predictions of the velocity components as and (~ in the immediate vicinity of a ship bow and stern. The velocity components as and of along the wave profile of a ship can be defined in terms of the nondimensional elevation e = Eg/U2 of the wave profile and its slope en = dE(L)
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From page 471... ...
oo _ o _ d. ~o _ no> _ o oh \ ~ ~ 0 VELOCITY AT WATER LINE WIGLEY HULL AT F=0.25 slender-ship approximation with nonlinear correction nonlinear analytical/ experimental prediction ~1 stern bow Fig.
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From page 472... ...
These numerical results indicate that the major contributions to the waterline integral (18) clearly stem from the ship bow and stern, and that the simple nonlinear correction of the linear numerical predictions of the wave-profile elevation presented in [15]
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From page 473... ...
in (46a,b,c) we may obtain the following expressions for the values of the wavelength X, the wave propagation angle 0, the waterline tangent angle l o l, and the wake ray angle or corresponding to a given value of p: (46a,b)
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From page 474... ...
CONCLUSION A simple practical analytical/numerical method for calculating the short divergent waves in the steady wave spectrum of a ship has been presented. The method is based on a waterline-integral approximation obtained from a modified Neumann-Kelvin integral representation of the wave-spectrum function.
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From page 475... ...
This result indicates that the short divergent waves in the wave pattern of a ship stem mostly from the ship bow and stern; a result that is not surprising but points to the fundamental difficulty of predicting the short divergent waves since the flow at a ship bow and stern is strongly nonlinear and quite difficult to compute. Numerical calculations for the Wigley hull showed that the steepness of the short divergent waves predicted on the basis of the foregoing linear far-field/nonlinear near-field flow analysis is too large for the waves to exist in reality within a sector of several degrees in the vicinity of the ship track.
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From page 476... ...
Lin and R Mellish, "Alternative mathematical expressions for the steady wave spectrum of a ship," Journal of Ship Research, in press.
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