Eighteenth Symposium on Naval Hydrodynamics (1991) / Chapter Skim
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The Dispersion of Large-Amplitude Gravity Waves in Deep Water
The Dispersion of Large-Amplitude Gravity Waves in Deep Water
Pages 397-416
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From page 397... ...
Level III theory is used to simulate a train of steep regular waves and a random wave record corresponding to steep seas measured during hurricane Camille. An analysis of the simulated random wave record shows that the linear dispersion assumed for referring a random wave train from one point in space to another does not result in conservative estimates of two important quantities used in design: the crest elevation and particle velocity under the crest.
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From page 398... ...
of a measured real storm wave system is captured by the usual spectral analysis approach. Time series analysis allows identification of the spectral composition of the wave surface elevation at the point of measurement, and allows identification of some of the directional character of the seaway if many such points of measurement are made close by concurrently.
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From page 399... ...
The basis of this model is rather different from traditional models derived from potential theory using perturbation methods or from the specialized methods often introduced to compute with high accuracy the characteristics of regular, twodimensional water waves. When viscosity and surface tension are ignored and the fluid flow is assumed to be irrotational, the field equation (Laplaces's equation)
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From page 400... ...
3. Large-amplitude waves of permanent form In this paper we use the GN level III theory for time domain calculations of the dispersion of random waves.
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c. Particle velocity Figure 4 shows the wave profiles computed From the point of view of design of many for waves of various elevations at the crest for the offshore platforms, the horizontal particle veloc case k- a.
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Also shown on this figure is the horizontal particle velocity prediction from Airy wave theory.
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From page 403... ...
Figure 8 shows the wave elevation time history as seen by an observer 644' from the wave maker. This observer sees almost twice as many waves as seen in the surface elevation view because the group velocity is much less than the celerity (a manifestation of dispersion)
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In order to investigate the dispersion of random waves, a numerical experiment was conducted. An existing measurement of steep waves, recorded during Hurricane Camille in the Gulf of Mexico, August 16-17, 1969 was used as a foundation for this experiment.
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From page 405... ...
. The time histories of the wave elevation at x = 0' are now parts of a consistent description in time and space of nonlinear wave systems, and these descriptions afford an opportunity for assessing of the effects of nonlinear dispersion.
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From page 406... ...
The time histories of wave elevation at the probes at x = 400' and 800' recorded in the simulations are part of a nonlinear wave system, but can also be estimated from the reference time history at x = 0' using finite Fourier transforms and linear dispersion (as was done in (3)
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From page 407... ...
o - ~ - : - ~ ~ l l ~ ~ ~ ~ ~ ~ l Hi: ~ ~ to Juntas JalaaU.M - U°!
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From page 408... ...
When viewed as a whole, the graphs in Figure 13 show that the relationship between horizontal particle velocity discrepancy and the wave crest and trough discrepancy is nearly constant. That is, when the wave crest and trough predictions are good, the horizontal particle velocity predictions are good; when the wave crest and trough predictions are poor, the particle velocities are corresponding poor.
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From page 409... ...
The GN level III model was used to predict the generation of regular waves and it was found (and confirmed by laboratory experiments that the leading edge of a packet of relatively steep waves always appears to break before very many waves are created. This nonlinear model was also used to model a real steep wave record, that measured during Humcane Camille in 1969.
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From page 410... ...
Wave profiles predicted by superposition of Airy waves and linear dispersion.
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From page 411... ...
so o - 5 0 50 o - 5 0 - 5 0 50 o - 5 0 50 o - 5 0 -400 0 400 800 1200 Figure 14b. Wave profiles predicted by GN Level III theory.
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From page 413... ...
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From page 414... ...
~ ~ ~1 X ~ (at)
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From page 415... ...
~ ~ | ~ m1 ~ - ~ C N HI K ~ | Nat = C';1 At, Cal =1 cat ~ 1 ~ -, ~C = ~C - ~ ~ 1 X ~ ~- ~ =~ ~ o =. ATE ~ ~ ~ ~, ~ ~, cat ~hi,, , 5 + ~a, Ct ~ ~Cal $ ~+ Cd ~ N + ^ ~CQ _ C:~ ~t ~at CD acts + ~+ Cal, ~ Cad Am, 0: ~Ct , - Hi a' + CD , , o | | = 1 ~o = = = (3o (1,, ~ X ~ =| K ~' ~= Q _ - ~ ~ ~$ N , - `'=L Cq N N ~C~ C+ ~C~ ~C'l+ C: C: + c ~e~; + ~cc, c~ ~a~, ~6 (= O c: ~ C¢ , ~.:, ~· C K `:, t ;| C ~ct C~;l L I + 1 1 ~ 415
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From page 416... ...
indicate the existence of a second order free wave of frequency twice the fundamental wave frequency generated by the wave maker. This free wave is parasitic in nature as it travels along with the wave of interest, i.e., it does not die out.
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