Twenty-Third Symposium on Naval Hydrodynamics (2001) / Chapter Skim
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Breaking Waves in the Ocean and Around Ships
Breaking Waves in the Ocean and Around Ships
Pages 713-745
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From page 713... ...
Basin, Italy, maulan@waves.insean.it ABSTRACT A wide ranging summary of research on ocean and ship breaking waves carried out within the Ocean Engineering Laboratory at the University of California, Santa Barbara, beginning in 1985, is presented in a coherent fashion. Emphasis is given to the role of naturally arising wave modulations in their crucial effect on wave breaking, as well as on the essential role which wave breaking plays in wave evolution.
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From page 714... ...
Their names will be found as authors of the OEL related papers in the References. During the last few years we have much benefited from a close working collaboration with my coauthor, Maurizio Landrini, of INSEAN, Roma, who is now in charge of our numerical simulations of breaking and post breaking ship waves.
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From page 715... ...
Neither of these observed characteristics were understandable in terms of conventional theory, and it remained for nonlinear simulations, based on the 2D + t approximations, much later to reproduce and explain these results, Tulin and Wu (19961. The splashing, mixing, air entrainment, and noise generation which occurred in the aftermath of breaking of both energetic ocean waves and divergent bow waves, and are of such great interest today, had been seldom studied, with the exception of the hydraulic jump, or bore, about which a little was known.
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:~: Of Figure 3: Wave energy density spectra at various fetches (9-36 m) from the wavemaker, measured with wave wires in the large GEL Wind Wave Tank.
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(1996) , and to study the response of flexible vertical cylindrical structures to excitation in deformed and breaking waves, Welch et al.
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for breaking waves in his tank experiments. These deforming waves found in LONGTANK simulations have also been observed in tank measure
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In Section 3 of this paper we present theory which explains the mechanism associated with this criterion, and also its experimental verification through surface particle tracking experiments. As we have noted, wave modulation in the ocean is a result of wave instability of the BenjaminFeir type, and this newly described mechanism leads to breaking at group-averaged steepnesses as low as about 0 1.
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From page 720... ...
. Owe e.o~ e.oz Figure 13: Wave breaking in LONGTANK, hobo formation of a plunging jet.
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This led us to the development of the high resolution numerical wave tank, LONGTANK, and to numerical experiments of wave group formation leading to breaking, wave deformation and of the inevitable formation of the jet and of its growth and descent in a ballistic trajectory, Figure 13. Most remarkably, a simple criterion for the initiation of deformation was found from the LONGTANK studies: "that upon passing through the peak of a modulation group, when the orbital velocity at the wave crest, tic, exceeds the wave group velocity dw/dk = cg, then the wave crest and trough both rise, the frontface steepens, the wave crest sharpens, and eventually a jet forms at the crest, leadingfinally to splashing and a breakdown of the wave." This criterion was found to apply not only for deep water waves where dc~/dk ~ c/2 where c is the wave celerity, but for modulating waves in shallow water too, where dc~/dk is significantly smaller, Figure 14.
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at a rate controlled by the breaking process. The way in which this works was studied in our large wind-wave tank through laboratory observations of wave group evolution, including breaking effects, Tulin and Waseda (19991.
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2.7 Surface Tension Effects; Microbreakers The local curvatures in the wave geometry are largest at the crest of a deformed wave in its later prejet stage and in the jet itself, whose thickness may only be a few percent of the wave amplitude. We have carried out LONGTANK simulations of modulating and breaking waves, including the effect of surface tension, for waves of varying length down to 25 cm.
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From page 724... ...
3 WHEN AND WHY DO MODULATED GRAVITY WAVES BREAK? 3.1 The breaking process, and criterion Questions of stability aside, Stokes waves in water of constant depth exist for height to length ratios, H/A, up to a limiting value where the orbital velocity at the crest of the wave, tic, becomes equal to the wave celerity, c, whereupon the limiting wave crest becomes pointed with an included angle of 120°.
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From page 725... ...
The mathematical demonstration of this failure of progressive wave motion reveals that the modulated sinusoidal progressive wave is incompatible with kinematical requirements while passing through the peak of a modulation once oc > Cg The demonstration of this incompatibility involves a calculation of the rate of change of the direction, or, of the crest particle velocity vector hew, as the crest, M, passes through the peak of the wave group, N For a progressive wave of stationary form, the Stokes wave for example, the trajectory of the crest is a horizontal line, so that dor/dt~M = 0YM = 0.
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, and utilized it for a variety of studies, including orbital velocities in mechanically produced wave groups, including breaking waves, and in wind waves, Matsiev et al.
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1. Monochromatic 2.
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initiated, and the peak orbital speed quickly increases as deformation proceeds. 3.4 The limits of breaking The earliest observation of wave breaking in the field, carried out in sheltered water, Weissman et al.
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Each particle moves in the force field generated by the whole particle system and the physical quantities evolve according to suitable evolution laws following from the original differential field equations. The essential feature of the resulting algorithm is the complete absence of a computational grid and, in the present version of the method, a fully Lagrangian character (see Belitschko et al.
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From page 730... ...
In the case here considered, the velocity of the piston is high enough and the wave front breaks soon, leading to one of the most celebrated examples of breaking waves: a breaking bore. The good agreement between the two solution methods is apparent, though the impact of the falling jet against the underlying free surface prevents the BEM to continue the simulation.
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From page 731... ...
A second plunging event is already detectable, giving rise to a second clockwise rotating structure, which, with a different rate of growth, assists in the formation of a backward facing jet. The formation of the mushroom-like structure, and the growth of the backward jet, are essentially related to the gravitational collapse of the mass of water which, deflected upward by the impact, eventually falls down, plots C-D.
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I'd ~ '1 it :1 ~ ~~ '1 ran ~ 1 -by.!
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The forced breaking bore features repeated plunging events, which is also typical of breaking in shallow water as in the case of wave trains approaching a beach. A detailed description of the first plunging event is instructive, also for deep water breaking waves, and is given through the plots of Figure 26.
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it:.
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The vertical component bounces up, changing in sign, because both portions are moving upward, and then oscillates consistently with the orbital motion of the particles entrapped in the cavities. Eventually, Veal attains an almost zero value, with small amplitude oscillations related to the orbital motion inside the vertical structures rotating in an uncorrelated way.
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From page 736... ...
4.3 Breaking Bow Waves Breaking ship waves have always captured the interest of hydrodynamicists and naval architects because of their role in contributing to the resistance of the hull. More recent, however, is the interest of the Navy in the very long narrow wakes behind ships which can be observed remotely, and which originate abeam the ship through extensive breaking of diverging bow and stern waves.
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From page 737... ...
0.1 oboe 0.06 0.04 0.02 o -0.02 ~ /L 1 at Fr=0.4 -0.04 ~ 0 1 0 2 0 3 X / L 0 4 0.1 0.08 0.06 0.04 0.02 o -0.02 it_ 1 Fr=0.5 -0.04 ~ 0 1 0 2 0 3 X / L 0 4 ~ ~~-~ = #~ = # F[oudc numDcr F[= /.
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From page 738... ...
. Upon adopting a stern viewpoint, we observe that the breaking crest is propagating with an almost unchanged phase speed, though the simulation time is rather short to be conclusive and
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From page 739... ...
n-1 n -0.05 _ I ~A'9 MA ,70.2 a Figure 30: Breaking of the bow wave generated by a Wigley hull (B/L = 0 1, D/L = 0 1, Fr = 0 461.
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From page 740... ...
It is worth stressing, in this case, that the fluid particles emerging forward from the splash-up in plots B-C, are then "surfing" the wave crest after the splashing event, plots D-F, thus resembling the weak eddy steadily moving with the hydrofoil breaking wave, as discussed at the beginning of this paper. We found a striking similarity between the present results and the experimental observations by Lamarre, reported in Melville (1996, Figure 21.
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From page 741... ...
Yao) , who conceived of the special domain decomposition technique and implemented it for the high resolution simulation of long wave trains and the breaking process- she is the Mother of LONGTANK; Yi Tao Yao, who utilized LONGTANK So brilliantly in studies of wave breaking, who discovered the breaking criterion, simulated surface tension effects, and who collaborated in a host of studies of ocean wave behavior; J.J.
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From page 742... ...
(1980) , Wave-wave interactions, current-wave interactions and resulting extreme waves and breaking waves, Proc.
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~ 1996) , Doppler radar measurements of wave groups and breaking waves, J
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(1997) , Prediction of deck wetness and divergent bow waves on fine ships - nonlinear numerical studies, PhD Dissertation, UCSB, also OEL, Tech.Rpt.No.97-150.
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From page 745... ...
.nxal . tact re is slow r Ed would appear to follow c roughly parabolic hack, although its asymptotic motion carmotyetbek ow fromfhelimited calculations which w have done he crest of the divergent wave is 19 ter Ed its shucture spreads with time his conesponds physically to the growth in extent of the broken water just behind She crest Ed which would appear es c foam scar in She oce m in front of this scar is She small so fing breaker his marks the front of She broken wave A line d awn th ough She center of the surfing eddies back to the touchdow of the original jet would appear to be recsorurbly straight Agam, further calculations in time must be mad to under t Ed She fate of the cm bng eddy it would seem re tSornble to expect that it must eventually disappear
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