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24~ Symposium on Naval Hydrodynamics Fukuoka, JAPAN, 8-13 July 2002 GENESIS OF DESIGN WAVE GROUPS IN EXTREME SEAS FOR THE EVALUATION OF WAVE/STRUCTURE INTERACTION ·. GUNTHER F. CLAUSS (Technical University of Berlin, Dept. of Naval Architecture and Ocean Engineering, Gennany) ABSTRACT For the design of safe and economic offshore structures and ships the knowledge of the extreme wave environment and related wave/structure interactions is required. A stochastic analysis of these phenomena is insufficient as local characteristics in the wave pattern are of great importance for deriving appropriate design criteria. This paper describes techniques to synthesize deterministic task-related 'rogue' waves or critical wave groups for engineering applications. These extreme events, represented by local characteristics like tailored design wave sequences, are integrated in a random or deterministic seaway with a defined energy density spectrum. If a strictly deterministic . . . .. . . process Is estan~snect, cause and effect are clearly related: at any position the non-linear surface elevation and the associated pressure field as well as the velocity and acceleration fields can be determined. Also the point of wave/structure interaction can be selected arbitrarily, and any test can be repeated deliberately. Wave-structure interaction is decomposable into subsequent steps: surface elevation - wave kinematics and dynamics - forces on structure components and the entire structure - structure motions. Firstly, the generation of linear wave groups is presented. The method is based on the wave focussing technique. In our approach the synthesis and up- stream transformation of arbitrary wave packets is developed from its so-called concentration point where all component waves are superimposed without phase-shift. For a target Fourier wave spectrum a tailored wave sequence can be assigned to a selected position. This wave train is linearly transformed back to the wave maker and - by introducing the electro- hydraulic and hydrodynamic transfer functions of the wave generator - the associated control signal is calculated. Based on this technique the seakeeping behaviour of ships or offshore structures is efficiently determined with just one single model test. The generation of steeper and higher wave groups requires a more sophisticated approach as propagation velocity increases with wave height. With a semi- empirical procedure the control signal of extremely high wave groups is determined, and the propagation of the associated wave train is calculated by iterative integration of coupled equations of particle tracks. With this deterministic technique 'freak' waves up to heights of 3.2m have been generated in a wave tank. For many applications the detailed knowledge of the nonlinear characteristics of the flow field is required, i.e. wave elevation, pressure field as well as velocity and acceleration fields. In this case a finite element method is used to determine the velocity potential, which satisfies the Laplace equation for Neumann and Dirichlet boundary conditions. So far, nonlinear wave groups in an ideal fluid have been investigated. If viscous effects are also considered an approach of transient viscous free surface flow computation with RANSE/VOF solver is used. As an application, an artificial reef- modeled as a submerged permeable wall - has been analysed. In general, extremely high 'rogue' waves or critical wave groups are rare events embedded in a random seaway. The most efficient and economical procedure to simulate and generate such a specified wave scenario for a given design variance spectrum is based on the appropriate superposition of component waves or waveless. As the method is linear, the wave train can be transformed down-stream and up-stream between wave board and target position. The desired characteristics like wave height and period as well as crest height and steepness are defined by an appropriate objective function. The subsequent optimization of the initially random phase spectrum is solved by a Sequential Quadratic Programming method (SQP). The linear synthetization of critical wave events is expanded to a fully nonlinear simulation by applying the subplex
method. Improving the linear SQP-solution by the nonlinear subplex expansion results in realistic 'rogue'-waves embedded in random seas. As an illustration of this technique a reported rogue wave - the Draupner 'mew Year Wave" is simulated and generated in a physical wave tank. Also a "Three Sisters" wave sequence with succeeding wave heights HS...2Hs...Hs, embedded in an extreme sea, is synthesized. For investigating the consequences of specific extreme sea conditions this paper analyses extreme roll motions and the capsizing of a Ro-Ro vessel in a severe storm wave group. In addition, the seakeeping behaviour of a semisubmersible in the Draupner New Year Wave, embedded in extreme irregular seas is numerically and experimentally evaluated. INTRODUCTION Considering rogue wave events as rare phenomena - according to Murphy's law - beyond our present modelling abilities, Haver (2000) suggests that freak waves (unexpected large crest height / wave height, unexpected severe combination of wave height and wave steepness, or unexpected group pattern) should be defined as wave events which do not belong to the population defined by a Rayleigh model. To yield a sufficiently small contribution to the overall risk of structural collapse, the structure should withstand extreme waves corresponding to an annual probability of exceedance of say 10-s _ 10-4 as the Rayleigh model underpredicts the highest crest heights indicating that real processes may be strictly affected by higher order coefficients. In addition to the ULS (ultimate limit state) based on a 100-year design wave an ALS (accidental limit state) with a return period of 10000 years is suggested. Based on observations Faulkner (2000) suggests the freak or abnormal wave height for survival design He 2 2.5Hs . It is also recommended to characterize wave impact loads so they can be quantified for potentially critical seaways and operating conditions. Present design methods should be complemented by survival design procedures, i.e. two levels of design wave climates are proposed: The Operability Envelope which corresponds to the best present design practice The Survivability Envelope based on extreme wave spectra parameters which may lead to episodic waves or wave sequences (e.g. the Three Sisters) with extremely high and steep crests. Wave steepness, characterized by front and rear steepness as well as by horizontal and vertical wave asymmetries seems to be a parameter at least as important as wave height (Kjeldsen an Myrhaug, 1979~. A probability analysis of rogue wave data recorded at North Alwyn from 1994 to 1998 reveals that these waves are generally 50 % steeper than the significant steepness, with wave heights HmaX > 2.3Hs (Wolfram et al, 2000~. The preceding and succeeding waves have steepness values around half the significant values while their heights are around the significant height. Steep-fronted wave surface profiles with significant asymmetry in the horizontal direction excite extreme relative motions at the bow of a cruising ship with significant consequences on green water loading on the fore deck and hatch covers of a bulk carrier (Drake, 1997~. Heavy weather damages caused by giant waves are presented by Kjeldsen (1996), including the capsizing of the semisubmersible Ocean Ranger. Faulkner and Buckley (1997) describe a number of episodes of massive damage to ships due to rogue waves, e.g. with the liners Queen Elisabeth and Queen Mary. Haver and Anderson, (2000) report on substantial damage of the jacket platform Draupner when a giant wave (HmaX = 25.63m with the crest height '7c = 18.5m hit the structure in 70m water depth on January 1, 1995 (Fig. 1-top). Related to the significant wave height H = 11.92m . the maximum _ a wave rises to HmaX = 2.15Hs with a crest of 77c = 0.72Hmax Not as spectacular but still exceptional are wave data from the Norwegian Frigg field - water depth 99.4m (Hs = 8 49m' HmaX = 19.98m id = 12.24m ~ (Kjeldsen, 1990) and the Danish Corm field - water depth 40m (Hs =6.9m, HmaX =17.8m, id ~13m) (Sand et al., 2000~. Also remarkable are wave records of the Japanese National Maritime Institute measured off Yura harbour at a water depth of 43m (Hs = 5.09m, Hmax = 13 6m, 71C ~ 8.2m ~ (Mori et al., 2000) (Fig. 1-bottom). All these wave data - with HmaX I Hs >2.15 and id IHmaX > 0.6 - prove, that rogue waves are serious events which should be considered in the design process. Although their probability is very low they are physically possible. It is a challenging question which maximum wave and crest heights can develop in a certain sea-state characterized by Hs and Tp. Concerning wave/structure interactions, with respect to response based design loads and motions or reliability based design: Is the highest wave with the steepest crest the most relevant design condition or should we identify critical wave sequences embedded in an irregular wave train? In addition to the global parameters Hs and Tp the wave effects on a
North Sea - Draupner jacket platform (Haver and Anderson, 2000) - New Year wave 01-01-95 Hs- 1 1.92m, HmaX = 25.63m = 2.15 HS; TIC = 18.5m = 0.72 HmaX (water depth 70m) Japanese Sea - off Yura harbour - Japanese National Maritime Institute (Mori et al., 2000) Hs- 5.09m, Hma,, = 13.6m = 2.67 Hs; ~c= 8.2m = 0.6 HmaX (water depth 43m) Fig. 1 Rogue wave registrations structure depend on superposition and the interaction of wave components, i.e. on local wave characteristics. Phase relations and nonlinear interactions are key parameters to specify the relevant surface profile at the structure. If wave kinematics and dynamics are known, cause-effect relationships can be detected. This paper presents a numerical as well as an experimental technique for the generation of design wave sequences in extreme seas. Based on selected global sea state data (Hs, Tp) the wave field is fitted to predetermined characteristics at a target location, such as wave heights, crest heights and periods of a single or a sequence of extreme individual waves. Starting with a linear approximation of the desired wave train by optimizing an initially random phase spectrum for a given variance spectrum we obtain an initial guess for the wave board motion. This control signal is systematically improved to fit the wave train to the predetermined wave characteristics at target location. Numerical and experimental methods are complementing each other. If the fitting process is conducted in a wave tank all nonlinear free surface effects and even wave breaking are automatically considered. Firstly, the linear procedure is presented, and illustrated by the generation of deterministic wave packets as well as the synthesis of the above target wave train into an irregular sea. Next, the nonlinear approach with its experimental validation is presented. Finally, the nonlinear fitting process of the target wave sequence embedded in irregular seas is developed. LINEAR TRANSIENT WAVE DESCRIPTION The method for generating linear wave groups is based on the wave focussing technique of Davis and Zarnick ( 1964), and its significant development of Takezawa and Hirayama (1976~. Clauss and Bergmann (1986) recommended a special type of transient waves, i.e. Gaussian wave packets, which have the advantage that their propagation behaviour can be predicted analytically. With increasing efficiency and capacity of computer the restriction to a Gaussian distribution of wave amplitudes has been abandoned, and the entire process is now performed numerically (Clause and Kuhnlein, 1995~. The shape and width of the wave spectrum can be selected individually for providing sufficient energy in the relevant frequency range. As a result the wave train is predictable at any instant and at any stationary or moving location. In addition, the wave
orbital motions as well as the pressure distribution and the vector fields of velocity and acceleration can be calculated. According to its high accuracy the technique is capable of generating special purpose transient waves. A continuous real-valued wave record ((t) may be represented in frequency domain by its complex Fourier transform F(co) which is calculated by Eq.~1~. Applying the inverse Fourier transformation, Eq.~2), gives the original record ((t): +~ F(~) = | ~ (t)e-ia't dt _00 ((I) = 2 |F(~)ei~ do') (2) ~00 where t represents the time and a' = 27f the angular frequency. In polar notation, the complex Fourier transform can be expressed by its amplitude and phase spectrum: F(~) = I F(co) leiargF(a)) (3) In practice, it is necessary to adopt a discrete and finite form of the Fourier transform pair described by Eqs. (1) and (2): N-1 ~4i Fir/ = lit ~ ((k~t)e-i2'`rk/N ~ J k=0 r = 0,1,2,. .., N /2 g(k/`t) = ~ F(r/`Go)e i2~ rk/N (5) ~{ r=0 k = 0,1,2,. .., (N -1), , . . . superposition with/ \ random phase / \- ~r I in-phase superposition (rare- but possible) . . .~ extremely long registration of a severe irregular sea state Fig. 2 Design wave as rare event of component wave superposition. where the values ((kAt) represent the available data points of the discrete finite wave record, with At denoting the sampling rate and /`a) = 2'z l(NAt) the frequency resolution. The summation in Eqs. (4) and (5) can be efficiently completed by the fast Fourier transform (FFT) and its inverse algorithm (IFFT). Extreme wave conditions in a 100-year design storm arise from the most unfavourable superposition of component waves of the related severe sea spectrum. Fig.2 presents the simulation of an irregular sea state by random phase superposition. As a rare - but possible - event, a very high freak wave is observed. Freak waves have been registered in standard irregular seas when component waves accidentally superimpose in phase. Extensive random time domain simulation of the ocean surface for obtaining statistics of the extremes, however, is very time consuming. In generating irregular seas in a wave tank the phase shift is supposed to be random, however, it is fixed by the control program on the basis of a pseudo-random process: consequently, it is also a deterministic parameter. Why should we wait for these rare events if we can achieve these conditions by intentionally selecting a suitable phase shift, and generate a deterministic sequence of waves, which converge at a preset concentration point? Assuming linear wave theory, the synthesis and up-stream transformation of wave packets is developed from this concentration point. At this position all waves are superimposed without phase shift resulting in a single high wave peak. From its concentration point, the Fourier transform of the wave train is transformed to the upstream position at the wave board (Kuhnlein, 1997~. The Fourier transform is characterized by the amplitude spectrum and the related phase distribution. During propagation the amplitude spectrum remains invariant, however, the phase distribution and the related shape of the wave train varies with its position. Fig. 3 (left hand side) shows a wave train as a function of time at different positions and the related amplitude spectrum of the complex Fourier transform. Note that the maximum wave ellevation is deduced from the registration at the concentration point, which starts with a deep trough, followed by an extremely steep and high crest, and ends symmetrically with a trough. The wave train can be transformed from a function of time at a fixed location xO to a function of space at a given time to. Fig. 3 (right hand side) shows wave elevations at selected moments. i.e. successive "photos" of the water surface. At the concentration point the wave is represented by a short and steep crest tapering off into extremely long and shallow troughs at both sides. As the process is strictly linear and deterministic, wave groups can be analysed back and forth in time and
)~/ ~ o - _ 5 O -5 ~ O .,,5 -5 5 ~-5 O u: - Fourier- ~\ spectrum , 1'LJUl 1~:1 go - ~/~\ spectrum c, - / \ / \ ~0.5 / \ 3 : /wave frequency O O i/ o~ [rad/s] \> 0 4 8 12 Pos. 1: wave packet converging no = 0 m - Pos. 4: concentration point, no = 107 m ~ Pos. 5: wave packet diverging, no = 120 m c' 1 - _' r , 5 ~ O I_ - 5 5 A_ O -5 5 1 lo °1 ~ - 51 - 5 a) °1- _5 5 O cn , ;\ Fourier I\ spectrum '., wave number k~d/s~ To ~ 10 1.5 _ instant: to=200 s wave packet converging I I I I ~ I I I I I I ~ ~ ~ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 ~ ~ ~ ~ - t=210 s j ~ ~ , -t=220s _ t=225 s concentration point ~ ,IIA ~ t=230 s wave Packet diverging v0 100 200 t [Sl -0 50 100 ~ Em 1 Fig. 3 Wave packet registration at different positions (left) as well as instantaneous wave profiles at selected instants (right). space. They also can be integrated into a specified irregular sea. Based on the linear wave packet technique the seakeeping behaviour of ships or offshore structures is efficiently determined with just one single model test (Clause and Kuhnlein, 1995~. The testing procedure is completely automated: Wave generation as well as carriage are operating computer controlled to ensure the predetermined interaction of wave train and vessel. First, a wave train of about 100 m length is generated. As each subsequent wave is slightly longer (and faster) than the preceding one, the length of the wave train is shrinking rapidly while propagating along the tank. Shortly before the concentration point, the cruising vessel meets the wave train exactly at the predetermined position. As shown in Fig. 4 this wave train excites heave and pitch motions. To prove the linear behaviour of the vessel in waves, spectra with different maximum wave height have been used resulting in identical RAOs, by amplitude and phase, with a resolution of about 400 frequency points. Note that the seakeeping tests for evaluating the entire ship motion behaviour takes just 10 seconds, i.e. precise and highly resolved results are achieved in a short time. In addition, the ship starts and stops under still water conditions. NONLINEAR TRANSIENT WAVE DESCRIPTION The generation of higher and steeper wave sequences, requires a more sophisticated approach as propagation velocity increases with height. Consequently, it is not possible anymore to calculate the wave train linearly upstream back to the wave generator to determine the (nonlinear) control signal of the wave board. To solve this problem, Kuhnlein (1997) developed a semi- empirical procedure for the evolution of extremely high wave groups which is based on linear wave theory: the propagation of high and steep wave trains is calculated by iterative integration of coupled equations of particle positions. With this deterministic technique "freak" waves up to 3.2 m high have been generated in a wave tank (Clause and Kuhnlein, 1997~. Fig. 5 shows the genesis of this wave packet and presents registrations which have been measured at various locations including the concentration point at 84 m. The associated wave board motion which has been determined by the above semi-empirical procedure is the key input for the nonlinear analysis of wave propagation. As has been generally observed - at wave groups as well as at irregular seas with embedded rogue wave sequences - we register substantial differences between the measured time series and the specified design wave train at target location if a linearly synthesized control signal is used for the generation of higher and steeper waves.
., 0.10 0.05 -o.oo ·_I ~ -o.os 0) -o. 10 a, : 0.10 0.05 ~q o.oos eO.004 L 0.003 C~ 0.002 ~ , 0.001 _ pitch n~otion _ of towed catamoran ~ -,,,, 1,,, 1 ~ ~ ~ ~ ~ ~ ~ ~ 1 ~ 1 _ 50 160 170 180 190 model wave packet ~_- . 1111~111116111161111~1111~1111~1111~1111~1111~111111111 - /~\ wave packets ~ ~/ ~ (dUlorent w. ~ heights) /~ w.uvv ' I ' " " ' , ' , ~ , , , ~ I ~ , , , ~ I I I I I,,,, 1,,,, 0.0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 B.0 9.0 10.0 11.0 12.0 Lq 0'005 L' ' ' " ' ' ' " ~ * e O.004 0.003 ~ 0.002 ·L~ 0.001 n ono ~ 1.00 q) > 0.50 r. ~> 0.6 c, 0- _ 1 t _ ~ I I ~ I ~ ~ ~ ~ I T I I I I ~ I I I ~ surface elevation (registrat~on of wave group ~, . at encounter position) ~ ~ 1 1 1 1 1 ~ 1 1~ . i ' ~ ~ ~ 1 ' ' ' 1 1 ' ' I ~ 1 ~ ~ ~ ~ encounter wave packet (measured with a wave , , , 1 , , 1 240 25C . I ' ' ' I 'A' I I I ' ~ ~ ~ I ~ ~ ~ , ~ = ~ _- ~ ~ decelerating vessel overrun by its own stern wave system~ 1,,,,1,,111 I , I ,1, ... probe on board of the moving carriage) . 1,,,,1,,,,~, 50 160 170 lBO 190 200 210 220 230 - ' ' ' ' 1 1 ~ ~ I 1 ~ ~ ~ ' 1 ' ~ ' ~ 1 , _ heave motion of towed cato m a ra n T ~ T ~~~ encounter vesse l/wave 1 ~ ~ ~ 1 , . . . -0.00 -0.05 -0.10 150 160 170 iBO 190 200 210 220 230 240 25C 3.0 2.0 1.0 0.0 -1.0 -2.0 -3.0 T r T r T l r l r ~'~ time window for evaluation ,,,, 1, . . . _l . I I ~ ' ' I I ~ I ~_' I I I I ~ I I I I ~ I I I I 1 1 1 1 1 ~ r I I r 1~ 1 1 iT ~ / ~~ Vu=4m/s 0.0 1.0 2.0 3.0 4.0 6.0 B.0 7.0 8.0 9.0 10.0 11.0 lZ.0 1 ~tl 1 1 1 ~ ~ I 1 1 1 ~ 1 1 1 1 ~ 1 1 1 1 ~ I 1 1 1 ~ 1 1 1 1 1 1 1 1 1 ~ 1 1 1 1 ~ I 1 1 1 ~ v=20.5kn RAO heave : `, o.oo ~ 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 ~ =o x~ c> ·.V ~ 1 1 1 1 ~ I I I I ~ 1 1 1 1 1,, 1 1 ~ 1 ~ - 0.0 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 C) rrad/s Fig. 4 Registrations, Fourier spectra, and transfer functions of a typical seakeeping test with a high-speed catamaran in transient wave trains (model scale 1:7, Vm=4~0 m/s; full scale: V=20.5 kn; Fn=0.56~. 0.5: 0.0 r . I I i I i I T i ~ ~ I ~ ~ ~ T I i i ~ i Note: stern of th e vessel is lifted - . ~mechanically by security rope . ~ I , , , , 1 205 time [s] 210 i ~ I ~ ~ ~ I I ~ ~ ~ I I ~ ~ I I I l,~ T~ ~ I ~ I I I I I ~ I ~ I I I I I I I I I I I I I I /~~ ~ ~ 0.150 7 e ; ~ 0.100 _ _ _ 0.050 _ 2L -~ pitch (modal soals) U.U~V ,5- ,- , ~ ,I,,,,l, ~ ~ ~ 0,0 1.0 2.0 3.0 4.0 5.0 6.0 7.0 8.0 9.0 10.0 11.0 12.0 Q r~r~ . . . V.VV 6.00 _ 4.00 _ 2.00 0.00 _ 0.0 1.0 0.6 _ 0.0 -0.5 ~ ~ : phase pitch ,~, . ~ ~ -1.0 ,,,, 1,,,, 1,,,, I, I, I 1,, ', I I,,, i,,,, 1 1,, I ~ I l~, ~ \, · I I 0.0 0.5 1.0 1.5 2.0 2.5 3.0 q-.5 4.0 4.5 5.0 C) rrad/s ,,,,1-l,,'.1. . ,1,,.~. ,,.~ 0.5 1.0 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 " ' ' ' " ' ' ' I I ' ' ' ' 1 ' ' ' ' I ' ' ' ' I ' ' ' ' I ' ' ' ' 1 ' ' ' ' ~ ' ' ' ', (tuU ·~1 - ) _ . ~ RAO pitch ~ ~ * . _~-
~ .' ~ -1.5 - registration at 3.6 in 0.5 -0.5 ~ .5 0.5 . _. -1.S -2.S 2.5 I.B n ~ at 50.05 m t [s] L ~ I_LlA_L~ _l_~.- I_I.J_J ~.J ~_I.~_Il.l l_~ _l LJ_l_L.~ )_~ ~.~ _l_Ld_I_~.LI_t ~ 1_1 [.~_1 tO 20 30 40 .'50 '30 7n so so 100 tin 12t) . ',,,,,,, I t [S] ~ a.:) O 10 20 30 40 50 60 70 SO So :CO 110 120 2.5 .._ 0.5 -t)S -IS -2.5 n 1.5 _ (conc,eIltration point is at 84 m) ,,,, 1: . ., I, . . . 1, I 1 1 a:, . I,,:, I, J 10 20 3D 40 50 60 ~ at 90.3 m (after hrt?akillg) Fig. 5 Genesis of a 3.2 m rogue wave by deterministic superposition of component waves (water depth Ant m). As illustrated in Fig. 6, however, the main deviation is localized within a small range (Clause et al., 2001~. This promising observation proves that it is sufficient for only a short part of the control signal in the time domain to be fitted. As a prerequisite, however, the computer controlled loop in the experimental generation process should imply nonlinear wave theory and develop the wave evolution by using a numerical time-stepping method. The two dimensional fully nonlinear free surface flow problem is analysed in time domain using potential flow theory. Fig. 7 summarises the basic equations and boundary conditions. nno =.02 _n net 0.03 t . Sudace elevations at target Ideation A I ~ ~ ~ ~ l .. ~ ·; I · - ~ Massured tree surtax elation .; 1 LTarot suna" aleva ~ Fig. 6 Comparison between target wave and measuredlime series at target location. 27
1 7) ~ at// Surface elevation and associated velocity potential ~ /- '/ ~ ~ ~ I//,,,,,,,,,, A. V2~ = 0 E -1 - -2 -1 Fig. 7 Numerical wave tank (Steinhagen, 2001). s-2 Fig. 8 Finite element mesh for nonlinear analysis. A finite element method developed by Wu and Eatock Taylor (1994, 1995) is used to determine the velocity potential, which satisfies the Laplace equation for Neumann and Dirichlet boundary conditions. The Neumann boundary condition at the wave generator is introduced in form of the first time- derivative of the measured wave board motion. To develop the solution in time domain the forth order Runge-Kutta method is applied. Starting from a finite element mesh with 8000 triangular elements (401 nodes in x-direction, 11 nodes in z-direction, i.e. 4411 nodes) (see Fig. 8) a new boundary-fitted mesh is created at each time step. Lagrangian particles concentrate in regions of high velocity gradients, leading to a high resolution at the concentration point. This mixed Eulerian-Langrangian approach has proved its capability to handle the singularities at intersection points of the free surface and the wave board. Fig. 9 shows wave profiles with associated velocity potential as well as registrations at different positions. Note that the pressure distribution as well as velocity and acceleration fields including particle tracks at arbitrary locations are deduced from the velocity potential. Fig. 10 presents numerical results as well as experimental data to validate this nonlinear approach. Excellent agreement of numerical and experimental v.u~v ~ ......... 4 1 50 60 1- O 7~- 7: : :: :::::: : 3 . . . . . . . . . . . . . . . :. : : 1 SO 60 1 l l n : 8.923 ~ An 7c AZ , . .. ... . . . . . . . .. . . 70 80 90 100 110 120 130 140 t=96258 1.64 , , l l 90 1X 110 120 50 60 70 80 90 100 110 120 130 140 x In m Fin. 9 Nonlinear numerical simulation of transient waves. results is observed. Note that all kinematic and dynamic characteristics during wave packet propagation are deduced from the velocity potential, i.e. registrations at any position (top, left) with associated Fourier spectra, wave profiles at arbitrary instants (top, right) as well as velocity, acceleration and pressure fields. Fig. 11 shows the maximum (crest) and minimum (trough) surface elevation in the wave tank {maX and (min as well as the difference, i.e. the wave height ~ - ~ . . Note the sudden rise of water level (crest and max mm trough) at the concentration point. Fig. 12 illustrates numerically calculated orbital tracks of particles with starting locations at x = 87m and at x = 126m, which is very close to the concentration point. Generally, the orbital tracks are not closed. Particles with starting locations z > elm are shifted in the x-direction, and due to mass conservation particles with lower z-coordinates are shifted in the opposite direction. Fig. 13 finally proofs that the technique for generating nonlinear wave packets is adaptable to different wave machines. The diagrams present results for a two-flap wave generator, i.e. the angular motions (and speed) of the lower and upper flaps as well as the resulting wave group registration. Excellent agreement between numerical and experimental results is observed. Note that the short leading waves are generated by the
Registrations wave profiles ("photos") . E _ . at ~ . . O '-- '2' V~ Ob '~5 ~ ~ ~ ~ t~ q~ q4~ to 2 Follrier Nectar v. ~ - ..~ Fig. 10 Wave packet registrations at different positions as well as instantaneous wave profiles at selected instants - numerical calculations validated by experimental results (Clause and Steinhagen, 1999). ! upper flap. As the lower flap starts working, the motion of the upper flap is reduced, and finally oscillates anti-phase with the lower flap (Pakozdi, 2002, Hennig, 2001). So far, nonlinear wave groups in an ideal fluid have been considered. If viscous effects are also considered and approach of transient viscous free surface flow computation with (RANSE/VOF) solver is used. As an application, an artificial reef - modelled as a submerged permeable wall - has been investigated: Using an unstructured grid, the dissipation loss is explained by overtopping phenomena and subsequent recirculation of the flow locked in chambers between filter elements (Fig. 14~. Jet flow between filter components is also fostering high energy loss. Due to non-linear wave/filter interactions long low-frequency incident waves with substantial erosive impact are transformed into irregular wave trains with high-frequency wave .' "." ~ ·0.5~ \ (min ~ l l ! i I l l ~ 20 40 GO 80 100 Fig. 11 Maximum (crest) and minimum (trough) surface elevations ~ (maX ~ {min ) as well as wave height ~ _ ~ max mm
/ 1~ ins -1.s ·2.5 , , I , 1 125,5 126 126.5 127 127.5 xhm Fig. 12 Particle tracks with starting location at x=126m. energy components, which cause less erosion to the sea floor (Clause and Habel, 2000~. 0.02 _ ~ O .0.02 0.060 · _,,u.`l`elill~l!llltit |~.; _ _ lows flap angular motion ~ . . . ~ I 1 200 250 300 ~ - Iower flap rotational speed ... . 41 u.~ ; ; ; 0 020 50 100 150 200 250 300 350 , 1 ,1 1 1 1 1 O 9~.= _ n me upper flap angular niotion ._~ _ ,,_ .... ......... . ~ ~ a ....... . . . . I 1 1 200 250 300 350 950 _.w 0 50 100 150 200 2SO t [all 900 HSVA Rolls H TS079 registration at various positions O.OQ ~ | _ S.88 m | . . . ~ A ~ I I A I l, ~ ~ I ~ d ~ !l . . ~ `. . i. A, , . . ~ JO 05 ~ ... ... ........ .... ... ' ' ' . \~ .,,~ ; .... ... ' ... ... ... 158 158 100 182 1B. 1 - ~ [S] Fig 13 Motions of a two-flap wave generator and related wave group registration comparing numerical and experimental results. Numencal simulations of Wave I filter interactions ~ _ 1. Submerged wall (WBAU) ~> " ~ I 2. Filter, 11% porosity (GWK) ., Fig. 14 Transient viscous computation of artificial reefs (RANSE/VOF) - velocities due to wave/filter interaction for submerged wall and 1 1% filter. rNTEGRATION OF DESIGN WAVE GROUPS IN IRREGULAR SEAS - LINEAR APPROACH 350 In general, extremely high 'rogue' waves or critical wave groups are rare events embedded in a random seaway. As long as linear wave theory is applied, the sea state can be regarded as superposition of independent harmonic waves, each having a particular direction, amplitude, frequency and phase. For a given design variance spectrum of an unidirectional wave train, the phase spectrum is responsible for all local characteristics, e.g. the wave height and period distribution as well as the location of the highest wave crest in time and space. For this reason, an initially random phase spectrum argF(~) is optimized to generate the desired design wave train with specified local properties. The phase values ~ = (me ~ p2 ~ pn)T are bounded by - adz < ~ < fez and are initially determined from pi=2'z(Rj-O.S) where Rj are random numbers in the interval 0 to 1 (Clause and Steinhagen, 2000). The set up of the optimization problem is illustrated for a high transient design wave within a tailored group of three successive waves in random sea. The crest front steepness of the design wave in time domain at as defined by Kjeldsen (1990): 2}Z Crest (6) £ = t gTr~seTzd
is maximized during the optimization process. acres, denotes the crest height, Trise the time between the zero-upcrossing and crest elevation, and To, the zero- downcrossing period which includes the design wave. The target zero-upcrossing wave heights of the leading, the design and the trailing wave are defined by H., H., and H. . The target locations in space and time of the design wave crest height if,` are x~arge, and tfarge`. These data define equality constraints. The maximum values of stroke x velocity u and m" ~ max ~ acceleration amaX of the wave board motion Aft) define inequality constraints to be taken into account. Hence the optimization problem is stated as minimize f (,B) = - £, - g5 = g6 = g7 = g7+j = 0 = 7+n+ j subject to Al = H. I -Hl = 0, g2 = Hi - Hd = 0, g3 = Hi+l - H. = 0, g4 ~ (Xtarge' ~ ttarge' ~ (d 0, max { | Aft) | } Xmax 0, max { | Aft) | }- umax < 0, max {|xb~t)|}-amax < 0' -'z-,Bj < 0, j = 1,...,n - Liz + Al < 0, j = 1,. .., n where fain is the objective function to be minimized. The general aim in constrained optimization is to transform the problem into an easier subproblem that can be solved, and is used as the basis of an iterative process. A Sequential Quadratic Programming (SQP) method is used which allows to closely imitate Newton's method for constrained optimization just as is done for unconstrained optimization. For evaluating the objective function and constraints, the complex Fourier transform is generated from the amplitude and phase spectrum. Application of the IFFT algorithm yields the associated time-dependent wave train at target location. Zero-upcrossing wave and crest heights as well as the crest front steepness c, of the design wave are calculated. The motion of the wave board xb(t) is determined by transforming the wave train at x = x,arge, in terms of the complex Fourier transform Forge to the location of the wave generator at x = 0 and applying the complex hydrodynamic transfer function Fhya,rO(~) which relates wave board motion to surface elevation close to the wave generator: xb(~t) = IFFT LF`arge'(O) F`ransfo) Fhy~ro(~)~] (~8) with F'rans(~);~=exP(ikix~arge,) The maximum stroke of the wave board is set to xmax = 2m, maximum velocity to up = 1 .3m I s and maximum acceleration to ama'` = 1.7m / s2 . The optimization terminates if the magnitude of the directional derivative in search direction is less than 10-3 and the constraint violation is less than lo-2 . In our example the design variance spectrum is chosen to be the finite depth variant of the Jonswap spectrum known as TMA spectrum (Bouws et al, 1985~: ~ ,~q) = ocq~s 1 2kd/ .(h`~2kd' e~ q y (~9' where q = ~ / Lop = f / fp represents the normalized frequency with respect to the peak frequency fp = 1/ Tp . The Jonswap peak enhancement factor y is set to 3.3 and the spectral width parameter of* to 0.07 for q < 1 and 0.09 for q > 1 with r = (q - 1~' / a* . The frequency- dependent wave number k is calculated from the dispersion relationship 602 = gk tanh~kd) where g is the (7) acceleration due to gravity and d the water depth. For the selected spectrum- significant wave height Hs = 0.7m, peak period Tp = 4.43s, water depth d = 5.5m - a high transient design wave within a tailored group of three successive waves in random sea is optimized. The target zero-upcrossing wave height of the design wave is Hd = 2Hs with a maximum crest height (~(Xtargett~arget)=06H~ =1.2Hs. Target location is at a distance of x,arge, = lOOm from the wave generator, and target time is ttarge~ = 80s . The heights of the leading and the trailing waves adjoining the design wave are set to be H`,=H,=Hs. Note that this wave sequence is quite representative for rogue wave groups as has been proved by Wolfram et al. (2000) who classified 114 extremely high waves with their immediate neighbours out of 345245 waves collected between 1994 and 1998 of North Alwyn. As illustrated in Fig. 15, the optimization process finds local minima, i.e. a number of different wave trains, which depend on the initial phase values. Hence the random character of the optimized sea state is not completely lost.
TMA - Fourier spectrum ., ,, ,,,.. i' . (Hs=0.7m,Tp=4.43s, d=5.5 m) . .. . .. . . ~ 2 2.5 3 3.5 co/co 10 unwrapped and detrended phase spectra P 3 5 O -5 ; -10 -0.E 0 20 40 60 80 1 00 t [s] Fig. 15 Optimized phase spectra and associated wave trains resulting from different initial phase distributions. · f 1 ~ - 3 3.5 cl) I co Associated surface elevations P From this linear approach we obtain an initial guess of the wave board motion which yields the design wave sequence at target location. INTEGRATION OF A NONLINEAR ROGUE WAVE SEQUENCE INTO EXTREME SEAS In the previous section it is shown how a tailored group of three successive waves is integrated into a random sea using a Sequential Quadratic Programming (SQP) method. As illustrated in Fig. 16 (which is one of the realizations of the wave trains in Fig. 15) all target features regarding global and local wave characteristics, including the rogue wave specification HmaX = 2Hs and '7c = 0 6 Hmax are met Of course, this result is only a first initial guess as linear wave theory used is not appropriate for describing extreme waves since nonlinear free surface effects significantly influence the wave evolution. However, the linear description of the wave train is a good starting point to further improve the wave board motion (i.e. time-dependent boundary conditions) required in the fully nonlinear numerical simulation. If the control signal from the linear approach and the related wave board motion is used as an input for the non-linear evolution of the wave train, Fig. 17 illustrates that the nonlinear wave train significantly deviates from the target values if this first guess of the wave board motion is used in the numerical simulation. As a consequence, the nonlinear wave train at target location that originates from the first optimization process must be further improved. This is achieved by applying the subplex method developed by Rowan (1990) for unconstrained minimization of noisy objective functions. 3 1 1.5 2 2.5 3 ~/e 3.S Unwrapped and detrended phase spectrum P 0~N ~,,,,,,,,,,N,,: ~ -2p :\~/ ^ ~ 0.5 1 1.5 2 2.5 3 0~1~3 3.5 Surface elevation at target location x/h=20 P 0.~ ~ I ~ Ad ~0.1 0 5 10 15 20 25 t / T 30 Zero~dowDcrossing wave heights P 2 .Target Wave Group: 3 ~ Q?T?TITIQTI?? IQl~IQ9IQQQQ IQOQITTT:T! T~IQTf 0 5 10 15 20 25 30 t/T ~ \ ................ Air ~/\~/~~ ~ Fig. 16 Linear wave train with predetermined wave sequence. The domain space of the optimization problem is decomposed into smaller subdomains which are minimized by the popular Nelder and Mead simplex method (Nelder and Mead, 1965~. The subplex method is introduced because SQP cannot handle wave instability and breaking since the gradient of the objective function is difficult to determine in this case. Nonlinear free surface effects are included in the fitting procedure since the values of objective function and constraints are Fourier spectrum a §05~ ~ \~N,( ~ 0 0.5 1 1.5 2 2.5 3 a,/m 3. Unwrapped and detrended phase spectrum P 20 _ K : : ~ O ., ~ -2OI ~ 0 5 ,~ 1 1.5 2 2.5 3 o)lco 3.5 Surface elevation at target location x/h=20 P or - 25 30 35 40 45 t / T Zero~owncrossing wave heights P 1 1 t2 ol Q?TT I9T 1 I tQII97, I T°OQ TT I TIME Q IQ IQ~ IQIQ?IQ~IQI 20 25 30 t / T 35 40 45 Fig. 17 Nonlinear wave train simulation with predetermined wave sequence. Wave board motion optimized with the linear SQP method.
determined from the nonlinear simulation in the numerical wave tank. The target wave characteristics define equality constraints. The maximum values of stroke xmax = 2m, velocity umax = 1 .7m I s, and acceleration amaX=2.2mls2 of the wave board motion xB(t) define inequality constraints to be taken into account. The subplex minimization problem is formulated as minimize f (C) = ( Hi,HI,~arpe! Hl,target ) Ti lTl~ta~et ~ ~ HiH2,ta~et ~ + H + 1,target ~ 2,target TiT2,ta et + c i c,ta et + ( )( ) T2,target (;c,target ( )2 ( )2 to c,target H3,ta~et Ti+lT3 target ~ ~ ~ (XB (t))(J(XB (t) initial ) 3 target ) ~ ~(xB (t) initial ) ) (10) subject to gl=maX{lXB(t)I}-Xmax < 0' (11) g2 = max {| JOB (t) | }UmaX < 0' g3 = max {| xg(t) | }- amaX < 0, where a(xB(t)) is the standard deviation of the wave board motion. Fig. 18 shows the improved wave board motion. The zero-downcrossing characteristics of the wave train are presented in Fig. 19. The target values of the transient wave are significantly improved. Note that the rogue wave sequence is exactly fitted, with Hmax = 2Hs and '7c = 0 6HmaX As a result we obtain a control signal of the wave generator which yields a specified rogue wave sequence embedded in an extreme irregular seaway characterized by the selected global parameters Hs and Tp (Clause and Steinhagen, 2001~. Fig. 20 illustrates the evolution of this design wave sequence, with registrations at 5 m, 50 m and 100 m (target position) behind the wave board (left side) as well as wave profiles ("photos" of surface elevation) at t = 75 s, 81 s (target) and 87 s (water depth h = 5 m, Tp-3.13s). The associated energy flux at the locations x=Sm, 50m and loom is shown in Fig. 21. As has been expected the energy flux focuses at the target position. 0.06 _ 0.04 .c 0.02 ~ O ~ K ~.02 ~.04 Inn _ v.w 0.04 _ 0.02 ~4 ~ O Ka) ~.02 .04 .06 , . . 0 5 10 15 20 25 30 t/T p Fig. 18 Comparison of optimized wave board motions. Wave board motion resulting from SQP optimization From the velocity potential which has been determined as a function of time and space all kinematic and dynamic characteristics of the wave sequence are evaluated. Fig. 22 presents the associated velocity, acceleration and pressure fields (Steinhagen, 2001~. Note that the effects of the three extremely high waves are reaching down to the bottom. Fourier spectrum a 0.5 ~~ V VV\~ 20 _ -A o A -20` ) Be, . 1 0.5 1 1.5 2 2.5 3 `~/~. 3 5 Unwrapped and detrended phase spectrum P ~ : ~ . _ 0.5 1 1.5 2 2.5 3 ~ / ~ 3.5 Surface elevation at target location x / h = 2n P 20 25 30 35 40 45 t / T Zero-downcrossina wave heights P ~ ~ 1 ~ 1 - ' ''Q 1 - ' t ; - . s o ~ ~ I I ~ T I I I A| ~ ~ Q ~ ~ Q ~ 191 ~ I ~Q i~ in. 97 20 25 30 t / T 35 40 45 Wave height and crest structure P Wave height and period structure 0.7 0 ° 1 1.21 o 0.6 . ., 0.5 . 0.4 . _ _ 0.3 ·O ° 0.2 . 0 0.5 8°o Oo ° OOO O.3 g ~ 80 '1 O 0 0 Go 0 O Coo Oo O 0 0 ....... ..°. 0 oo 0 1 on . . :, 1 1.5 2 0 0.5 1 1.5 2 H'H H/H~ Fig 19 Nonlinear wave train simulation with predetermined wave sequence. Wave board motion optimized with Subplex method.
Su~ace eleva~ion at x t h = 1 ~.05 ~.OS .............. 0.11 ..... 0.05 ~ O ~ 0.05 1 10 IS 20 2S 30 n Surface elevation as x ~ h = 10 -0.1 ~ n l r nn. .os J)1 . . . . · · . . . 5 10 15 20 2S 30 Surface devsdan 8t x / h = 20 ~ ~ ~ . Su~face elevation at t/T =24 p : . . . . ... ' ~ ~ 2 : ........... ~ .. ... ....... ~ ~:Vi~0'~ _1 10 12 14 16 18 20 22 24 26 28 30 0.1 ~ .. : ' : 0.05 . ~ O ~ .ns . -°.l1 n ! ! ..... ~ ,. q _ , ~ ~--:'-~ . . .. . . .. . ... . . .. ... . . . . . .. . . .. . . . . . _ .. . . ... _ . . . _ . .. . . ... . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . · , · · . · . . · 12 14 16 18 20 22 24 26 28 30 S=face devation at t i T = 28 p . . . . . . . . . . . . . . . ..... ~ ........... , ........... ~ . . . . . . . . . : : : : : : ^: : : · · · · · · 11- A ................. . . . . .. . ~ -'-°'W'.~\1'',:~.. \ iW ..... \ , : w: : n1t n.os~ -0.05 ~ ; : ; ; . : : : : : : 0 5 10 IS 20 25 30 ~.ll 0 12 14 16 18 20 22 24 26 28 ~ O tl p x/h Fig. 20 Evolution of rogue wave sequence - registrations at x = 5m, SOm and 1OOm (left) as well as wave profiles at t= 75s, 81s and 87 s (right hand side) (water depth h=Sm, Tp-3.13s). Energy flux at x / h = 1 0.02 ',~ 0.015 g ~,, 0.01 O.WS 0~021 ',; 0.015 c~ ~~. 0.01 E~ ~ 0.005 ......... ......... . L ~ . _~ 5 10 15 20 25 30 ttTp Fig. 21 Energy flux of nonlinear wave at x = S m, 50 m and 100 m (target). . . . . ... ... .. . .. ... .. ... : . . : : . .. . . .. .. . . : . . . . . . _~_^A~ 042r ~1 ~1 ~41 ~1 ..8 Id 16 :IB ~ ~ 24 ~7~ ~i~C ~elerml" b$/g i," ~ paruck velocity `'~J''~Igh) ~ . 1~1 t6 18 20 Dymm~c pm~sum PdJ(P~) 10 i1 1 1~, 1 1 10.1 In ns 14 ~16 18 20 ~;:2 ~ 26 xJh Fig. 22 Kinematic and dynamic characteristics of rogue wave sequence HS ... 2HS ... HS at target time t = 81 s.
Wave X~et Gauge Improved Control Signal Fig. 23 Computer controlled experimental simulation of tailored design wave sequences. The above optimization method has also been applied to generate the Yura wave and the New Year wave (see Fig. 1) in the wave tank (Fig. 23). Firstly, for the specified design variance spectrum, the SQP- method yields an optimised phase spectrum which corresponds to the desired wave characteristics at target position. The wave generator control signal is determined by transforming this wave train in terms of the complex Fourier transform to the location of the wave generator. The measured wave train at target position is then iteratively improved by systematic variation of the wave board control signal. To - synthesise the control signal wavelet coefficients are used. The number of free variables is significantly reduced if this signal is compressed by low-pass discrete wavelet decomposition, concentrating on the high energy band. Based on deviations between the measured wave sequence and the design wave group at target location the control signal for generating the seaway is iteratively optimised in a fully automatic computer-controlled model test procedure (Fig.23). Fig. 24 presents the evolution of the Yura wave at a scale of 1 : 112. The registrations show how the extremely high wave develops on its way to the target position at x=7m. As compared to full scale data the experimental simulation is quite satisfactory. The evolution of the Draupner New Year Wave is shown in Fig. 25. Again the full scale data correlate quite well with model test results at target position x=7.9m. The wave tank tests illustrate how these extremely high waves are developing from rather inconspicuous wave trains and disperse shortly later. If wave/structure interactions are investigated the tank tests allow for considering memory effects. In addition, the mechanism of nonlinear structure dynamics is evaluated, and cause- effect relationship can be analysed. . w ~ EWE x= 6 ''3 ~ ~~ Rae ) ~ by\ ~ ~ It ~~ ~ ~ ~ ~ ~ ~ in< t~ .- sit ~ ~ ~ ~ if" ~ \ ~ ~ V ~ I- ~ ~ ~ ~~ it ~ ~ I- V, Y 'tJ-V Hi' ~ ~ ~ ~~ \1 ~ . itt ~ I ,.. .. _ .. _ .. . . . Fig. 24 Evolution of the Yura wave (scale 1:1 12) (full scale wave data collected by National Maritime Research Institute, Japan (Mori et al., 2000)). .A A ~ . ~WU ^. WOW:. 4 K.: :~.^ :~ 4.~ ~ -:~4 .'~ W~ _ ._ I ~ . ^ ~ ^ . - . ~ I .... ~ - Fig. 25 Evolution of the New Year Wave (scale 1 :175) (full scale wave data collected by Statoil (Haver and Anderson, 2000)).
COMPUTER CONTROLLED CAPSIZING TESTS USING TAILORED WAVE SEQUENCES The technique of generating deterministic wave sequences embedded in irregular seas is used to analyse the mechanism of large roll motions with subsequent capsizing or cruising ships (Clause and Hennig, 2002~. The parameters of the model seas - transient wave elevation at ship center (moving frame) - ~ , r I ! I I i I I 1 - ~ --- --~- T T I j .- Fj I-' tIl' IA ~ ~'' ~f ~ ,~,:~' >; ' ,: ,~ K 178.60T~ T'66.04 i .~,- r ship position X 1~.o. h (x-coordinate' [m],,: - ~ ~ 1060 ~- - 1~$.00 t;;~.~ 64 00 ~ ' ' ' ~ ' ' ' ' . - ~ . i .- i -- ~---- -.J--- -~- t_ ~ ~ i _ . . I no..o 13Q0' 1~. 1,C.tO 13t4.Ctt ' ' I ' ~ ' I I ' ~--- T- ----------~-------'--- I I ' i ' I ' T ~. _ '3t' _ x _ L)e _ [m]' ,'' .,,.,~ ~3t; _ _ IQt~ 31Lt~ 2G.0O ~ 1~- [O] ~t4 ~2tt4 ~0 ^16 11~C0 1~ - 26.t ~I-T~ I~ T--T-l~ T~ l-' 12Ce.to - ~v - ~t 4~ ~3 ~t4 ~- ta get course ~t~ Y .1S. - _ ~tC.t. :: t ~ 1 _ 11 Ct.CO "tO _ ~C t4 2C.t~ ~ 1`i.W [°] {i.{O mtt.'. -2C.tO ,. ~i.60 _ J' t~ 11 C,CO 1 ~OJR 1 S~.W ^~[ - , 1,,, i,,, ! 436 110.X =~ - :~~ ship position ~ br-coordmate) N~% . I. . 1 . , I 1 . ., ., . . 1, ,. ,,, . 1,, ,' tS0D. 1.,QtO 13hCO r--^i~~~r-~~~i~T T- .__.~._. - r- - --l----r---l------l------------T------~- roll motion 150.W 1r~40 10ti4CO T -'r-T-r-.r.-..~._..1]-· -T--~- - .~--... ~%,,~Nx ~ Be = 1~ ._ _._ ~.__ - . ~ _ A ~_~~,, ,~_ . 1broachip'' with ~bsequer~t ca~sizipg ~4 ~ .... .. , ~ ._ .. . .~ _,_ _.1 _ .~. ... ,.~ 130^ 150.00 1~tC0 13(:40 r I I I r- ~--T-~-~ r-. '. r f `/'d '\~/ iSii _ 17~C0 13~CO t [S] Fig. 26 Roll motion of the RO-RO vessel in a severe storm wave train (Tp=14.6s, Hs=15.3m) at GM=1.36m v=151m, z-manoeuvre with ,u = ~ 10°. wave sequences consisting of random seas or regular wave trains with an embedded deterministic high transient wave - are systematically varied to investigate the ship model response with regard to metacentric height, model velocity, and course angle for each of both ship types. The wave elevation at the position of the ship model at any position in time and space is calculated (and controlled by registrations during model tests) in order to relate wave excitation to the resulting roll motion. Fig. 27 RO-RO vessel in a severe storm. Fig. 26 presents a model test with a RO-RO vessel (GM=1.36 m, natural roll period TR = 19.2 s, v = 15 kn) in extremely high seas from astern (ITTC spectrum with Hs=15.3 m, TP = 14.6 s, z-manoeuvre: target course ,u=110°~. The vessel broaches and finally capsizes as the vessel roll exceeds 40 degrees and the course becomes uncontrollable (Fig. 27~. Note that the wave elevation refers to the ship center (moving frame), and has been calculated from the registration at a stationary wave probe - 10 meters in front of the wave board. Thus, relevant wave elevation is directly related to the associated ship motions. DYNAMICS OF SEMISUBMERSIBLES IN ROGUE WAVES The method of synthesizing extremely high waves in severe irregular seas is also applied to analyse the impact of reported rogue waves on semisubmersibles. As the procedure is strictly deterministic we can compare the numerical (time-domain) approach and model test results (Clause et al., 2002~. For the numerical simulations the program TiMIT (Time-domain investigations, developed at the Massachusetts Institute of Technology) is used, a panel- method program for transient wave-body interactions (Korsmeyer et al, 1999) to evaluate the motions of the semisubmersible. TiMIT performs linear seakeeping analysis for bodies with or without forward speed. In a
first module the transient radiation and diffraction problem is solved. The second module provides results like the steady force and moment, frequency- domain coefficients, response amplitude operators, time histories of body response in a prescribed sea of arbitrary frequency content on the basis of impulse- response functions. The drilling semisubmersible GVA 4000 has been selected as a typical harsh weather offshore structure to investigate the seakeeping behaviour in rogue waves in time-domain. The wetted surface of the body is discretized into 760 panels (Fig. 28~. The number of panels is sufficient to simulate accurate results. Operatlon displacement A=25940t ................. . ~:Q.~.iC: ...... ....... 1 _ `:4720 ~ 1 'r ~ `. i.,. ~ :' (O 5' At)! Fig. 28 Semisubmersible GVA 4000- main dimensions and discretization of the wetted surface using 760 panels. For validating TiMIT results of wave/structure interactions in extreme seas the Draupner New Year Wave (see Fig. 1) has been synthesized in a wave tank at a scale of 1:81. Using the proposed wave generation technique, the wave board signal is calculated from the target wave sequence at the selected wave tank location. Fig. 29 presents the modelled wave train at target location. For comparison the exact New Year Wave is also shown to illustrate that we have not reached an accurate agreement so far. However, this is not detrimental since the associated numerical analysis is based on the modelled wave train, registered at target position. Fig. 30 presents the modelled wave train as well as the heave and pitch motions of the semisubmersible comparing numerical results and experimental data (scale 1:81~. The airgap as function of time is also shown. Note that this airgap is quite sufficient, even if the rogue wave passes the structure. However, wave run-up at the columns (observed in i ~ ~ . ~ 1 100 150 200 250 300 time [a] 350 Fig. 29 Comparison of model wave (scale 1:81) as compared to the registered New Year Wave (Haver and Anderson, 2000) presented as full scale data. model tests) is quite dramatic, with the consequence that green water will splash up to the platform deck. As a general observation, the rogue wave is not dramatically boosting the motion response. The semisubmersible is rather oscillating at a period of about 14s with moderate amplitudes. Related to the (modelled) maximum wave height of HmaX = 23m we observe a maximum measured double heave amplitude of 7m. The corresponding peak value from numerical simulation is 8.6m. As a consequence, the measured airgap is slightly smaller than the one from numerical simulation. The associated maximum double lo. pitch amplitudes compare quite well. Note that the impact results in a sudden inclination of about 3°. Considering the complete registration it can be stated that the _ 20- ~ : ~ 10- ~ - - O~ ! ~ :^ ire ryes 550 600 650 700 time [s] 750 1 0.0 calculated pitch motion ~ ~ I 5.0 -memuret pitch motto" _ ~ ~L\~ Boor ~~V~ \1~ Q^~ · ~ ~ ~ tJ `7 in V ~ , _~.o: I .,,, i, ., . I .... 550 600 650 700 Me [a] 750 815~ ~ cc! - gap ~ | ! I 550 600 650 700 time [a] 750 Fig. 30 Results of numerical simulation and experimental tests for semisubmersible GVA 4000: Heave, pitch and airgap (measured at a scale 1 :81, presented as full scale data).
. numerical approach gives reliable results. At rogue events the associated response is overestimated due to the disregard of viscous effects in TiMIT calculations. CONCLUSIONS For the evaluation of wave-structure interactions the relation of cause and effects is investigated deterministically to reveal the relevant physical mechanism. Based on the wave focussing technique for the generation of task-related wave packets a new technique is proposed for the synthetization of tailored design wave sequences in extreme seas. The physical wave field is fitted to predetermined global and local target characteristics designed in terms of significant wave height, peak period as well as wave height, crest height and period of individual waves. The generation procedure is based on two steps: Firstly, a linear approximation of the desired wave train is computed by a sequential quadratic programming method which optimizes an initially random phase spectrum for a given variance spectrum. The wave board motion derived from this initial guess serves as starting point for directly fitting the physical wave train to the target parameters. The Subplex method is applied to improve systematically a certain time frame of the wave board motion which is responsible for the evolution of the design wave sequence. The discrete wavelet transform is introduced to reduce significantly the number of free variables to be considered in the fitting problem. Wavelet analysis allows one to localize efficiently the relevant information of the electrical control signal of the wave maker in time and frequency domain. As the presented technique permits the deterministic generation of design rogue wave sequences in extreme seas it is well suited for investigating the mechanism of arbitrary wave/structure interactions, including capsizing, slamming and green water as well as other survivability design aspects. Even worst case wave sequences like the Draupner New Year Wave can be modelled in the wave tank to analyse the evolution of these events and evaluate the response of offshore structures under abnormal conditions. ACKNOWLEDGEMENTS The fundamentals of transient wave generation and optimization have been achieved in a research project funded by the German Science Foundation (DFG). Applications of this technique, i.e. the significant improvement of seakeeping tests and the analysis of wave breakers and artificial reefs in deterministic wave packets have been funded by the Federal Ministry of Education, Research and Development (BMBF). Results are published in outstanding PhD theses (J. Bergmann, W. Kuhnlein, R. Habel, U. Steinhagen). The technique is further developed to synthesise abnormal rogue waves in extreme seas within the MAXWAVE project funded by the European Union (contract number EVK-CT-2000-00026) and to evaluate the mechanism of large roll motions and capsizing of cruising ships (BMBF funded research project ROLL-S). The author wishes to thank the above research agencies for their generous support. He is also grateful for the invaluable contributions of Dr. Steinhagen, Dipl.-Ing. C. Pakozdi, Dipl.-Math. techn. Janou Hennig and Dipl.-Ing. C. Schmittner. REFERENCES Bouws, E., Gunther, H., Rosenthal, W. and Vincent, C. (1985~: Similarity ofthe wind wave spectrum in finite depth water- 1. Spectral form, Journal of Geophysical Research, 90(C1) Clauss, G. and Bergmann J. (1986~: Gaussian wave packets - a new approach to seakeeping tests of ocean structures, Applied Ocean Research, 8~4) Clauss, G. and Habel, R. (2000~: Artificial reefs for coastal protection- transient viscous computation and experimental evaluation, 27th International Conference on Coastal Engineering (ICCE), Sydney, Australia Clauss, G. and Hennig, J. (2001) Tailored transient wave packet sequences for computer controlled seakeeping tests, 20th International Conference on Offshore Mechanics and Arctic Engineering (OMAE), Rio de Janeiro, Brazil Clauss, G. and Hennig, J. (2002) Computer controlled capsizing tests using tailored wave sequences, 21 St International Conference on Offshore Mechanics and Arctic Engineering (OMAE), Oslo, Norway Clauss, G. and Kuhnlein, W. (1995~: Transient wave packets - an efficient technique for seakeeping tests of self-propelled models in oblique waves, Third International Conference on Fast Sea Transportation, Lubeck-Travemunde, Germany Clauss, G. and Kuhnlein, W. (1997~: Simulation of Design Storm Wave Conditions with Tailored Wave Groups, 7eh International Offshore and Polar Engineering Conference (ISOPE), pp. 228-237. Honolulu, Hawaii, USA. Clauss, G., Pakozdi, C. and Steinhagen, U. (2001~: Experimental Simulation of Tailored Design Wave Sequences in Extreme Seas, 1 lth International Offshore and Polar Engineering Conference (ISOPE), Stavanger, Norway.
Clauss, G. and Steinhagen, U. (1999~: Numerical Simulation of Nonlinear Transient Waves and its Validation by Laboratory Data, 9th International Offshore and Polar Engineering Conference (ISOPE), Brest, France. Clauss, G. and Steinhagen, U. (2000~: Optimization of Transient Design Waves in Random Sea, 1 oth International Offshore and Polar Engineering Conference (ISOPE), Seatle, USA. Clauss, G. and Steinhagen, U. (2001~: Generation and Numerical Simulation of Predetermined Nonlinear Wave Sequences in Random Seaways, 20th OMAE Symposium, Rio de Janeiro, Brazil Clauss, G., Schmittner, C. and Stutz, K. (2002~: Time-domain investigations of a semisubmersible in rogue waves, 21St International Conference on Offshore Mechanics and Arctic Engineering (OMAE), Oslo, Norway Davis, M. and Zarnick, E. (1964~: Testing Ship Models in Transient Waves, 5th Symposium on Naval Hydrodynamics. Drake K. (1997~: Wave profiles associated with extreme loading in random waves, RINA International Conference: Design and Operation for Abnormal Conditions, Glasgow, Scotland Faulkner (2000~: Rogue Waves- Defining Their Characteristics for Marine Design, Rogue Waves 2000, Brest, France. Faulkner, D. and Buckley, W. (1997~: Critical survival conditions for ship design, RINA International Conference: Design and Operation for Abnormal Conditions, Glasgow, Scotland Haver, S. (2000~: Some evidence of the existence of socalled freak waves, Rogue Waves 2000, Brest, France Haver, S. and Anderson, O.J. (2000~: Freak Waves: Rare Realizations of a Typical Population or Typical Realization of a Rare Population?, 10th International Offshore and Polar Engineering Conference (ISOPE), Seattle, USA. Kjeldsen, S.P. ( 19964: Example of heavy weather damage caused by giant waves, Techno Marine, Bull Of the society of Naval Architects of Japan, No. 820 Kjeldsen, S.P. (1990~: Breaking Waves. Water Wave Kinematic, Kluwer Academic Publisher, NATO ASI Series, ISBN 0-7923-0638~, pp. 453-473. Kjeldsen, S.P. and Myrhaug, D. (1997~: Breaking waves in deep water and resulting wave forces, Offshore Technology Conference, OTC 3646 Korsmeyer,F., gingham, H. and Newman, J. (l999~:TiMIT- A panel-method program for transient wave-body interactions, Research Laboratory of Electronics, Massachusetts Institute of Technology Kuhnlein, W. (1997~: Seegangsversuchstechnik mit transienter Systemanregung, PhD Thesis, Technische Universitat Berlin, D83. Mori, N., Yasuda, T. and Nakayama, S. (2000~: Statistical Properties of Freak Waves Observed in the Sea of Japan, 10th International Offshore and Polar Engineering Conference (ISOPE), Seattle, USA. Nelder, J. and Mead, R. (1965~: A Simplex Method for Function Minimization. Computer Journal, 7, pp. 308- 313. Pakozdi, C. (2002~: Numerische Simulation nichtlinearer transienter Wellengruppen - Bericht zum DFG- Vorhaben Cl 35/30-1, Selbstverlag Rowan, T. (19901: Functional Stability Analysis of Numerical Algorithms, PhD Thesis, University of Texas at Austin. Sand, S.E., Ottesen, H.N.E., Klinting, P., Gudmestad O.T. and Sterndorff, M.J. (19901: Freak Wave Kinematics. Water Wave Kinematics, Kluwer Academic Publisher, NATO ASI Series, ISBN 0- 7923-0638~, pp. S35-549. Steinhagen, U. (2001): Synthesizing Nonlinear Transient Gravity Waves in Random Seas, PhD Thesis, Technische Universitat Berlin, D83. Takezawa, S. and Hirayama, T. (1976~: Advanced Experiment Techniques for Testing Ship Models in Transient Water Waves, 1 1th Symposium on Naval Hydrodynamics Wolfram, J., Linfoot, B. and Stansell, P. (2000~: Long- and Short-Term Extreme Wave Statistics in the North Sea: 1994-1998, Rogue Waves 2000, Brest, France. Wu, G-X., Eatock Taylor, R. (1994~: Finite Element Analysis of Two-Dimensional Non-Linear Transient Water Waves, Applied Ocean Research, 16~6), pp. 363-372. Wu, G-X., Eatock Taylor, R. (1995~: Time Stepping Solutions of Two-Dimensional Non-Linear Wave Radiation Problem, Ocean Engineering, 22~8), pp. 785-798.
DISCUSSION P. Kjeldsen The Norwegian Maritime Academy, Norway The wave generation technique described and used in this work is not new, but has been developed by Gunther Clauss and other researchers for many years. Attention can here be given to the paper " 2- and 3-dimensional Deterministic Freak Waves" by S.P. Kjeldsen in Proc. 18th International Conference on Coastal Engineering, Cape Town, South Africa 1982. Here it is shown that a very important parameter that must be taken into consideration is the directional spreading of the wave spectrum. The norwegian technique that was made to generate deterministic wave groups therefore was designed to generate 3-dimensional freak waves. In some cases these waves appeared also with 3- dimensional breaking wave crests in coherence with famous photos of such waves, see " A Sudden Disaster - in Extreme Waves." by Kjeldsen in Proc. Conference on RogueWaves, Brest, France 2000. The research presented by Gunther Clauss deals only with 2-dimensional waves. It is fair to assume that some of the severe marine accidents that we have encountered appeared in complex and confused 3-dimensional seas. Another very important point that should be considered here is to investigate if a freak wave observed at sea is breaking or not. It is well known that the largest risk for a capsizing event is associated with a breaking wave. Here attention should be given to a Norwegian investigation of wave forces on platform legs in deterministic freak waves. It was found that the largest forces appeared in violent deep water breaking waves with moderate wave heights. In the same tests it was found that the highest waves gave lower forces, see Kjeldsen ,T0rum, Dean :" Wave Forces on Vertical Piles caused by 2- and 3-dimensional Breaking Waves." In Proc. 20th International Conference on Coastal Engineering,Taipei, Taiwan 1986. The last important point to consider is therefore that it is not the wave height but the particle crest velocity and acceleration in the crest of a breaking wave that shall be measured experimentally and documented properly from wave tank tests. In Norway measurements of both crest velocity and crest accelerations were made with a wave-following current-meter- technique, before capsizing test were undertaken, see Kjeldsen " The Wave Follower Experiment " in Proc. Of the Symposium on the Air-Sea Interface, Radio and Acoustic Sensing, Turbulence and Wave Dynamics. Marseille, France, 1993. I wish to congratulate Gunther Clauss with very important research, and I hope he will continue this work. DISCUSSION T. Hirayama Yokohama National University, Japan The author proposed the concept of the "task- related design waves or extreme waves" and showed concrete methods of synthesizing such waves both in numerical and physical simulation. This concept seems very valuable like the concept of using the time history of E1 Centro earthquake for the assessment of infrastructures in the field of civil engineering and architecture. About the extreme waves, the phenomenon become nonlinear, and the author introduced nonlinear treatment and succeeded. So the discusser wants to express his congratulations to the authors. My discussion is about the importance of 3- dimensional effects of design waves or extreme waves interacting with floating structures. The examples shown in the present paper are all related to long crested waves. Of course long crested waves will be enough if we consider the extreme waves near shore, because the crest lines become parallel and long for this case. On the other hand, if we consider the extreme waves in deep ocean, the higher waves exceeding the theoretical existing limit of 2-dimensional wave steepness occurs by the simple superposition of two wave system with different direction. This will be called as triangular waves or pyramidal waves. The time history measured at one point in the ocean cannot detect if this is the result by long crested wave or short crested wave. So, it will be important to consider in which wave the target phenomena is more severe in two dimensional or three dimensional extreme wave with similar time history of wave group. Furthermore, the discusser wants to know if the method proposed here is applicable to 3- dimensional rogue waves or not. For reference, I will refer to the picture showing both long
crested and short crested concentrated transient wave. The pyramidal waves can be generated even in a narrow and long experimental tank. Ref. 1,3 are typical examples. We call this at one-point concentrated Transient Water Waves. In these waves, the velocity profile is not uniform from wave surface to the sea bottom and the capsizing phenomena will different from long crested rogue waves. Here the non-linear treatment about wave generation as the author is not introduced. REFERENCES 1. Hirayama,T. Ma.N,Harada,T. and Lee J-H.~1995~: Application of Side Wall Reflection Type Directional Wave Generator and Laser Beam Type Wave Surface Probe-Especially on the Linear Characteristics of the One Point Concentrated Transient Water Waves-, Proceedings of the Wave Generation'95~ pp60- 82 2. Hirayama T. et al.~1995~: Capsizing and Restoration of a Sailing Yacht in Breaking Isolated Triangular Transient Waves and Breaking Long Crested Transient Waves, Journal of Kansai Society of Naval Architects Japan,No.223,pp59-66 (in Japanese) 3. Hirayama,T.(1997~: Modeling of Multidirectional Waves in Naval Architectural Field Proceedings IAHR Seminar on Multidirectional Waves and their Interaction with Structures(San Francisco),pp23 1-239 One Point Concentrated TWW(T=Osec, just concentrated)(left). In Line Concentrated TWW(just oncentrated)(right). (from ref.3) AUTHOR'S REPLY First I would like to thank the discussants for their highly competent and encouraging comments. It is a special pleasure to present our recent developments in wave focussing at the ONR-Symposium in Japan as significant contributions to this technique have been achieved by S. Takezawa at the Yokohama National University. As pointed out by Tsuguikiyo Hirayama who continued these research activities 3-dimensional effects play a major role in wave-structure interactions as shown with his pyramidal waves. Directional spreading and the generation of 3-D freak waves is also discussed by Peter Kjeldsen. In addition, he emphasizes the importance of wave breaking for the evaluation of platform forces, and comments that wave kinematics play a key role. As has been stated, our contributions to the evolution of the wave focussing technique are limited to long-crested linear and nonlinear waves. Of course, 3-D effects are indispensable, and I am grateful that both discussants are engaged in this important research. I also agree with Peter Kjeldsen that wave height is not the most important parameter. However, not only wave particle (crest) velocity and acceleration but also wave steepness, wave sequence and memory effects play a vital role for evaluating wave impacts and the associated response of offshore structures. Actually, this is the most important aspect of our deterministic technique with which all wave characteristics can be evaluated in space and time. In conclusion, the rogue wave story and the development of wave focussing procedures as well as the deterministic generation of extremely high waves and wave sequences embedded in realistic seas must continue to reveal the secrets of wave-structure interaction and to improve the design of safer ships and offshore structures. DISCUSSION C. M. Lee Pohang University of Science and Technology, Korea It is an interesting paper which gives an intelligent method for testing seakeeping quality of ships and floating platforms under the extreme wave environment. I suppose when we say the extreme wave condition, it should mean for a specific ship or platform since each marine structure has its own resonant frequencies or vulnerable load conditions. I don't think the extreme wave condition not necessarily mean only an impulse-type wave, thus to use the terminology "extreme wave environment." We
should specify whether it is the amplitude, frequency, and/or wave slope for swell type waves or the significant height, model period, and/or significant wave slope for irregular waves. Not only that the wave heading angle should be included as well. I would like to know how the author define would the "extreme wave environment" for a given ship or marine structure? DISCUSSION Dr. Stephane Cordier Bassin d'Essais des Carenes, France Our experiences with force measurements during transient wave tests, in particular in the case of segmented models, stationary or with speed of advance, shows that bending moment or shear forces transfer function obtained in transient wave tests match data obtained either through regular wave or irregular wave tests. Can the author suggest a method for choosing a wave group which should be used for design of a marine structure? AUTHOR'S REPLY I wish to thank Prof. Lee and Dr. Cordier for their valuable comments and delicate questions. As both are brilliant experts in this field, they know that there is no pat solution, however, I will discuss some aspects: In fixed structures the maximum wave elevation might be the most decisive parameter as the lower decks should clearly raise above the maximum wave crest with a sufficient air gap because the impulsive peak forces increase sharply if the wave hits the superstructure. In case of flexible or floating stationary structures a quick look at the (linear) response amplitude operators reveals the neuralgic natural frequencies which is the key for the evaluation of wave/structure interaction. If resonance effects play a major role, these investigations must be supplemented by analysis. In this case even the "real world" can be simulated as has been presented in Figs. 29 and 30 showing the interaction of the giant New Year Wave sequence with a semisubmersible. For details see Clauss et al. (2002a). Note that the highest wave in the "real world" wave train (see Figs. 1 and 29) can be stretched or compressed arbitrarily to vary frequency and nonlinear time-domain steepness. Also the preceding waves can be designed specifically to introduce tailored memory effects. If the floating structure is cruising with a defined speed and course, the selection of a critical (response based) design wave group becomes even more delicate. In general, a non-linear time- domain analysis is required. As has been sketched in Figs. 26 and 27 this procedure is used to analyse the mechanism of capsizing. Firstly, the physical mechanism of extreme roll motions (sometimes with subsequent capsizing) is investigated by the evaluation of the non- linear cause-reaction relations of wave/structure interactions. Next, dedicated computer- controlled capsizing tests with deterministic wave trains are carried out at model scale embedding rogue wave sequences in severe seas. Based on these results, we finally developed a non-linear numerical method for simulating ship motions in extreme seas. As a result of this project which has been accomplished by our institute in cooperation with the Hamburg Ship Model Tank Basin (HSVA) and the Flensburger Shipyard FSG, we determined polar plots with limiting wave heights for the capsizing of a specific vessel depending on its speed and course (Clause et al., 2002b). As shown in Fig. Al - left hand side - the most critical regions of resonance motions as well as of parametric rolling are clearly identified. Only a change of trim by lm to stern (see right hand side) reduces the capsizing risk considerably. Consequently, the assessment of the seakeeping behaviour of a floating structure requires a highly complex procedure combining non-linear numerical simulation methods validated by deterministic seakeeping tests. As a result, safer ships can be designed and loading conditions optimized, improving ship operation and navigation significantly. In conclusion, the application of deterministic wave sequences for the evaluation of wave/structure interactions is recommended as an additional tool in NWT investigations and physical model tests. Aiming for a response based design we may assume critical extreme waves or wave sequences, and the analysis will reveal whether we really succeeded in finding the "extreme wave environment", i.e. systematic variations are inevitable. a) In detail, the method can be used as a
tool to analyse the mechanism of the structure behaviour in waves because the non-linear cause-reaction effects are deduced from deterministically given wave field characteristics like pressure field, particle accelerations and velocities as well as non-linear wave elevation in space and time. b) Wave trains can be designed individually to investigate a specific structure at a certain tank position, i.e. some dedicated regular waves can precede an extremely high wave or wave group for simulating memory effects. By stretching or compressing the peak wave its frequency and slope can be tuned accordingly. Also phase relations between incident wave and structure motions can be selected and varied deterministically. Any test can be repeated identically if a specific effect is analyzed. c) Observed wave registrations, like the extremely high New Year Wave sequence (Fig. 1) can be generated in a wave tank at a selected model scale. Thus, the genesis of extreme events in such wave groups can be analyzed in space and time. Also, the seakeeping behaviour of any structure can be evaluated in such extreme environments. d) Finally, non-linear numerical methods can be validated by dedicated seakeeping model tests in deterministic wave sequences. By systematic simulations even the most critical wave group may be identified. I wish to thank all discussants for their excellent comments and demanding questions. REFERENCES 1. Clauss, G., Schmittner, C. and Stutz, K. (2002a): Time-domain Investigation of a Semisubmersible in Rogue Waves, In Proceedings of 21 st Int. Conf. on Offshore Mechanics and Arctic Engineering (OMAE'02), Oslo, Norway, June 23-28 2002. 2. Clauss, G., Hennig, J., Kuhnlein, W., Brink, K.E., Buhr, W., and Cramer, H. (2002b): Entwicklung von Schiffen mit hoherer Kentersicherheit durch deterministische Analyse extremer Rollbewegungen in schwerer See (Development of Safer Ships with Reduced Capsizing Risk by Deterministic Analysis of Extreme Roll Motions in Severe Seas), Summer Meeting of the German Society of Naval Architects (STG), Flensburg/Gluckburg, Germany, May 21-24 2002. ~c- ~;&1 ` ~_ ~_ 1~ ._ . ~ 0. t~ ~:~ ~e-~ :~eof~ - F: ar [tt m11 r#sonance
