E L S E V I E R Applied Ocean Reseaich 21 (1999) 219-234
AppSfad O c e a n
wvvw.elsevier.com/locate/apor
Task-related wave groups for seakeeping tests or simulation of design
storm waves
G.F. Clauss
Berlin Umversity of Technology, Institute of Naval Architecture and Ocean Engineering, SG 17, Salzufer 17-19, 10587 Berlin, Germany
Received 28 January 1999; received i n revised form 17 June 1999; accepted 17 June 1999
Abstract
The chaotic wave field of a natural seaway can be decomposed into an infinite number of independent harmonic waves, and its spectrum follows from the associated wave amplitudes and frequencies. If superimposed with random phase we register the well-known iiTegular sea, which is characterized by its significant wave height and zero-up-crossing period. As rare events very high waves are observed accidentally.' Smce RAOs of wave/structure interactions are independent of the random phase shift between superimposing component waves this parameter can be selected arbitrarily to compose an optimum and short-duration transient wave train which allows the precise determination of all response amplitude operators within the relevant spectral range. Applications of the wave group technique are presented for: (i) standard seakeeping tests of stationary or moving (self-propelled) marine structures; (ii) simulation of design storm waves for the investiga-tion of coastal and offshore structures. The paper illustrates the generainvestiga-tion of task-related wave packets, the determinainvestiga-tion of the associated acceleration, velocity and pressure fields, as well as the related energy flux. Based on the dispersion relation the propagation behavior is exactly predictable. Consequently, the kinematics and dynamics of the wave field can be determined at any positiori and time. I f the converging wave group approaches its concentration point the associated particle motions are analyzed by a nonlinear procedure using coupled Lagrangian expansion equations. The efiiciency and the limitations ofthe transient wave technique are demonstrated by presenting typical test examples. These include the determination of the RAOs of stationary offshore structures and towed or self-propelled ships as well as the investigation of coastal structures in 100-year waves. As the entire process is deterministic, the action/reaction chains can be evaluated m detail. The paper demonstrates that the wave group technique is a reliable and efiicient tool for all standard investigations related to wave/ structure interactions, and opens a new area for the analysis of transient processes in the sea, e.g. dynamic stability of floating vessels or design wave impacts on coastal or offshore structures. © 1999 Elsevier Science Ltd. All rights reserved.
Keywords: Transient waves; Seakeeping tests; Design storm waves; Freak waves; Wave/structure interaction
Nomenclature
Fourier transform of wave train a{xfy (ms) energy (kgmVs^) mean energy (kgmVs^) kinetic energy (kgm^/s^) potential energy (kgm^/s^) normal force (N) differential force (N) Froude number
freak wave height for survival design (m) maximum wave height (m)
significant wave height (m)
wave information (linear deep water surface velocity: I = U^^Q + W^^Q) (m/s)
number of registration values
wave period or duration of registration (s) E È £'kin •È'pot Fn Hi Fhx) N T
E-mail address: clauss@ism.tu-berlin.de (G.F. Clauss)
0141-1187/99/$ - see front matter © 1999 Elsevier Science Ltd. A l l rights reserved PH: 5 0 1 4 1 - 1 1 8 7 ( 9 9 ) 0 0 0 1 7 - 6
T zero-upcrossing-period (s) V f u l l scale vessel velocity (m/s) VM model velocity (m/s)
W(t,x) Fourier transform of wave infonnation (m)
a{x,t) wave elevation, surface wave train (m)
ah cij value of wave amplitude (m)
c{d,k) wave celerity of regular wave (m/s)
CaddC''.^') additional wave celerity due to nonlinear
convection (m/s) group velocity (m/s)
' ' l i n e a r ( ^ ! ^ ) linear wave celerity (m/s)
Ci(t,x) velocity of information propagation (m/s)
d water depth (m)
g acceleration due to gravity, g = 9.81 m/s^ (m/s 2)
k wave number k = (ITT/L) (rad/m) wave number, ;th iteration step (rad/m)
km wave number, nith iteration step (rad/m)
220 G.F. Clauss / Applied Ocean Research 21 (1999) 219-234
m frequency step £3 phase shift of heave motion
n number of time steps phase shift of pitch motion
p(x,t) pressure field (N/m^) at,x) vertical position of wave particle (m)
P porosity of wave filter (%) wave crest elevation (m)
s structure motion s = {si,S2, s^,s^, s^, s^) (m), (°) I. wave elevation at time step / (m) structure motion amplitudes, i = 1,2, ...,6 (m), vertical elevation of water particle (m)
C) iit,x) horizontal position of wave particle (m)
t time (s) p density of water, p = 1000 kg/m^ (kg/m'')
At time step (s) (1) circular frequency w = ITT/ (rad/s)
fc concentration point (time) (s) A(o circular frequency (step size) (rad/s) ^eiid time of water particle reaching its end position (Oj,(0,„ circular frequency, iteration step j, m (rad/s)
(s) ^max maximum circular frequency (rad/s)
tt /th time step (s) minimum circular frequency (rad/s)
ts time shift (s) W m measured circular frequency (rad/s)
to u w A' m Xc Xl,m Xo z Zkj Zo
fixed location in time (s)
horizontal velocity component (m/s) amplitude of horizontal surface velocity component (linear theory) (m/s)
horizontal velocity component, time step /, z-step j (m/s)
horizontal particle velocity (m/s) cuiTent velocity due to convection (m/s) vertical velocity component (m/s) amplitude of vertical surface velocity component (linear theory) (m/s) vertical velocity component, time step /, 2-step j (m/s)
vertical particle velocity (m/s) coordinate (m)
average shift of water volume element (m) concentration point (m)
modulation term of coupled equations fixed location in space (m)
coordinate (m) depth step size (m)
modulation term of coupled equations fixed location in space (m)
1. Introduction
Extreme wave conditions in a 100-year design storm arise from the most unfavorable superposition of component waves of the related severe sea spectrum. Fig. 1 presents the simulation of an iiTegular sea state by random phase superposition. As a rare—but possible—event, a very high freak wave is observed. Extensive random time-domain simulation of the ocean surface for obtaining statis-tics of the extremes, however, is very time consuming. A n efficient approach to simulate extreme storm loading is the NewWave methodology which describes the most likely extreme wave profile in a storm (Tromans et al. [1]). Comparison of load predictions with other wave models and with measurements on the Tern structure during a severe storm prove the applicability of the NewWave method (Rozario et al. [2], Jonathan et al. [3]). Similarly, de Jong et al. [4] have compared the NewWave with Stokes V and Dean 7-stream function and found nearly congruent loading for the Europipe platform. I t is stated, however, that the theory models the surface elevation as a Gaussian
component waves — of seaway
extremely long registration of a severe irregular sea state
G.F. Clauss / Applied Ocean Research 21 (1999) 219-234 221 structure motion wave motion pressure field wave motion structure force pressure field
wave motion at surface
orbital motion
structure motion s
pressure, velocity and acceleration field structure motion structure force /\ ' I ^1 W pressure field p{x, t) on wetted surface motions s forces normal component of p{x, t) results in differential force dFf., and structure motion t
Fig. 2. Wave/structure interaction.
random process and does not account for nonlinearities in the wave environment.
Taylor et al. [5] point out that the extreme response of dynamically responding structures does not always coiTe-spond to the extreme input surface elevation as the load history and the structural dynamics may interact with local extreme wave conditions. They propose a constrained random time-domain simulation, which integrates a large crest into a random time series for surface elevation (Harland et al. [6]). This technique is used to investigate the variability of global extreme wave forces on offshore structures in directional spread seas (Harland et al. [7]).
Another approach to efficient hydrodynamic analysis is presented by Monison and Leonard [8] who propose the "Quickwave" and the "Designer Wave" technique for preli-minary design of compliant towers. Reasonably accurate design forces are achieved without time consuming random wave nins and f u l l 3-D structural models.
NewWave, Quickwave and Designer Wave—models are dependent on maximum wave height observations. In this context Faulkner and Buckley [9] present invaluable freak wave data. Based on observations Faulkner [10] suggests the freak or abnormal wave height for survival design > 2.5Hg. 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.
The wave model presented in this paper has been deduced from thorough model observations: peak waves have been registered in standard iiTegular seas when component waves accidentally superimpose in phase. In generating iiTegular seas 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 i f 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? In
this case we can study the propagation behavior and related nonlinear phenomena as the wave train has a linear past and a linear future. Thus, nonlinearities close to the concentra-tion point are developed frora linear condiconcentra-tions. Cause and effect are clearly related: at any position we can determine the (nonlinear) surface elevation as well as the associated velocity and acceleration fields. Also the point of wave/ structure interaction can be selected arbitrarily, and any test can be repeated deliberately. Wave/structure interaction and the associated transfer function is decomposable into subsequent steps: surface elevation; wave Idnematics and dynamics; forces on structure elements and on the entire structure; structure motions (Fig. 2). Whatever happens in the tank, a physically real wave is generated with regard fo all physical laws and boundary conditions, i.e. i t is a
Real-Wave, which is used for model excitation, and the associated
numerical wave model is based on a validated concept.
2. Transient wave technique
Transient waves for model excitation v/ere originally proposed by Davis and Zarnick [11], and further developed by Takezawa and Hirayama [12]. Clauss and Bergmann [13] recommended a special type of transient waves, i.e. Gaus-sian wave packets, which have the advantage that then-propagation behavior can be predicted analytically (Berg-mann [14] Chakrabarti and Libby [15]).
With increasing efficiency and capacity of computers the restriction to a Gaussian distribution of wave amplitudes has been abandoned, and the entire process is now performed numerically ([16]). The shape and width of the wave spec-trum 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
222 G.F. Clauss /Applied Ocean Research 21 (1999) 219-234
D E T E R M I N I S T I C T R A N S I E N T W A V E T R A I N S based on target spectrum,
selectable wave profile and associated velocity/acceleration fields
S E A K E E P I N G TESTS fast, efficient, accurate
-Response A m p l i t u d e Operators of stationary offshore structures or towed/self-propelled ships for S P E C I A L W A V E / E X T R E M E S T R U C T U R E ( F R E A K ) I N T E R A C T I O N S WAVES Dynamic stability, Slamming - Green water, Counterpro-pagating wave groups
Worst case studies: maximum forces k motions in 100-year
design waves
S T A N D A R D T O O L design wave spectrum represented
by tailored wave group
N E W T O O L
accurate prediction of wave/structure interaction point
Fig. 3. Applications of the RealWave technique.
its high accuracy the technique is capable of generating special puipose transient waves (Fig. 3):
• for standard seakeeping tests;
• for special wave/structure interactions; • for worst case studies in extreme waves.
The simulation technique is based on a computer controlled nonlinear procedure which governs the generation of a short, specifically tailored wave train with a "design" spec-trum. As the wave train is exactly defined in space and time it is easy to transpose the registration to any position along the tank. The paper proposes a new method for the descrip-tion of the shape variadescrip-tion of nonlinear transient wave pack-ets during its propagation. Short and high wave groups with strong nonlinear characteristics evolve from long and low wave groups, which are described by linear principles.
Based on this fact, the complex Fourier transform of the surface velocity of the long and low wave group is used as the characteristic information of the wave train (Kiihnlein [17]). From this linear wave information, all nonlinear wave elevations, velocities and accelerations are derived. Also the transformation of the wave train registration from one posi-tion to any other posiposi-tion is feasible. During its metamor-phosis the total energy of the transient wave is invariant, i f breaking phenomena are excluded.
• A t first, this paper describes the generation of linear transient wave trains and its linear transformation to selected positions. This is an important prerequisite as the same procedure will be used for the transformation of the linear wave information to establish a nonlinear wave train. In this case the linear wave celerity as a function of
concentration point time window for evaluation encounter position of wave group and model wave at
wave generator position
wave maker,,. motion a suitable time window is selected 3;o=25m xo=15m a:o=Om
Fig. 4. Wave packet as a function of time at different positions, top: XQ = 25 m (concentration point); .VQ = 15 m (preferred position for model testing); Xo = 0 m (wave generator position); bottom: fiap motion of wave generator.
G.F. Clauss/Applied Ocean Research 21 (1999) 219-234 223 1.5 . i . n ^ . 5 0.0
F o u r i e r
-spectrum
•/wave f r e q u e n c /tJu [ r a d / s ]F o u r i e r
-s p e c t r u m
12 wave n u m b e r k _ J > a d / m ] 15 3Pos. 1: wave packet converging xo = 0 m
Pos. 2: xo = 70 m
Pos. 3:
I'iilllllllN^
Xo = 95 m
Pos. 4: concentration point, xo = 107 m
Pos. 5: wave packet diverging, xo = 120 m
100 200
t
[s_3
t=210 s
instant: fo=200 s wave packet converging
«=220 s
t=225 s concentration point
i=230 s wave packet diverging
50 100
X m _
Fig. 5. Wave packet registration at different positions (left) as well as instantaneous wave profiles at selected instants (right) (water depth d = 4.2 m).
Fourier transform A(xi, w,) the wave frequency is replaced by a nonlinear
"informa-tion" celerity which depends on frequency, space, and time.
The next section introduces the development of the numerical nonlinear description of the entire wave field of the transient wave train by integrating the mutually dependent particle motion equations in time-domain. The wave information is the primordial cell in which all nonlinearities are hatched.
Finally, the paper presents model test results to illustrate the potential of the transient wave technique. The exam-ples include standard seakeeping tests and experiments in counteipropagating wave trains as well as the impact force of freak waves on permeable walls. Any experi-ment performed with this technique is exactiy repeatable, its duration is short and the energy fiux is predictable. Even complicated interactions of wave group and perme-able walls are easy to analyze, as the reflected and trans-mitted wave train can be separated from the initial wave packet.
2.1. Linear transient wave description
The synthesis and up-stream transformation of wave packets is developed from its so-called concentration point. At this position all waves are superimposed without phase shift resulting in a single high wave peak. Starting from this concentration point, the transient wave is trans-posed to the selected interaction position of structure and wave train, and finally to the position of the wave generator (Fig. 4).
The wave packet a(xi, ti,) is defined by the given discrete
«(x,, t,) = X |A(x,, d^-^^'^-'^^-¥-^'--^-'^^^^^^ ( i ) ;=o
with CÜJ =jAw (j = 0, l,...,N - 1), Aw = ( ( Z i r y r ) = ((2'IT)/(A'A0) (T = duration of registration), and yt,- =
f(tj)j, d). As N is the number of registi-ation values t^. = kAt
(/c = 0 , 1 , - 1), we. obtain n = {NI2) + 1 frequency steps. In space we define Xi = lAx {I = 0,1, ...,N - \). The Fourier transform is characterized by the amplitude spectium 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. At the concentration point Xl = A'c, all waves are superimposed resulting in a single high wave peak. To center the resulting wave train in its time frame, the Fourier transform is shifted by Til =
{NI2)AT, i.e. the phase alternates between the values 0 and TT.
flCtc, = X I^C-^c, « , ) | ( - l y e ' " ^ ( ' ' ^ ' ' A w . (2)
From its concentration point, the Fourier transform of the wave train is transformed to the upstream position at the wave board by introducing an average group velocity (l/2)[cgr(ft)njn)ICg/cumax)] and replacing cot by a t -k{w)(x - Ac) :
a{x„ t,) = X ( - iy|A(x„ coj)\ e i ( - ; f o - ' c - ( ™ ) ) - / ^ ( x , - . v . » ^ ^ ^
(J)
(3) Fig. 5 (left) shows a wave train as a function of time at
224 G.F. Clauss / Applied Ocean Research 21 (1999) 219-234 „ 1 Ë : wave elevation at =51.10 m are higher waves slightly faster 2 1 " 0 wave elevation at a;2 =84.85 m v J ^ ^ ^ i g h wave is faster, arrives 0.73 s earlier '0 10 20 30 40 50 60 70
Fig. 6. Compmison of measured water elevations of low and high wave packets at different positions (water depth d = 4.01 m).
different positions and the related amplitude spectrum of the complex Fourier transform. Note that the maximum wave height is deduced from the registration at the concentration point, which starts with a deep trough, followed by an extre-mely steep and high crest, and ends symmetrically with a trough.
The wave train can be transformed from a function of time a(xQ, t) at a flxed location XQ to a function of space
a{x, to) at a given time to. Fig. 5 (right) shows wave
eleva-tions at selected moments, i.e. successive "photos" of the water suiface. At the concentration point the wave is repre-sented by a short and steep crest tapering off into extremely long and shallow troughs at both sides.
Low amplitude wave groups can be efficiently used for standard seakeeping tests of stationary offshore structures as well as towed or self-propelled ships. High wave packets close to the concentration point are applied at "freak" wave tests to investigate extreme forces or motions. Its generation and numerical simulation requires a modified procedure, which includes nonlinear effects.
The following key observations are in contrast to linear theory:
9 Propagation velocity of wave trains increases with height: Fig. 6 shows the comparison of low and high wave trains, measured at two positions. It illustrates that a high wave train is slightly faster when propagating. Note that all three wave trains are generated by synchro-nous wave maker motions, which have been calculated by linear theory. The right hand diagram at position = 84.95 m illustrates that the entire high wave packet is about 0.73 s faster. The illustration also visualizes the existence of lower waves following the wave train. This phenomenon is a consequence of incon-ect wave maker motions, which have been calculated by linear theory.
9 The maximum crest height of an extreme wave is substantially higher than the sum of all component amplitudes: the highest wave generated in the Large Wave Tank in Hannover with /7n,ax = 3.2 m has a steep crest, 2.1 m above still water level, followed by a long flat trough, which is only 1.1m below still water level (see Fig. 15). Due to this asymmetry, the crest height surpasses the sum of component wave amphtudes ^ a,- = 1.6 m by 3 0 % , and the vertical asymmetry of crest height/wave height is 0.65. Fig. 7 shows the genesis of
a "freak" wave registered at subsequent positions in the wave tank. Note how the leading short waves are swal-lowed by the last low frequency component. Just shortly before the concentration point the wave crest reaches its peak value while the preceding deep trough becomes less pronounced.
• The superposition of identical counteipropagating wave trains yields substantially higher elevations at the center plane: as shown in Fig. 8 a single wave train is propagat-ing from wave generator A and registered at the center plane C. An identical test with wave generator B yields a congruent registration at plane C. I f both wave generators are operating simultaneously, the supeiposition gives higher peaks and lower troughs as compared to the sum of the individual wave trains.
• The entire energy of a small-amplitude wave group is accurately calculated by linear theory. Close to the concentration point, however, the results become incor-rect: Fig. 9 shows the energy distribution, calculated by linear wave theory for a wave packet, measured at tln-ee positions. The diagrams illustrate that linear wave theory is satisfactory for small-amplitude wave trains, e.g. the converging and diverging wave train at position A {x^ = 20.25 m) and B (xg = 170 m). The energy dissipation of the wave train after a distance of almost 150 m is less than 3%, i.e. the decrease of wave height is less than 1.5%. In case of higher amplitudes at the concentration point, however (wave train C at Xc = 1 0 5 m) the energy distribution calculated by linear wave theory is inaccu-rate as it gives unrealistic high values, inconsistent with the energy law of conservation).
A n improved method for describing nonlinear transient waves has to consider the above observations. It should incorporate the metamorphosis of the wave train during propagation as well as the nonlinear treatment of wave elevation, velocities, and accelerations.
2.2. Nonlinear transient wave description
For regular waves nonlinear solutions have been intro-duced by Gerstner [18], Stokes [19], and Crapper [20], Recent solutions for irregular seas have been proposed by Sand [21], Mansard et al. [22], and Stansberg [23]. None of these methods is applicable to the analysis of converging wave groups, which become shorter, higher, and faster during their way through the channel.
O O tt c QJ) ö O
I
i
G.F. C / O i f j i / A p p l i e d Ocean Research 21 (1999) 219-234position of wave probe behind wave board
225 : registration at 3.6 m " t [ s ] : 0 10 20 30 40 50 60 70 80 BO 100 110 120 : at 70 m : L [ s ] : 0 10 20 3D 40 50 60 70 BO 90 100 110 12Q : at 50.05 m
\
-1.5 0,5 , • • I l l l l l l l l ] . I J 1 : at 81.15 m ; -: t [ s ] ; -0.5 -1.5 • (concentration U : point is at 84 m) I [ s ] ; 0 • 10 20 30 40 50 60 70 BO go 100 no 1 0 10 20 30 40 SO 60 70 60 ' 0 100 no 12 ; at 61.28 mIr i
1.5 0,5 : at 90.3 m (after breaking) : V i [s] ; -0.5 -1.5 -2,5 t [s] ; 0 10 20 30 40 50 GO 70 90 100 no 120 0 ID 20 ao 40 SO 90 100 no 120Fig. 7. Genesis of a 'freak' wave by deterministic superposition of component waves (water depth rf = 4 m).
The new method proposed in this paper is based on the fact that short and high wave groups with strong nonlinear characteristics evolve from long and low wave groups, which are basically characterized by linear principles. During propagation a metamorphosis of the transient wave train is observed, its local amplitudes, phase relations, envelope and total length are changing, however, the entire energy remains invariant. Far from the concentration point, at growth and decay, the energy of the long, low-amplitude wave group is accurately calculated from linear wave theory, and only a single set of data, e.g. the Fourier trans-form of the surface velocity is required to derive the kinetic
and potential energy as a function of time (Fig. 9). The Fourier spectrum of the linear surface velocity is an ideal indicator of the metamorphosis of the wave group during propagation as its envelope is converging on its way to the concentration point, and diverging after this extreme event (Fig. 5). For this reason, the Fourier transform of the linear surface velocity (deep water condition) is selected as the backbone of the wave group. Transformed to time-domain
the complex surface velocity (real part is horizontal velocity,
imaginary part is vertical velocity) of a linear deep water
wave .is introduced as the wave infonnation l{t) as it
contains all relevant information which is needed to
r = 2 . 0 m
'////}////////////////////////////////////////7////////
wave train a ^wave liaiii b I—10.0 m
l O f 5 0 -- 5 ¬ 1 0 -single wave t r a i n
constituent wave trains at x=2.0 m (a) and 1=10 m (b)
2 2 l [ s ] 2 6 - I B IB 20 22 24 ^ [ ^ j 26
Fig. 8. Supeiposition of identical counterpropagating wave trains.
n o n l i n e a r . A
• l i n e a r A \\ x=G.O m
: superimposed "' W V • wave train (a+b) \j
226 G.F. Clauss / Applied Ocean Research 21 (1999) 219-234 mil III" 20.25 m' « Xc — 105 m I " 0.0 i [s] V 30 1 15 %0 k i n e t i c energy ^ K 512cm2 es 100 t [s] "a 25 potential energy ^ w 511cm2 •?5. B II' .. " X B = 170 m 150 t [s] 100 ^=0 total energy « 1023cm2 Q9 "freak wave" near concentration point total energy ^ « 1105cm2 eg I [s] V 30 V 30 1 ' 5 i ?: V 50 "G 25 kinetic energy t [s] potential energy 499cm2^ es 300 t [s] ?
(i.e. linear theory is invalid!)
total energy f R . 998cm2
300 t [s]
8192 8192 100 i = l 1 = 1 j~X
time steps i = 1 • • • 8192 (At=0.05 s), level steps j = 1 • • • 100 (A«=0.042 m)
Fig. 9. Energy distribution of a measured wave paclcet, water depth = 4.2 m, calculated with linear wave theory. The linear wave theory is satisfactory for the calculation of the energy of a converging wave train A and the diverging wave train B (small-amplitudes), but not for wave train C (measured at a short distance in front o f the concentration point).
describe a transient wave train (Kiihnlein [17], Clauss and Kühnlein [24]).
In the case of a regular (high) wave the complex wave information I is simply given by the harmonic oscillation
Iit,x) w„ e i(a)t-fcv) (4)
which coiTesponds to the orbital surface velocity iv^ = = ^nCi) of a linear deep water wave. At first, the procedure is applied to analyze the propagation of high regular waves, and w i l l be then extended to nonlinear wave packets. The nonlinear particle motions are developed from the iterative integration of the coupled equations of particle positions
^{t,x,z) and ij(t,x,z) with improved values of the average
shift x(t) of the respective element. Generally, one or two loops are necessary to get convergent results. As has been pointed out, the Hnear description is insufficient in the vici-nity of the concentration point. Due to the high wave ampli-tude the particles are traversing through different velocity levels during orbital motions, and the particle velocities are evaluated in con-espondence with their respective positions: according to Kiihnlein [17] (Clauss and Kiihnlein [24,25]) the nonlinear motions are developed from the iterative inte-gration of the coupled equations of particle positions, which
are based on the wave information / ( f ) , i.e.
f ( / , X o , Z o ) '1 . 0 { X tanh(M) cosh[k{z+ aT,xo,zo) + d}] 2l(kd) sinh(/rd) X w„ c o s [ - k{x + X(T)) -I- WT Re I{t,x,x) dr; ^(^•-VO.^O) tanh[/c{^(T,A-o,Q)-t-rf}] V'''^''^ tanh(M) ^ (5) X s i n h [ M z + ^ ( T , A o , Z o ) + r f } ] sinh(W) X sin[-^(x-Hx(T))-f- WT] ' \/^— ' Im /(MVÏ) dT.
k is the wave number, XQ and zo are starting positions of the
water particle before the wave has anived, i.e. ^{t = 0,x,z) = 0 and f(r = 0,x,z) = z (particle at depth z). After
G.F. Clauss / Applied Ocean Research 21 (1999) 219-234
particle motion
. 'X \x + x t = 0.65 s At = 0.05 s t i 0.65 s) x{t = 2 s) 0.5 1.0 t = 0.65 s 1.5 t [s] 2.0Fig. 10. Integration of particle motions f r o m the linear wave information l{t,x), T = 2 s.
the wave has passed the particle reaches the end position
+ ^(?end>^o>Zo) andzo + ^(?end.^o>Zo)- « r is the associated cunent velocity due to convection.
The first term of Eq. (5) is a correcting function due to the wave induced variation of water depth d (shallow water effects). Note that for deep water waves as well as for very small amplitude waves (linear) in shallow water this function yields 1, and can be neglected without affecting the results. For higher regular waves in shallow water the
c o i T e c t i o n by using this function is confirmed by experimen-tal (measured) results.
As shown in Fig. 10, the particle position follows from the orbital motion and convection. The wave information is related to the position x + X(T), with X(T) being the mean value of the excursion due to its con'ected convection:
x(t) = 'end 0 idzdt ^ 0 d t fend (6)
At the first iteration step, x{t) is set to 0, and the celerity c of the regular wave follows from the sum of the linear celerity
8
tanh(M)
and the wave induced convection velocity, i.e. ê(Und,Xo,Z = 0) cid, k) = C]inear(^?, k) +
il)
(8)
'end
Fig. 11 shows a 0.45 m regular wave (period T = 2 s, water depth d = 105 m). Note that the wave is asymmetric, and the particles at the water surface are travelling down-stream whereas at deeper levels an opposite convective cun-ent is observed. These results are confirmed by experi-mental investigations. Due to convection, the period of the moving water particle at the surface is slightiy higher, and at the bottom is slightly lower as related to the wave period of
r =
2s.I f switching from this Lagrangian description of orbital motions (individual particles in regular (high) waves) to Eulerian description giving the motion characteristics at a specified location (with different particles passing by) we
simply have to assign the position-related data to fixed loca-tions. With regular waves this can be done easily, as only the starting position of these particles has to be changed.
A A - = -C{d,k)t - ^{t,Xo,ZG). (9)
As a result, Fig. 11 shows the surface elevation at a fixed location.
After illustrating the application of the "wave informa-tion" technique for analyzing the propagation of high regu-lar waves we extend our model to transient wave trains. In order to consider the actual wave number k at each time step the nondimensional first part of Eq. (5) is evaluated in frequency domain. These terms are called A7_,„ resp. z,„, because of their influence on the horizontal resp. vertical particle motion components:
tanh[fc„,(^oj + d)} 2/(k,„d) cosh[k,„(z + d)] tanh{k,„d) sinh(/r„,(i)
tanh[^,„(4,/ + d)]^'^''"'^ smh[k,„(z + + d)] (10)
tanh{k,„d) sinh{k„,d)
with / = 0 , 1 , 2 , . . . , « - 1 (time steps), m = 0,1,2,..., in/2)
(frequency steps) and ^, := C{t,,Xo, ZQ), ^O,I •= CithXo, 0). In analogy to Eq. (4) we introduce the complex wave informa-tion ƒ as the sum of the linear horizontal and vertical deep-water particle surface velocities, u and >i'. As their amplitudes are identical, the wave information is calculated from the associated Fourier transform of the vertical velocity W (note the phase shift e'^""'^' = 0 , I . e .
I{t,x)
(m)
(11)and calculate the wave particle velocity according to the modified Eq. (5) by using Eq. (10)
li^{h,X,z) = Y.'H,nW(x, CO,,,) e ' f " ' 2 ) ^ i » , „ r ^ ^ ("0
11' ,{t,,x,z) = X^i,„.W{x, or,,,) e'"'"'Aw.
(12)
Eqs. (10) and (12) have to be solved at every dme step in order to calculate the actual position of the respective water
228 G.F. Clauss / Applied Ocean Research 21 (1999) 219-234 50 •looH -150 10 20 30 Xo = 0 (starting position of
' selected water particles)
40 , r T 50 t [s] !,) particle m o t i o n ^ at different levels -100 f zo = 0 , -0.25, -0.5, -0.75, 1.0, -1.25, and -1.5 m 100 200x [ c m ] 50 25 3^ hJ T = 2.0 s,a; = 3.14 rad/s e n l a r g e d , 16 24 „ higher harmonics 10 20 u [ r a d / s ] 3 0
Fig. 11. Calculated surface elevation, water particle motion, and Fourier spectrum of a regular wave T = 2 s, = 1.5 m.
particle;
(Mp - H f ) dr.
M'p dr.
(13)
(14) is the associated cuiTent velocity due to convection. The surface motions at a specified location (Eulerian description) follow from the interpolation of motion char-acteristics of particles passing this fixed location. On this basis, all elevations, motions, velocities, and accelerations of nonlinear transient wave trains are predictable at arbitrary instants and locations.
The celerity, i.e. the propagation velocity, of information follows from linear celerity and an additional term due to nonhnear convection (see Eq. (8))
Cj{d,k) = C,inear('^>^) + C^^idJi), (15)
Cadd =x(t,X,Z= 0).
The transformation of the linear wave information I(t, XQ) from one position to any other location is similar to the transformation of a linear wave packet: only the linear wave celerity has to be replaced by the nonlinear informa-tion speed c,{d,k) (see Eq. (15).
Fig. 12 demonstrates the transformation of a transient wave train, registered at position x^ = 10 m (A), to position Xj = 25 m (H), and A-3 = 39.1 m (I). The registered wave train A is highly nonlinear with steep crests and flat troughs. Its associated Fourier spectrum A F shows characteristic iiTegularities. By iterative procedures the linear information D with its associated spectrum DF is filtered from wave train A (note: the first derivation of the reduced (low-pass filtered) registration A is used as a take-ofl" function for the linear wave information D). The nonlinear wave elevations
a t A ' i = 10 m are expanded from this initial wave informa-tion by iterative integrainforma-tion of the coupled equainforma-tions of particle positions (5). The associated particle motions are
shown in Fig. 12 illustrating a wave induced convective velocity in the dhection of wave propagation at and near the water suiface and a flow in the opposite direction at the bottom of the wave tank. The comparison between calcula-tion G and registracalcula-tion A is used to improve the wave infor-mation (the nonhnear elevations G are recalculated and' compared again to registration A and the procedure will be repeated until the comparison is satisfying).
I f the linear wave information and its associated Fourier spectrum at the position Xi = 10 m is sufficiently satisfac-tory, it is transferred to positions X2 = 25 m and X3 = 39.1 m. The resulting linear wave informations E and F are then expanded into the nonlinear wave trains H and I with their associated spectra H F and I F . This numer-ical result is confirmed by experiment (measured wave trains B, C as weh as the comparison of the associated Fourier spectra BF/HF and CF/IF).
The numerical method confirms the experimental obser-vation that nonlinear high-amplitude waves
® are significantly higher as predicted by linear theory,
9 are slightly faster than small amplitude waves, and
there-fore also slightly longer, • generate a wave induced cuiTent.
It is a tremendous advantage of the proposed method, that the nonlinear wave field is only expanded at positions, where it is needed. The transformation of the wave train to different positions is easily done by transposing the linear wave information. The wave information / of different wave frequencies is simply superimposed as it is known from linear wave theory. Finally, at selected points, the nonlinear wave elevations are expanded from the superimposed wave information. The technique is capable of generating special purpose transient waves:
® short wave groups for seakeeping tests;
9 tailored wave groups for special wave/structure interac-tions (dynamic stabihty, slamming etc.);
G.F. Clauss / Applied Ocean Research 21 (1999) 219-234 REGISTRATIONS xi = 10 m, 1 2 = 25 m, nonlinear calculation to extract linear information WAVE INFORMATION x i = 10 m, D 5 0 I [ s ] 7 5 t [ s ] 7 5 0 t [ s ] £ 0 . 0 ^ 0 , £ E t W X3 = 39.1 m 7 5 ""0 t [ , ] Fourier spectrum of L I N E A R WAVE I N F O R M A T I O N (at positions D, E , F ) X3 = 39.1 m t W " 229 a ( s i =• 10 m,t) i linear information ci{d,k{t)) information speed 0(12 = 25 m,t) t linear information ci{d,kit)) information speed a{x3 = 39.1 m,t) t linear information N O N L I N E A R P A R T I C L E M O T I O N S (from iterative integration of coupled equations)
a
o o - 5 0 -100 -150 - 5 0 0 -50 X [ c m ] SURFACE E L E V A T I O N (nonlinear) Xl = 10 m, X3 = 39.1 m 5 0-s
O 5 0 --100 -100--150 -50 0 50 X [ c m ] X2 = 25 m, -150-' — $: 1
-: 7
-50 0 50 X [ c m ] X3 = 39.1 m t [ , ] 7 5 - 0 t ( s )ASSOCIATED FOURIER SPECTRA
Xl = 10 m, X2 = 25 m, B F / H F X3 = 39.1 m 8 a [ r a d / s ] 12 H F c a l c u l a t e d B F m e a s s u r e d u [ r a d / s ] I S B Ü [ r a d / s ] 12
Fig. 12. Transformation o f a wave packet, measured at.Xi = 10 m, to the position X 2 = 25 m and.V3 = 39.1 m, as well as comparison between calculated and measured water surface elevations (water depth = 1.5 m).
• very high freak waves for worst case studies (100-year design waves).
Any experiment performed with this technique is exactly repeatable, its duration is short, and the energy
flux is predictable. Even complicated interactions of wave groups and structures are easily analyzed, as the relevant registrations are weU defined within a limited time window, and statistical uncertainties are excluded.
230 G.F. Clauss / Applied Ocean Research 21 (1999) 219-234 0 . 0 5 - 0 . 0 0 _ 1 1 J 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 s u r f a c e elevation E ( r e g i s t r a t i o n of wave g r o u p Mt\l\n / v _ 1 1 ( 1 1 i 1 1 1 1 1 1 1 1 -e n c o u n t -e r w a v -e p a c k -e t J ( m e a s u r e d with a wave E - at e n c o u n t e r p o s i t i o n ) = 1 1 , 1 1 1 1 1 1 1 1 1 . 1 1 1 1 1 1 < 1 1 1 p r o b e on b o a r d of the m o v i n g c a r r i a g e ) -1 1 1 1 1 1 -(Ö - 0 . 0 5
I
- 0 . 1 0 I D 1 0 . 1 0 0 . 0 5 ( D - 0 . 0 0 > to 170 2 1 0 2 2 0 _ 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 L h e a v e motion of towed c a t a m a r a n I l l l l l l l l •All 1 1 1 fll 1 1 1 1 1 1 1 1 1 1 1 1 -- 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I 1 1 e n c o u n t e r v e s s e l / w a v e d e c e l e r a t i n g v e s s e l o v e r r u n : by its own s t e r n w a v e s y s t e m ; -- 0 . 0 5 - O . I O 1 3.0 2 . 0 ^ 1.0 :1i - 1 . 0 <^ - 2 . 0 - 3 . 0 150 2 1 0 2 2 0 1 1 1 1 1 1 1 1 1 1 1 1 1 r 1 1 1 1 1 — , .. V Macceleration " ' = 4 . 0 m / s 4i\r 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 I _Note: stern of the vessel is l l f t e d -mechanicolly by security rope 1 pitch motion Z. of towed c a t a m a r a n - 1 1 1 1 1 r 1 1 I 1 1 t 1 . 1 - 1 f 1 1 time window f o r e v a l u a t i o n I l l l l l l l l \J\J\ 1 1 1 1 1 , 1 , 1 , , , , -150 190 2 2 0 2 3 0 t i m e [ s ] model 0.005 t . 0 . 0 0 0 0 . 0 0 5 3, 0 . 0 0 0 wave packet 4m/s wave p a c k e t s ( d i f f e r e n t w a v e h e i g h t s ) 0.04 0.00 -0.0"^ 0.04 0.00 • 0 . 0 4 , . , 1.0 • 0.0 -'•1
•iM
A ^ „ wave p a c k e t • 90 0.15 BC 0.00 200 200 . „ A A heave 210 \ f \ ^ p''^'^ \ j ^ t [ s ] 210 1.5 > 1 . 0 \ 0 . 5 w 0.0 1.0 io.o -1.0 RAO h e a v e\
v = 2 0 . 5 k n 0 1 2 3 4 5 , , , , 1 , , , , 1 i > , , 1 , , , p h a s e h e a v e 4 5 Wo [ r a d / s ] 4.0 0.0 1.0 1=0.0 - 1 . 0 RAO p i t c h p h a s e p i t c h ( f u l l s c a l e ) Wo [ r a d / s ]Fig. 13. Registrations, Fourier spectra, and transfer functions of a typical seakeeping test with a high-speed catamaran in transient wave trains (model scale 1:7,
G.F. Clauss /Applied Ocean Research 21 (1999) 219-234 231
3. Application of the transient wave techniqoe
The transient wave technique offers new opportunities for all types of wave/structure interactions: the (nonlinear) surface elevation as well as the velocity and acceleration fields, and the shape variation of the wave train on its way to the concentration point are predictable. The numerical model is physicaUy true as has been confirmed by model tests. Due to the accuracy and repeatability of identical wave trains it is possible to investigate a model (stationary or moving) at different wave/structure interaction points. Test series of this type are of great interest as the highest load or response must not coincide with the concentration posidon at the structure. Dynamic stabihty or capsizing of ships can also be investigated in detail as the cause-effect-chain can be analyzed in a deterministic, repeatable wave train at different interaction positions. Last but not the least, it is possible to integrate the freak wave signal into a stan-dard irregular sea. A combination or comparison of the transient wave technique with the constraint random simu-lation (Harland et al. [6]) seems to be promising. The following examples illustrate the efficiency of the technique as a standard tool for seakeeping tests and as a new tool for worst case studies in freak waves.
3.1. Seakeeping tests
The application of the wave packet technique is illu-strated at a typical towing experiment with a high-speed catamaran (model scale 1:7). The test was performed at the Berlin ship model tank (VWS) (width 8 m, water depth 4.2 m, length 250 m) using the new high-speed caniage as well as the unique two-flap wave generator. The testing procedure is completely automated: wave generator as well as caniage 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 proceeding one, the length of the wave train is shrinking rapidly while propagating along the tank (see Fig. 5 for wave train registrations). Shortly before the concentration point, the oncoming vessel meets the wave train exactly at the predetermined position: consequently heave and pitch motions ai'e observed (Fig. 13). Within only 10 seconds the seakeeping test is completed. Note that the ship starts and stops under still water conditions. For safety reasons, every model test begins with the start of the caniage. This signal activates the control computer, which is simultaneously starting the wave generation, data acquisition, and control of the carnage. While the waves are propagating to the wave-model interaction area, the caniage is running first at low speed {Vu = 0.2 m/s). After 166 s the caniage is automatically accelerating up to the preset speed, and meets the wave train exacdy at the predicted position. To prove the linear behavior of the vessel in waves, spectra with different maximum wave height (at model scale:
^ m a x = 0.04, 0.06, and 0.08 m) have been used during the tests. The resulting motions for heave and pitch prove the linear behavior of the vessel thi-oughout the entire frequency range as the respective amplitude operators (RAO) are not depending on wave height (up to H^^^ = 0.56 m , — f u f l scale). The high accuracy and the short duration of seakeep-ing tests in deterministic waves is outstandseakeep-ing. As the inter-action between wave train and ship model is exactly predictable this specific section of the towing tank has been equipped with side wall wave absorbers (Fig. 14) to avoid wave reflections which would deteriorate the vessel—RAOs.
The application of optimized wave packets shows consid-erable advantages in comparison to conventional techni-ques: the duration of the test is very short; reflections from beach or wave board do not interfere with the results. The converging wave train just in front of the concentration point is short. This facilitates short duration seakeeping and manoeuvring tests. Precise and highly resolved results are achieved in a short time. In our case, the duration of the entire model test with a self-propelled model (Fig. 13, VM = 4.0 m/s) is about 250 s, with a relevant registration time window of about 18 s only. In conclusion, it needs just one single test to determine all relevant transfer functions with a resolution of about 400 frequency points Aw = 0.03 rad/s). In comparison, 400 model tests in regular waves or at least 40 tests in irregular seas would be neces-sary to anive at similar results. Thus, the work of weeks can be done in hours.
3.2. Worst case investigations infi-eak waves
Our second example illustrates model tests with so-called "freak" waves. As the research project is still on its way, just one preliminary test of this program is presented to illustrate the potential of the transient wave technique. Extreme wave conditions in a 100-year design storm arise from the most unfavorable supeiposition of component waves of the related severe sea spectrum (Kjeldsen and Myrhaug [26]). When generating irregular seas at model scale these crucial conditions, related to the most critical storm spectra, even-tually may occur i f the random phase shift of all superim-posing waves happens to be zero at a certain position—a coincidence which requires a very extended test duration.
As an alternative, the component waves of a project-oriented design spectrum are tentatively generated i n such a sequence that all waves superimpose without phase shift at a given position (see Fig. 1). This option is based on specdal analysis, which describes the apparently chaotic wave field of a natural seaway as the supeiposition of an infinite number of independent waves. Each component wave contributes an amount of energy to the seaway proportional to its squared wave amplitude (Clauss et al. [27,28]). The most unfavorable event in storm wave conditions is the in-phase supeiposition of component waves in the seaway. As these freak waves are possible events during the life cycle of
232 G.F. Clauss / Applied Ocean Research 21 (1999) 219-234
Fig. 14. Vertical side wall wave absorbers on both sides of the towing tank.
a marine structure it may be selected as the relevant design wave.
To illustrate the potential of the transient wave techniques in generating design wave loads, the interaction of waves and a transparent vertical structure is presented. The inves-tigated wave filter consists of 24 horizontal heams (DISO X 180 x 7 mm). The gap between neighbouring beams is 65 mm, i.e. the porosity of the wall is ;? = 26.6% (Fig.
15). Wave forces are measured individually, as each beam is connected to the vertical test structure using an integrated force probe. The test has been performed at the Large Wave Research Tank, "GroBer Wellenkanal", Hannover (length 250 m, width 5 m, water depth d = 4.01 m) which is jointly run by the Universities of Braunschweig and Hannover.
Fig. 15 presents two realizations of the sea spectrum = 1.25 m and Tp = 8 s, both measured 3.6 m behind the wave maker, i.e. irregular waves with random phase and a speci-fied tailored wave train which finally develops to a 3.2 m freak wave at its concentration point.
Note that the maximum wave height of the 1000-s i i T e
-gular- wave registration gains about H^,^,^ = 2.2 m which appears dramatic as compared to the harmless 1.5 m high transient wave train at the position x= 3.6 m. However, 93 m and 15 s later this transient wave train rears up and breaks into the vertical wave filter with terrifying conse-quences. As shown in Fig. 15 more than 125 IdSf are measured on the top beam of the filter wall, a blow which only lasts for a few milliseconds. Extremely high loads are also measured at all other beams. I f compared to iiTegular wave tests, these loads are at least twice as high, and at the top beam even 20 times as high. A more detailed analysis reveals that the i i T e g u l a r waves reach the top beam of the
transparent wall only a few times, and the measured force gives a maximum value of about 6 kN.
At a first glance, these measurements seem puzzling, and caution is recommended in evaluafing the associated conse-quences.
» Firstly, it should be noted that the maximum wave height in the irregular wave train is 2.2 m as compared to 3.2 m in the transient wave. As the investigated wave filter is a drag dominated structure, and the associated drag force follows from the squared wave height ratio, i.e.
(3.2/2.2) = 2.12 the observed doubling of the maximum wave force on the entire filter is in agreement with expec-tations. Regarding the extremely high force on the top beam it should be noted that this is just a short impact between structure and breaking wave lasting only a few nulliseconds.
e Secondly, the selected extreme wave height in the
tran-sient wave, as related to the significant wave height 3.2
1.25 = 2.56,
is an unlikely event, i.e. the probability of occurrence is miniscule. In general, the maximum wave height in hostile seas follows from the number of observed waves N, with the ratio to the significant wave height following from
InN
With N = 1000 waves in an extreme 3-h seastate we obtain H^^JH^ = 1.86 which is an accepted design value. With A? = 10'*...10^..10'' the associated ratio
Hnmx/Hs yields 2.15...2.39...2.62, i.e. the synthesized
huge breaking wave in our test program seems quite unrealistic. However, freak or abnormal wave heights have been reported by Faulkner [10] and Faulkner and Buckley [9] who suggest to complement present standard design methods with survival design procedures. In this context the loss of the semisubmersible OCEAN RANGER presumably caused by a freak wave should also be mentioned as all neighbouring platforms in the Grand Banks area simultaneously observed a harsh sea state without significant anomalies.
In summary, the investigation of the probability of freak waves and the related risk potential is still a challenging future problem. It seems inevitable to establish reliable design loads by model test series with tailored wave packets, which represent realistic supeipositions of all spectral component waves. With the transient wave technique proposed in this paper we are offering a procedure
G.F. Clauss / Applied Ocean Research 21 (1999) 219-234 233
I [ s ]
T r a n s i e n t wave g r o u p (selected phase r e l a t i o n ) , measured at a; = 3.6 m b e h i n d wave m a k e r p o s i t i o n 2.5 i r r e g u l a r sea s t a t e Tp=8s, H , = 1.25m 200 400 800 I [s]
I r r e g u l a r sea state ( r a n d o m phase), measured at a: = 3.6 m b e h i n d wave m a k e r p o s i t i o n w a v e p a c k e t I [=1 f o r c e o n t o p e l e m e n t ( w a v e p a c k e t ) • 1 : ! f o r c e o n t o p e l e m e n t
1
( w a v e p a c k e t ) • 1 ( e n l a r g e d t i m e s c a l e ) ^Ifyvvw. 1
t o p element o f wave filter
wave p a c k e t *•*-* i r r e g u l a r waves Tp=Bs, H,= 1.25m 1 I I I I 1 I I I I - L
f o r c e [ k N ]
50°Fig. 15. Application of fransient wave groups in the design of wave filters and absorbers: breaking transient wave packet ( f f ^ , , = 3.2 m) with its resulting wave force on the top element o f a permeable wall used as a vertical wave filter (porosity p = 26.6%, water depth = 4.01 m), as well as the comparison of the maximum horizontal wave forces as a function of depth, as measured with irregular waves or with the breaking transient wave train (,H, = 1.25 m, T = 8 s).
• to generate tailor-made and task-related wave groups which are physically real waves and
• to superimpose these wave groups to regular or irregular seas with a 'customer-selected' ratio of H^^JHs. Currently, the nonlinear transient wave technique is further developed to improve ship safety i n hostile seas, and to evaluate capsizing processes.
4. Conclusions
This paper illustrates the analysis and applications of realistic nonlinear transient wave trains. The technique is based on the definition of a complex wave information, which corresponds to the (linear) suiface velocity of a wave group. Combined with modified wave celerity (infor-mation speed) the propagation of high wave groups is calcu-lated. As a result, the nonlinear registrations and associated wave group kinematics are derived from the relevant wave
information at selected positions. The procedure allows the superposition of counter-propagating wave trains, as well as the synthesis of freak waves by skilful superposition of component waves. As all relevant wave parameters (motion, pressure distribution, velocities, and accelerations) can be calculated at arbitrary positions and time, the method serves as a sound basis for the analysis of offshore structures. The numerical wave model which has been validated by exten-sive model testing ahows a step by step verification of cause-effect-chains: suiface elevation—wave kinematics and dynamics (orbital motions, pressure field)—forces on structure components—structure motions: as all physical laws and boundary conditions without assumptions and simplifications are satisfied, the method can be character-ized as i?efl/Wave-technique. It is a tremendous advantage of the proposed method, that the nonlinear wave field is expanded from the linear information I. Thus, its calculation is only necessary at selected positions.
234 G.F. Clauss / Applied Ocean Research 21 (1999) 219-234 wave technique is illustrated. Model tests with breaking
transient "design" wave packets demonstrate that the Real-Wave-technique is also an excellent new tool for survival design procedures. Tests with a permeable wall prove that the obtained maximum wave force on a structure is much higher as compared to model tests with inegulai' waves, both relating to the same spectrum. As a consequence, it is stated that seakeeping tests in high i i T e g u l a r waves are not sufficient for evaluating design wave loads. Only test series with deterministic transient wave groups promise a reliable assessment of extremes.
Acknowledgements
The development of the transient wave technique has been funded by the Federal Ministry of Reseai'ch and Devel-opment—BMFT—for more than ten years. Results have been published in two outstanding PhD theses (J. Bergmann and W. Kiihnlein) and more than 10 reviewed papers i n international conferences and journals. The related projects dealt with analytical and numerical methods for generating and optimizing tailored wave trains and their application to seakeeping tests. The author wishes to thank the sponsor for the long-standing support, which allowed us to develop and improve the technique and expand it to include nonlinear effects of very high wave groups. Based on this technique the above Ministry granted a new project on the develop-ment of wave absorbers for harbour and coastal protection (MTK 0578). In this project our Institute of Naval Archi-tecture and Ocean Engineering is jointly cooperating with the LeichtweiB-Institute of the Technical University Braunschweig and the Large Wave Tank, "GroBer Wellen-kanal Hannover" (GWK; a joint coastal engineering research facility of the Universities of Braunschweig and Hannover). The author is indebted to the research members Dipl.-Math. Janou Hennig and Dipl.-Ing. Katja Stutz for critical review and valuable discussions. He also wishes to thank Prof. Douglas Faullcner for his support.
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