AND MD•IWN6 - Wegemt...2019/04/02 · 1. Overview Measurements have been made of the velocity field and wave parameters for large waves on a moderately sheared current in a wave

Book Ref. HH96001

WEGEMT WORKSHOP

WAVES

AND MD•IWN6

THE MARINE ENVIONMEN5

~ednesdla,, 11 September, 1996

venueRiccarton Site, Heriot Watt University

hosted byDepartment of Civil & Offshore Engineering

.. Eu tiv Heriot Watt University

WVEGEMT Workshop on

Waves and Modellingthe Marine Environment

Abstracts of papers from a one-day Workshop held onWednesday II September 1996

Riccarton Site, Heriot Watt University

Hosted by the Department of Civil & Offshore Engineering,Heriot Watt University

SCOTLAND

Published by WEGEMT

Publication reference number HW96001

ABOTF[ WEGEMT

WEGEMT is a European Association of 37 universities in 17 countries. It was formedin 1978 with the aim of increasing the knowledge base, and updating and extending theskills and competence of engineers and postgraduate students working at an advancedlevel in marine technology and related science.

WEGEMT achieves this aim by encouraging universities to be associated with theFoundation, to operate as a network and therefore actively collaborate in initiativesrelevant to this ainj

WEGEMT considers collaborative research, education and training activities at anadvanced level, and the exchange and dissemination of information, as activities whichfirther the aim of the Association.

NB For "marine technology and related science", this includes all aspects ofoffshore oil & gas exploration and production, shipping and shipbuilding,underwater technolo2ies and other interdisciplinary areas concerned with theoceans and seas.

ABOLUT THE PUBLICATION

This publication represents a series of abstracts of lecturers' notes which werepresented at a one-day Workshop on Waves and Modelling the MarineEnvironment first presented at Heriot Watt University on Wednesday 11 September1996.

ISBN - 1 900453 01 0

Published by WEGEMT

Copyright © 1997 WEGEMT. AlD Rights Reserved. No part of this publication maybe reproduced. stored in a retrieval svstem or distributed in any form or by any meanswithout the prior written consent of the publisher.

This volume has been made available so that it contains the original authors'tvpescripts. The method may fiom time to time display typographical limitations. It ishoped however, that they do not distract the attentions of the reader. Please note thattie views expressed are those of the individual author(s) and the publishers cannotaccept responsibility for any errors or olnissions.

"WAVES and MODELLING the MARINE ENVIRONMENT"Wednesday 11th September 1996

Heriot-Watt University

Experimental modelling of large waves on sheared currents Paper I

D.J. Skyner. W.J. Easson (University of Edinburgh)

Wave asymmetry and extremes in second-order random wave trains Paper 2

C.T. Stansberg (MARINTEK. Norway)

Estimating extreme sea states - some methodological considerations Paper 3

G. Feld (Heriot-Watt University)

On some advanced physical and numerical models for studying sea waves and their Paper 4

effectsM. Benoit (EDF - Laboratoire National d'Hydraulique - France)

Storm waves and forces on structures in the northern north sea Paper 5

P.H. Taylor ( Shell International E and P)

Modelling DB3 wave spectra Paper 6

E.G. Pitt (Applied Wave Research)

The development of response-based criteria for the design of FPSO's west of Shetland Paper 7R.G. Standing (BMT Fluid Mechanics Ltd)

Modelling the behaviour of a semi-submersible in an extreme environment Paper SJ. Bowers. I. Morton. G. Mould. (University of Stirling) A. Incecik. (University of

Newcastle upon Tyne) 0. Yilmaz (University of Glasgow)

An investigation of the wave behaviour around a TLP in extreme seas Paper 9A. Arnott. A. McLeary. C. Greated. (University of Edinburgh) A. Incecik (University ofNewcastle upon Tyne)

Joint probabilities of extreme waves, wind and current: one way forward Paper 10J. Wolfram (Heriot-Watt University)

WA TEGEM,



PAPER 1

Experimental modelling of large waves on sheared currents

D.J. Skyner, W.J. Easson (University of Edinburgh)

EGEMT

EXPERIMENTAL MODELLING OF LARGE WAVES ON SHEAREDCURRENTS.

William J Easson & David I Skyner

Department of Mechanical Engineering. The University of Edinburgh. KingsBuildings. Edinburgh. EH9 3JL, UK

1. Overview

Measurements have been made of the velocity field and wave parameters for large waves ona moderately sheared current in a wave flume. Comparisons are made between the velocityfields measured with particle image velocimetry and the predictions due to irrotational wavetheory with current stretching; irrotational wave theory and Doppler shifting; and a constantvorticity model. Values of the equivalent current derived for the surface parameters arecompared with near-surface current weighting methods and are found to be better predictedby the surface current value. It is shown that, in the investigated regime, a choice of surfacecurrent is sufficient to predict the kinematics from Doppler theory in the crest, but themethods show significant differences with the measured wave trough values.

The presence of a current can significantly affect the wave loading on an offshore structure.The effect of a slab current can be viewed in two ways. In the first case the wave can beregarded as moving from an area of still water onto a current. If a regular wave moves fromstill water onto an adverse current, then the wave will steepen, and breaking may occur. Ifthe wave moves into an area with a following current then the wave will lengthen. with aconsequent reduction in wave steepness. However. storm waves may be generated on anexisting underlying current, or the wind shear may produce a current at the surface. Thechallenge in this second case is to describe the wave kinematics of a combined wave andcurrent field.

2. Velocity Fields

In this paper the results of velocity measurements under the crest and trough of large waveson a moderate shear current, measured with Particle Image Velocimetry. are compared withthe predictions obtained from a fully non-linear model and from current stretching. Figure Ishows the velocity profile under the crest of a steep wave on a moderately sheared current.The velocity profile under the wave crest may be adequately predicted by using eithercurrent stretching techniques, or a constant vorticity technique. The velocity profile underthe wave trough is underestimated by both of these methods.

01 0.1

E o.o -. .-0.4 1-0.2 0:0 0.2 C 0.0 0.2 0.4w'-- 0.62--. -0.1- f'l- -0.1 - • ¢•-.0 0 .

0 0o

-0.2 -0.2

0.) * -0.3 0.3

- . CA -0.4

Velocity (m/s) Velocity (m/s)Figure 1: Horizontal velocity profile on a sheared current (case 17).

(a) under the trough. (b) under the crest. -.- measured wave, with rms turbulence levels;- - - unperturbed current; - numerical prediction; - -urrent stretching prediction

3. Effective uniform currents

A number of authors have proposed the concept of an "equivalent uniform current", andpropose methods for calculating the equivalent value on a linear shear current, or an irregularcurrent profile. The underlying assumption is that, to a good approximation, the wave maybe treated as riding on a steady uniform current.

Wave parameters and kinematics have been measured for large waves travelling on amoderately sheared linear current profile. By measuring the wavelength and periodindependently it was possible to deduce an equivalent steady current in the wave flume. Inall cases this was closely approximated by the value of the current at the water surface. Themethod of equivalent current was shown to be useful, but the values were different fromthose predicted by depth averaging the current.

"WAVES and MODELLING the MARINE ENVIRONMENT"Wednesday l1th September 1996


PAPER 2

Wave asymmetry and extremes in second-order random wave trains

C.T. Stansberg (MARINTEK, Norway)

EGEMT

"Waves and Modelling the Marine Environment"WEGEMT Workshop, Heriot-Watt University,Edinburgh,11th September 1996:

WAVE ASYMMETRY AND EXTREMES IN SECOND-ORDER RANDOM WAVE TRAINS

Carl Trygve StansbergNorwegian Marine Technology Research Institute A.S. (MARINTEK)P.O.Box 4125 Valentinlyst, N-7002 Trondheim, Norway

Synopsis (2 pages)

Background. purpose:

The short-term statistical behaviour of the largest waves insevere sea states is important for the proper design ofoffshore structures. Thus the expected largest wave and crestheights in a sea state of a given duration, and the resultingasymmetry, need to be calculated properly.

For deep water conditions, which is the case considered inthis paper, prediction methods based on the Rayleigh modelhave been extensively applied in the offshore industry. Suchmethods are simple, and work satisfactorily in a variety ofcases. In recent years, however, one has realized that incertain severe wave conditions, the Rayleigh model mayunderpredict extreme wave crest levels. This is especiallycritical for platform air-gap problems, and modificationprocedures taking into account a systematic non-linearskewness of the steepest waves are now being considered in theindustry. This is mainly to account for deviations inparameters as: statistical skewness, extreme crest levels, andhorizontal asymmetry of individual waves.

One way to do such non-linear adjustments is to introducecorrection factors, empirical or theoretical, on the actualparameters. Alternatively, one may take the full step into aconsistent nonlinear wave model for numerical simulation ofrandom waves. This may, at the first sight, seem computer-consuming, but limiting the modelling to second order onetakes care of a mjor part of the mentioned effects, andrelatively modest computational efforts are needed.

The purpose of the present paper is to demonstrate thestatistical properties of deep-water second-order random waveelevation records. Particular emphasis is made on: 3rd and 4thorder statistical moments (skewness and kurtosis), extremecrest and wave heights, and the symmetry of the largest waves.Some comparisons are made to theory and to experimental data(from laboratory and field).

Method, results.

The main part of the presented work is done throughnumerically simulated second-order random wave trains. A briefreview on the simulation procedure is given first. A largenumber of records have been simulated, with a systematicvariation of of sea states included. Each sea state is runwith 48 different statistical realisations, to obtainstatistically stable extreme wave results. Record durationsare systematically varied from 15 minutes up to 4 hours. Fromthes simulations, statistics including expected (average) andthe connected variability are obtained for the relevantparameters. Comparisons to linear wave model results, as wellas to available theoretical reusits, are also made.

The relevance of the second-order wave model, in particularfor severe sea states, is discussed by comparison to availablemeasurements - mainly laboratory data, but also to somepublished full scale data results. A reasonably good agreementis observed, showing a significant improvement from lineartheory for these cases.

Second-order random wave modelling refreshes the need for adiscussion on how to model the high-frequency tail of the wavespectrum. The reason is that the actual wave model is based ona Stokes type of perturbation of the Airy model (the latter ishere called the "free wave") , which requires limitations onthe nonlinear contents for the physics to make sense. This isin particular seen in the interaction between long and shortwaves: A glance on the kinematics of such wave combinationsindicates a maximum" free wave" frequency which can be allowedin a sea state of a given significant wave height. Such acriterion has been applied in the simulations above. Theconsequences of the actual choice of criterion has also beeninvestigated.

In many practical cases with severe sea states, however, thedealing with the high frequency part of the spectrum may seemnot to be a serious practical problem. This is because theactual spectra are often narrow-banded, or, at least, they maydecay rather rapidly at high frequencies, and the choice of amaximum "free wave" frequency may therefore not be verycritical. The problem should still be kept in mind.

Summary.

The main practical implications of applying a second-orderrandom wave model, compared to the use of a linear model, areaddressed. This involves parameters like extreme crest andwave heights, and the corresponding extreme wave asymmetry,and the statistical variance of these. Some of the questionswhich are raised and discussed are: What is the statisticalsignificance of going from 1st to 2nd order? How easy is it toimplement? How relevant is the model for actual field andlaboratory conditions?



PAPER 3

Estimating extreme sea states - some methodological considerations

G. Feld (Heriot-Watt University)

EGEMT

Estimating Extreme Sea States - some MethodologicalConsiderations

by

Graham FeldDept. of Civil and Offshore Engineering.


Abstract

Whilst purists may argue that there is no sensible rationale for performing probabilityextrapolations, the need to estimate the worst conditions that are likely to occur in.say, a fifty year period makes the process a necessary one. That being said. theproblem is to develop methods which are both scientifically rational and practicallyuseful. The problem of estimating extreme loading on offshore structures is essentiallyone of multivariate probabilistic modelling and any methodology should therefore alsoreflect this aspect of extreme estimation.

The presentation outlines a method described in Coles and Tawn (1994) for modellingmultivariate extremes which is easy to generalise to as many variables as required.The model initially entails the fitting of the tail of each of the d marginal distributionsto a generalised pareto distribution (gpd) above a certain threshold. The advantage ofusing this particular distribution is that a suitable threshold can be determinedobjectively using a mean excess plot. That is to say that a plot of the mean value ofexcesses of a threshold against the value of the threshold itself will be linear if the tailis a gpd. Identification of the point at which such a plot becomes approximately linearalso therefore establishes a reasonable threshold level.

Each margin, X,. is then transformed to a unit Frechet distribution. Xi I and then a

new set of variables is created. namely:

' = 1'r for i = I to d

where, n is the number of observations. The d-dimensional vector 1v represents thedependence structure of the multivariate process and r is in some sense the"magnitude" of the overall multivariate process. The purpose of the particulartransformations used now becomes apparent. since above a suitably high thresholdand as n tends to infinity r and w become independent. In order to extrapolate to thedependence structure in the extremes. therefore, the shape of vv for increasing valuesof r is plotted and the threshold found above which the shape of w stabilises. Thisfunctional form for iv (which represents the dependence structure of the multivariateprocess) can now be imposed into the extrapolation region. From here. r and iv can be

transformed back to the original variables. Xi, along with the transformed multivariatecorrelation structure.

The main advantages over classical limit approaches is that it makes use of all dataover a particular threshold level instead of just the largest value in a year or month etc.Additionally. the formulation allows for a flexible correlation structure which can beapplied across any number of variables.

The methodology is illustrated using an example of a bivariate data set of significantwave height and mean wind speed measured every twenty minutes over a 16 monthperiod at the Alwyn North platform. It highlights some of the practical problems withthe application of the theory which include interpretation of the mean excess and wplots.

Reference:

Coles.S.G.. Tawn.J.A. "Statistical methods for multivariate extremes: an applicationto structural design ". Applied Statistics, Vol. 43, No. I. pp 1-48. 1994



PAPER 4

On some advanced physical and numerical models for studying sea wavesand their effects

M. Benoit (EDF - Laboratoire National d'Hydraulique - France)

EGEMT

Workshop "Waves and modelling the marine environment" September 11, 1996Heriot-Wait University - Edimburgh Page 1

ON SOME ADVANCED PHYSICAL AND NUMERICAL MODELSFOR STUDYING SEA WAVES AND THEIR EFFECTS

Michel BENOIT and Charles TEISSON

EDF - Laboratoire National d'Hydraulique6. quai Watier BP 49

78400 CHATOUFRANCE

Phone: +33 130877252Fax: +33 130878086e-mail : [email protected]

1. OVERVIEW OF WAVE MODELLING AT LNHThe Laboratoire National d'Hydraulique (LNH) in Chatou (France) is part of the

Research and Development Division of Electricit6 de France (EDF), the Frenchcompany in charge of electrical power supply.

EDF and LNH have no interest in the sea in terms of the production of electricityfrom wave energy, as one might at first be led to think. On the contrary, their objectiveis to study the water intake and discharge devices of power stations located on the coastwhich use sea water as their coolant. These require channels to be built for supplyingwater to the pumping stations, along with the design of sea defences against storms andthe choice of a geometry which will minimise the risk of silting up. etc. In short, theypresent the designer with a full set of coastal and inshore engineering problems whichare combined with draconian safety requirements for good measure. Beside this activityfor EDF. the LNH is also performing applied studies for public or private companies inthe maritime and coastal domains : determination and modelling of hydrodynamicalconditions (namely waves. 2D or 3D currents. storm-surges,....), breakwater and sea-defence structures design, harbour agitation problems, morphodynamical changes of theshore, water quality aspects and dispersion of pollutants....). Finally. LNH is involvedfor all these aspects in numerous research programs. in close collaboration with otherinstitutes which share the same concerns not only on a national level but also on aEuropean level (e.g. MAST programs).

Concerning surface gravity waves more specifically. LNH is currently developing aset of numerical models to study the waves and their effects (propagation towards thecoast, inshore wave climate, platform movements. etc.). However. these programs donot cover all the aspects related to the action of the waves, and for certain problems.(dimensioning of the sea walls, sediment movements. etc.) we still rely on reduced scalemodels in the laboratory as the preferred research method. For forty years. the LNH hasbeen thus developing and evolving a raft of research tools based on these two modellingapproaches. namely numerical and physical. In this paper, a very brief presentation ofsome latest developments performed in both these directions is proposed. focusing ontwo particular tools : the multidirectional wave basin (part 2) and a spectral thirdgeneration wave model (part 3). Additional information may be obtained either from thebibliography or by contacting one of the authors.

Workshop "Waves and modelling the marine environment" September 11, 1996Heriot-Watt Universit , - Edimburgh Page 2

2. SIMULATION AND ANALYSIS OF MULTIDIRECTIONAL SEAS IN THELABORATORY: THE LNH EXPERIENCE.

2.1 General presentation of the multidirectional facilityThe LNH multidirectional wave facility is a rectangular wave basin of 50 m by 30 m

used for maritime and coastal studies. The maximum water depth in the basin is 0.80 m.The segmented wavemaker is composed of 56 piston-type paddles. The width of the

paddles is 0.40 m (see Figure 1). The total wavemaker length is thus 22.4 m.Furthermore, it is movable along the main side of the basin.

The wavemaker can operate in the range from 0.2 to 2 Hz. The maximum stroke ofthe wave-paddle is 0.50 m (± 0.25 m from the middle position), which allows for thesimulation of wave heights up to 0.40 m in a water depth of 0.80 m.

This wavemaker was set up in 1992 and is monitored by advanced digital programsfor wave generation (see § 2.2) and for wave measurement and analysis (see § 2.3).

The facility is equipped with numerous mobile upright progressive wave absorbers.Each absorber unit measures 2.8 m by 2 m, allowing variable and adaptable absorberconfigurations in the basin. The facility is also equipped with a mobile cross-beam (3axis motions) monitored by a computer.

Tidal currents may also be simulated in addition to waves by using six pumps onthree sides of the basin.

Figure 1 a view of LNH segmented wave-maker under operation.

Workshop "Waves and modelling the marine environment" September 11, 1996Heriot-Watt Universirv - Edimburgh Page 1

ON SOME ADVANCED PHYSICAL AND NUMERICAL MODELSFOR STUDYING SEA WAVES AND THEIR EFFECTS

Michel BENOIT and Charles TEISSON

EDF - Laboratoire National d'Hydraulique6. quai Watier BP 49

78400 CHATOUFRAýNCE

Phone: +33130877252Fax: +33 130878086e-mail : [email protected]

1. OVERVIEW OF WAVE MODELLING AT LNHThe Laboratoire National d'Hydraulique (LNH) in Chatou (France) is part of the

Research and Development Division of Electricit6 de France (EDF), the Frenchcompany in charge of electrical power supply.

EDF and LNH have no interest in the sea in terms of the production of electricityfrom wave energy, as one might at first be led to think. On the contrary. their objectiveis to study the water intake and discharge devices of power stations located on the coastwhich use sea water as their coolant. These require channels to be built for supplyingwater to the pumping stations, along with the design of sea defences against storms andthe choice of a geometry which will minimise the risk of silting up, etc. In short, theypresent the designer with a full set of coastal and inshore engineering problems whichare combined with draconian safety requirements for good measure. Beside this activityfor EDF, the LNH is also performing applied studies for public or private companies inthe maritime and coastal domains : determination and modelling of hydrodvnamicalconditions (namely waves. 2D or 3D currents, storm-surges,....), breakwater and sea-defence structures design, harbour agitation problems, morphodynamical changes of theshore, water quality aspects and dispersion of pollutants,....). Finally, LNH is involvedfor all these aspects in numerous research programs. in close collaboration with otherinstitutes which share the same concerns not only on a national level but also on aEuropean level (e.g. MAST programs).

Concerning surface gravity waves more specifically, LNH is currently developing aset of numerical models to study the waves and their effects (propagation towards thecoast, inshore wave climate, platform movements. etc.). However. these programs donot cover all the aspects related to the action of the waves, and for certain problems.(dimensioning of the sea walls, sediment movements. etc.) we still rely on reduced scalemodels in the laboratory as the preferred research method. For forty years. the LNH hasbeen thus developing and evolving a raft of research tools based on these two modellingapproaches. namely numerical and physical. In this paper. a very brief presentation ofsome latest developments performed in both these directions is proposed. focusing ontwo particular tools : the multidirectional wave basin (part 2) and a spectral thirdgeneration wave model (part 3). Additional information may be obtained either from thebibliography or by contacting one of the authors.

Workshop "Waves and modelling the marine environment" September II. 1996Heriot-Watt University - Edimburgh Page 2

2. SIMULATION AND ANALYSIS OF MULTIDIRECTIONAL SEAS IN THE

LABORATORY: THE LNH EXPERIENCE.

2.1 General presentation of the multidirectional facilityThe LNH multidirectional wave facility is a rectangular wave basin of 50 m by 30 m

used for maritime and coastal studies. The maximum water depth in the basin is 0.80 m.The segmented wavemaker is composed of 56 piston-type paddles. The width of the

paddles is 0.40 m (see Figure I). The total wavemaker length is thus 22.4 m.Furthermore, it is movable along the main side of the basin.

The wavemaker can operate in the range from 0.2 to 2 Hz. The maximum stroke ofthe wave-paddle is 0.50 m (±- 0.25 m from the middle position), which allows for thesimulation of wave heights up to 0.40 m in a water depth of 0.80 m.

This wavemaker was set up in 1992 and is monitored by advanced digital programsfor wave generation (see § 2.2) and for wave measurement and analysis (see § 2.3).

The facility is equipped with numerous mobile upright progressive wave absorbers.Each absorber unit measures 2.8 m by 2 m. allowing variable and adaptable absorberconfigurations in the basin. The facility is also equipped with a mobile cross-beam (3axis motions) monitored by a computer.

Tidal currents may also be simulated in addition to waves by using six pumps onthree sides of the basin.

Figure I a view of LNH segmented wave-maker under operation.

Workshop "Waves and modelling the marine environment" September 11, 1996Heriot- Wart University - Edimburgh Page 3

2.2 Review of techniques for generating multidirectional sea-states

In order to generate high-quality sea-states in the multidirectional wave basin, theLNH has implemented several techniques for the computations of the drive signals forthe wave boards, together with a numerical model to compute the wave field in thebasin from a given set of drive signals. These developments are best described in Benoit(1995) and we just mention here their main features with some examples of application.

The general frame adopted at LNH for simulating directional seas is the so-calledsuperposition (or summation) technique. in which the sea-state is obtained as the sum ofa large (but finite) number of elementary monochromatic and unidirectional wavetrains.

Mf M

l(x'y't) = flmn(X.y't) = •16 ei(kmx cosOm + kmy sinOm - -o0mt + (Pmo)

m=1 m=lThe characteristics (height Hm, frequency co.n, wave-number km and direction Om) of

each component are determined according to the directional spectrum to be simulated,whereas the phases (pi are usually taken as randomly distributed over [0:2n], withuniform probability density function.

Several methods are operational at LNH for the computation of the drive signals

a) The basic method for generating obliquewaves with a segmented wavemaker is based onthe Huygens principle, also known as the "snake vprinciple". The wavemaker is assumed to haveinfinite length and is driven by an harmonicmotion of the following type (see figure 2):

X(yt) = i !f ei "(koY- o.t)- X

This regular motion produces a 0monochromatic and unidirectional wave train,

with angular frequency w. wave-number k anddirection 8 :

fl(x,v,t) = Hp ei[k.(x.cos e + v.sin 0)- wo.t]'2

with the relationship : ko = k sin 8The wave height H. is related to the stroke Figure 2 : Definition sketch for the

of the paddle motion So by the transfer function : 'Snake principle' method

H° - G(kd).tanh(kd) I sinz with G(kd) - 2.sinh(2kd)SO N, cos8 2kd + sinh(2kd)

Transfer function for Correction for " for finite .= ki.B - k.B.sin B

normal direction oblique angle paddle width B 2 2

Workshop "Waves and modelling the marine environment" September II. 1996Heriot-Watt University - Edimburgh Page 4

b) As the wavemaker has usually a limitednumber of paddles and finite length. a techniqueto increase the work-area where the wave field is Paddleshomogeneous is based on the use of reflective at restwalls set up on both sides of the basin. This is theso-called "corner reflection" method (Funke and Generation ofMiles. 1987) as described on figure 3. Some of "direct" wavesthe paddle are at rest on one side of the onlywavemaker whereas on the other side the paddleshave "double" motion. producing "direct" and Genractiond of Relce"reflected" waves. "reflected" waves

This technique allows to extend the work- waves "area at a given distance from the wavemaker.However, it is a "geometrical" approach that Figure 3 : Definition sketch for theneglects the effects of diffraction for both direct "Corner reflection" methodand reflected wave components. I _

c) In order to include the effects of diffraction when using reflective walls,Dalrymple (1989) proposed a new method, based on the decomposition on the wavepotential as a sum of a finite number of modes. Details about this sophisticatedmethod can be found in the original paper by Dalrymple (1989) or in Benoit (1995).

These three methods are running operationally at LNH. Figure 4 illustrates thewave fields computed by these method for a monochromatic and unidirectionaloblique wave train when 5 meters long reflective walls are used. These simulationshave been performed by using the PHISAX wave model (Benoit, 1995). One cannote the differences between the different methods. In particular, at 5 meters from thewavemaker. the most homogeneous wave field is obtained from the Dalrymplemethod (see Benoit (1995) for a full description of this test-case). The correspondingmotions of the segmented wavemaker are plotted on figure 5. Again. differences areevident between the methods. In particular. it is interesting to examine the slightdifferences between the Corner Reflection method and the Dalrymple method.introduced by a correct modelling of wave diffraction. Both motions are quitesimilar, but not identical : for instance there is no paddles at rest with the Dalrymplemethod.

2.3 Measuring and analysing multidirectional sea-statesThe measurement of directional wave spectrum may be performed through various

systems, including co-located gauges (directional buoys, pressure sensor combined witha 2D currentmeter....). arrays of gauges (wave probe arrays or mixed instruments arrays)or remote-sensing systems (satellite synthetic aperture radar, aerial stereo-photographytechniques....). Each of these measuring devices delivers a rather limited amount ofinformation and the estimation of directional wave spectrum is then an awkward inverseproblem. mathematically speaking. LNH has been developing such techniques ofdirectional analysis for several years now (e.g. Benoit. 1992 : Benoit. 1993 : Benoit andTeisson. 1994).

Workshop "WVaves and modelling the marine environment" September 11. 1996He riot- Wait University- Edinibutrgh Page 5

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Workshop "Waves and modelling the marine environment" September11. 1996Heriot-Wat University - Edimburgh Page 7

a) for the measurement of directional sea-states, several devices may be set up forpractical use in a multidirectional wave basin . Among them, the three following onesare currently used at LNH (Benoit and Teisson, 1994) :

- a wave probe array : the array is composed of five probes (see figure 6-a) laidout on the same configuration as the one used by Nwogu (1989). The waveprobes are resistive-type wires mounted on a frame that allows a precisepositioning. The radius R of the array is usually equal to 20 % of thewavelength corresponding to the peak frequency of the spectrum.

- a "heave-pitch-roll" gauge : this gauge aims to deliver the same type of signalsas the heave-pitch-roll buoy used in the field. To that extent, four wave probesare set up close to each other in a very simple way (see figure 6-b). From thefour recorded free-surface elevation time series, the elevation and twoorthogonal slopes of free-surface at the centre of the gauge are computed

9(t) = (T6 + 117 + T18 + fl9)/4.

a3 r _ fl8(t) - Tq6(t)axd6-8aV t ) -(t) - ii9(t) with d6- = 11.4cm and d t9 = 13.2cm

V d7-9

- a wave-velocity gauge as the previous one. this gauge is also a "single-point"gauge, recording at the same location the free-surface elevation (through awave probe) and the two horizontal components of velocity (through a 3Dacoustic velocimeter. from which only the two velocity signals U and V arekept).

x R

\ 8y 7 yI v l

6

a) wave probe array b) heave-pitch-roll gauge c) wave-velocity gauge

Figure 6 : the three directional measuring devices used at LNH.

b) for the analysis of directional sea-states, a good number of methods have beenproposed in the literature. Most of them have been implemented and are runningoperationally at LNH. both for "point" measuring systems and for wave gauges arrays.They are simply listed below (for more details. see references in the bibliography):

- Fourier Series Decomposition- Fit to unimodal parametric model- Fit to bimodal parametric model- Maximum Likelihood Method- Iterative Maximum Likelihood Method

Workshop "Waves and modelling the marine environment" September 1I, 1996Heriot- Watt Universin' - Edimburgh Page 8

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Workshop "Waves and modelling the marine environment" September 11. 1996Heriot-Watt University - Edimburgh Page 9

- Eigenvector method- Variational Fitting Technique - Long-Hasselmann Method- Maximum Entropy Method (2 versions for the definition of entropy)- Bayesian Directional Method

An example of laboratory generated bimodal test-case is given on Figure 7 from theexperiments of Benoit and Teisson (1994). It is seen on this severe case (two main wavedirections at the same frequency) that advanced methods (e.g. Maximum EntropyMethod or Bayesian Method) are capable of resolving the complex shape of thedirectional spectrum, in particular when they are used with a wave gauge array.

3. TOMAWAC: A THIRD-GENERATION SHALLOW-WATER WAVE MODEL

3.1 General presentation of the TOMAWAC model :

The TOMAWAC wave model is being developed at LNH within the finite elementssystem called TELEMAC. This TELEMAC system contains numerous hydrodynamicalcodes sharing the same formalism and the same computer environments andmathematical libraries, for instance TELEMAC-2D for tidal currents and storm-surges,TELEMAC-3D for tridimensional currents. ARTEMIS for wave agitation. SUBIEF andTSEF for modelling morphodynamical changes (suspension and bed-load transport) orthe dispersion of a pollutant .....

TOMAWAC is a so-called "sea state" model, which can be used to reproduce theformation of the waves and their development over large spatial scales. At each node ofan unstructured spatial grid, TOMAWAC models the evolution of the directional waveenergy spectrum. both in space and over time. It is a third generation model as it allowsthe directional spectrum to develop freely under the combined action of the followingphysical processes. without imposing any particular constraints on energy distribution :

* Wind input : first of all. the action of the wind causes the surface of the ocean toripple, then waves begin to form and progressively develop (interaction betweenthe sea-surface and the atmosphere).

* Non-linear wave interactions (quadruplets) : next, this rather chaotic "wind-sea"becomes more ordered as it propagates. The short waves interact in a non-linearway with each other, which changes the shape of the energy spectrum andcontributes to the increase in mean wave period.

* White-capping : At the same time. some of the waves break and dissipate part oftheir energy in their foaming crests (white-capping).

* Refraction-shoaling : near the coast, the contours of the sea bed start to play apart. The waves grow and become steeper under shoaling. At the same time. thecrests of the waves tend to align themselves to become parallel with the shore(refraction)

* Bottom friction : in intermediate and shallow water depth, some of the wave'senergy is dissipated through friction with the sea bed.

* Surf-breaking : In shallow water, steep waves may break and dissipate a goodamount of energy through turbulence in the roller.

* Wave-current interactions : In areas where tidal currents are strong or certainwatercourses run into the sea, the waves may grow if they come up against thesecurrents, which have even been known to stop them dead and cause them tobreak.

Workshop "Waves and modelling the marine environment" September 11, 1996Herior- Watt University - Edimburgh Page 10

As other spectral third-generation wave models, the TOMAWAC model can be usedfor a number of purposes :

* to predict the waves 12 to 24 hours (if not several days) in advance, from winddata measured or predicted by atmospheric models:

* to simulate and reconstruct past storms with exceptional characteristics whichcaused significant damage. In such cases, digital modelling is used as a back-upto the a posteriori analysis of the event and to fill in the missing measurements:

* to characterise the wave climate at a given site prior to carrying out developmentwork on the coast. Different project conditions are then simulated to study theeffects introducing a construction into the natural environment would have.

3.2 About the equation solved by the TOMAWAC model :All the physical processes listed in the previous section are included in the

TOMAWAC wave model, which solves the wave action balance equation in sphericalor Cartesian co-ordinates for infinite or finite water depth :

@(B.F) a(B.F) .a(B.F) D(B.F) . 8(B.F)S-. - V. ±+. + B.Qa t axo 003

The model is unsteady (variable wind forcing conditions) and can also take intoaccount a bidimensional current field U. In the present version of the model, this currentfield is assumed to be steady. The above balance equation is originally written for theaction density spectrum Ný(x,y,a,8,t) obtained as the ratio of the energy densityspectrum F(x,y,0.,O,t) by the relative angular frequency a :

N(x,y, a,O,t) = F(x,vlaO,t),/a:x and y are the spatial co-ordinates of a point. 0 is the direction of propagation of the

waves and t is the time. The absolute (w) and relative (a) wave frequencies are relatedby the Doppler relationship. in the case where there is a current superimposed to waves

co= a0+ k.U.k is the wave-number, as given by the linear dispersion relationship

G2 = g.k.tanh(k.d)

The transfer rates k and V represent the spatial propagation of wave energy. togetherwith the shoaling in finite water depth. The transfer rate 0 models the effects ofrefraction in shallow water and a. models the effects induced by a current on therelative frequency of the waves. All these transfer rates are computed from the linearwave theory.

On the right-hand side. the Q term models the effects of the aforementioned physicalprocesses : generation bv wind. white-capping, non-linear quadruplets interactions.bottom friction and depth-induced breaking. Triad interactions, related to very shallowwater depth. are also under development.

The wave action balance equation is solved by a fractional step method# The convection step is treated by a method of characteristics (piecewise ray

method). Due to the fact that the convector field is stationary, the characteristicshave to be computed only once and are then stored. This makes the propagationscheme very fast and efficient.

# The source terms integration is carried out through an implicit scheme similar tothe one used in the WVAM model (WAMDI Group. 1988 ).

Workshop "Waves and modelling the marine environment" September II. 1996Heriot- Watt UniversitY - Edimburgh Page /I

80

I LARGE MODEL

570

30

40-

4039 nodes7654 elements

3010.5 deg resolution (in rotated grid)

-60 -50 -40 -30 -20 -10 0 10 20

Longitude (deg.)FINE MODELJ

V 60

57.5

6205 nodes11444 elements

55

"•• Zoom over the Channel52.5 -.

47.5

45

-10 -5 0 5

Longitude (deg.)

Figure 8 computational grids used for the simulations with TOMAWAC

Workshop "Waves and modelling the marine en vironmnenh" September 11, 1996Heriot- Watt University -Edimbeirgh Page /2

Computed directional spectra

5.2

50.1

50

52

-9 6.-4.-2....

12.5Hmo m Coparion wth masurment lonitud (deg)

oneJanuar buoy 1de9h90 m)

-S T13:0WA I 1

51 -6-4- 0 2

10 ýI I0 0\

0 c

2.5 0 0 I wav bu

2.5 21 222.42 2Figre soe rsuls romTONIAWC o th sormof anury 5, 99

Workshop "Waves and modelling the marine environment" September 1I. 1996Heriot-Want UniversitY - Edimburgh Page 13

Spectral wave models usually use regular or irregular finite differences grids forspatial discretization. This may however become a limitation for nearshore applications.where complex bathymetry and irregular shoreline often require a refined resolution.The first solution to this problem is to use nested grids, but this implies an heavymanagement of input/output files, complicates programming and significantly increasesthe computational effort. The finite elements technique used in TOMAWAC. and in allthe models of the TELEMAC system as well, overcomes this problem quite elegantlybecause the user can determine locally the size of the mesh and then optimise thenumber of nodes according to the accuracy expected in the various parts of thecomputational domain.

TOMAWAC is fully vectorized and may be run either on supercomputers or onworkstations, depending on the size of the computational domain.

3.3 An example of application : the storm of January 25, 1990 in the Channel:Of all the storms to hit the Atlantic coasi of France during the winter of 1989-

1990. the one on January 25, 1990 was one of the most violent, with winds of force 9 toII (on the Beaufort scale) over Brittany. On this particular day, the strongest gust ofwind recorded at the Hague signal station was measured at 46 m/s (166 km/h). Thewinds blew continuously from the West. which was particularly conducive to theformation of strong waves to the West of Cotentin. and on that day. the buoys located atOuessant registered wave heights of over 16 metres I

The period chosen for computer simulation with TOMAWAC runs from January 16to 30. 1990, with values calculated every 5 minutes. The computational mesh consistsof 6 205 nodes and I1 444 triangular elements (figure 8). The broadest meshes coverapproximately 40 km. whereas the most detailed cover less than 5 km. The directionalwave energy spectrum has been broken down into 25 frequencies and 12 directions. Thesimulation was carried out without taking tidal effects into account. and required lessthan two hours of computing time on a Cray computer C98 for an actual duration of 14days.

The figure 9 shows a chart of the significant wave heights calculated at theparoxysm of the storm, along with the energy spectra at the same moment at variouspoints in the Channel. We can see that the storm's maximum intensity occurs to theWest Brittany. The further we move into the Channel, the smaller the wave heights,even though heights still manage to reach 5.5 m to the West of Cotentin (Flamanville).To validate the simulation, computational results are compared with the buoymeasurements at Ouessant on figure 9. The TOMAWAC model gave a good overaflaccount of itself as far as reproducing the height of the waves was concerned, eventhough it slightly underestimated the January 25. 1990 peak at Ouessant. The meanperiods are fairly well reproduced, despite being generally rather overestimated by thecode.

4. CONCLUSIONS - FUTURE WORKAs it can be seen from these two examples. there are a lot to gain from detailed and

refined modelling of real sea-states. By using advanced (physical and numerical)models, it is possible to represent a large range of different wave conditions (wind sea.swell, crossed seas,...) and consequently to improve our ability to study the effects ofwaves on structures. ships. beaches....

Of course, there are still (large) fields of progress both for numerical and physicalmodelling. Concerning TONWAC for instance, present efforts are dedicated to theextension of the model toward the coastal zone and the very shallow water area. in

Workshop "Waves and modelling the marine environment" September 11. 1996Heriot-Watt University - Edimburgh Page 14

particular by considering the non-linear interactions between triads of waves. Thepossibility to deal with unsteady currents and water levels will also be included in thecode, in order to study the interactions between waves and tides. On the physicalmodelling side, there are ongoing research activities to extend the directional analysismethods for the case where the wave field results from the superposition on incidentand reflected components (close to a maritime structure for instance). Theimplementation of active wave absorption for multidirectional wavemaker is also aresearch topic of interest at LNH.

What should however be kept in mind from these brief presentations is the fact thatphysical and numerical modelling remain -maybe more than ever- in very closeconnection. There is evidence that we need accurate numerical models to run amultidirectional wave basin in the best conditions. On the other hand, every numericalmodel needs to be calibrated and parameterized against experiments either from fieldcampaigns or from the laboratory. This latter approach is often preferred as it allows onone side a precise control of the test conditions and on the other side the possibility tovary quite easily these conditions.

5. BIBLIOGRAPHY

BENOIT M. (1992) : Practical comparative performance survey of methods used forestimating directional wave spectra from heave-pitch-roll data. Proc. 23rd Int.Conf on Coastal Eng. (ASCE), pp 62-75, Venice (Italy).

BENOIT NI. (1993) : Extensive comparison of directional wave analysis methods fromgauge array data. Proc. 2nd Int. Svvmp. on Ocean Wave Measurement andAnalysis (ASCE), pp 740-754, New-Orleans (USA).

BENOIT M. and TEISSOn C. (1994) : Laboratory comparison of directional wavemeasurement systems and analysis techniques. Proc. 24th Int. Conf on CoastalEng. (ASCE). Kobe (Japan).

BENOIT M. (1995) : Quelques aspects du ddveloppement d'un bassin num6rique ahoule multidirectionnelle. Proc. Smes Journees de l'Hydrodynamiqiie, 22-24mars 1995, Rouen (France) (In French).

DALRYMPLE R.A. (1989) : Directional wavemaker theory with sidewall reflection.Journal of Hydraulic Research. vol 27. N'0.

FUNKE E.R.. MILES M.D. (1987) : Multidirectional wave generation with cornersreflectors. Technical Report HY-02 1, National Research Coun cil Canada.

NWOGU O.U. (1989) : ,Maximum entropy estimation of directional wave spectra froman array of wave probes. Applied Ocean Research, vol 11. N°4, pp 176-182

WAMDI Group, (I988) : The WAM Model - A third generation ocean wave predictionmodel. J. Phys. Oceanogr., Vol 18, N'12, p 1775-1810.



PAPER 5

Storm waves and forces on structures in the northern north sea

P.H. Taylor ( Shell International E and P)

EGEMT

Abstract for "WAVES and %TODELLING the \IARINE ENVIRCNMENT". IrTemaiq.\, I "nivcr'ir',- Ediniihirch. I Ih S.cpc. "6

Storm waves and forces on structures in the northern North Sea

Newý,Vave. Lindgren's model and spreading

Paul H. Tax or

Shell International Exploration and Production B.V

The Hague. The Netherlands

Ocean waves are irregular. spread and non-linear. However. standard engineering models neglectaspects of at one of these features. This talk will review analysis of wave and force measurementstaken in the northern North Sea at the Tern platform during se,,ere storms. interpreting both in termsof the randomness of the environment.

What is the average shape of a wave in both time and space? The answer depends on the size of thewave. For small waves comparable to the random background, the full solution due to Lindgren(1970) is required. For larger rarer waves, the average shape tends to a much simpler result :NewWave - the auto-correlation function (Bocconti 1983. Tromans et al. 199 1. Phillips et al. 1993.Jonathan et al. 1994). at least if non-linearit. is neglected. Waves are in general rather short cresteddespite the difference in the local structure of waves ofidifferent size. a simple frequency-independentspreading factor is consistent with both the fluid particle velocity field at -41m and simultaneousmeasurements of surface elevation at two points along the mean crest direction. Wave crests andtroughs are different, but most of this non-linearity can be explained in terms of standard 2nd orderwave ticon (Jonathan and Taylor i995).

The NewWave methodology is then extended to estimate the wvave-induced loads on fixed offshorestructures given the occurrence of a maximum of the surface elevation time-series at some sensorlocation. Again a random Gaussian ocean environment is assumed, together with mixed inertia anddrag loading defined according to the Morison equation. The analysis is based on the statistics of aGaussian process near an extreme excursion of a different but related Gaussian process. Theinfluence of both the spreading of the wave field and the wave sensor location on expected waveloads given a measured wave crest and their variability is shown to be large. Comparisons based ontheoretical models of the w\ave field with full-scale offshore measurements at Tern shows goodagreement (Jonathan and Tay.lor 1996).

Standard fluid loading models for space-frames usually treat spreading via a simple in-line velocityreduction factor. However, this does not correctly account for the reduction in peak drag force on anon-square fixed structure due to the actual spreading of the wave field. The extent of the inaccuracyis a function of structural dimensions: in general broad-side loads are over-predicted and end-onloads slightly under-predicted. Comparison of force records for Tern with storms from two directionsmade by Heideman and Weaver (1992) is consistent with this directionality effect.

The COV on force on a structure associated with a I in 3 hour crest is shown to be very large. up to25%. This degree of variabilitx, arises solely from lack of knowledge of the wave field over thestructure. Although this could be taken as implying that the I in 3 hour extreme force is equallyvariable, this is a misinterpretation : the largest force in a given period is much closer todeterministic (Efthxvmiou et al. 1996). Of course, this force may not arise from the largest crest at thew\ax'e sensor. Again. this theoretical result is confirmed by force measurements at Tern.

The talk will also touch on two other extensions of the NewWave methodology. Full random timedomain simulation is considered to be the most accurate wax of estimating the extreme response of

WOLFRAM.DOC

d-namically sensitive structures (Rodenbusch 1986). Unfortunately. this technique is too

computationallv intensive for routine use. requiring the simulation of many hours of real time. Anextension of the NewVa\e approach. embeddinu an extreme %a,,c in a number of short random

series, leads to accurate statistical estimates of the I in 3, hour extreme response using simulations of

onlx -3 hours of real time (Taylor et al. 1905).

Real xýates are both broad-banded and non-linear For computer simulations with a 'numerical wNave

tank-, the New\Vave model is usefiul as a simple initial condition Nkuich captures some important

features of the random environment. A series of non-linear simulations could then be made to test the

adequacy of engineering approximations : such as the stretching models for x•axe kinematics

(Wheeler 1970. Rodenbusch and Forristall 1986). A few concluding remarks will be made aboutfully non-linear, spread-sea waves and their kinematics.

References

Boccorti P. (1983) 'Some new results on statistical properties of wind waves'. Appl. Ocean Res..5(3), 134.

Efthynmiou M.. van de Graaf J.W.. Tromans P.S. and Hines IM. (1996) 'Reliabiliw% based criteria

for fixed steel offshore platforms'. Proc. 15th OMAE Conf. Florence. IA.

Heideman J.C. and Weaver T.O. (1992) 'Static wave force procedure for platform design'. Proc. ofCivil Eng. in the Oceans. College Station. Texas. 5. 496.

Jonathan P. and Taylor P.H. (1995) 'Irregular. non-linear waves in a spread sea'. Proc. 14th OMAE

Conf.. Copenhagen. IA.. 9.

Jonathan P. and Taylor P.H. (1996) 'Wave-induced loads on fixed offshore platforms - anassessment of "\ave-by-\wave" load variability and bias'. Proc. 15th OMAE Conf. Florence. [A.313.

Jonathan P.. Taylor PH. and Tromans P.S. (1995) 'Storm waves in the northern North Sea'. Proc.Behaviour of Offshore Structures (BOSS) Conf, Boston. 2. 481,

Lindgren (1970) 'Some properties of a normal process near a local maximum'. Ann. Math. Statist.41. 1870,

Phillips 0A.M Cu. D. and Donelan NI. (1993) 'Expected structure of extreme waves in a Gaussian

sea. Part I : Theory and SWADE buoy measurements'. J. Phvs. Oceanog. 23. 992.

Rodenbusch G. (1986) 'Random directional wave forces on template offshore platforms'. Proc. I8th

Offshore Technology Conf. Houston. OTC5098.

Rodenbusch G. and Forristall (1986) 'An empirical model for random directional wave kinematicsnear the free surface'. Proc. 18th Offshore Technology Conf.. Houston. OTC5097

Taylor P.H.. Jonathan P. and Harland L.A. (1995) 'Time-domain simulation of jack-up dynamicswith the extremes of a Gaussian process'. Proc. 14th OMAE Conf.. Copenhagen. [A. 313.

Tromans P.S.. Anaturk A.R. and Hagemeijer P. (1991) 'A new model for the kinematics of large

ocean waves - application as a design vwave'. Proc. 1st ISOPE Conf. Edinburgh. 3. 64.

Wheeler J.D. (1970) 'Method for calculating forces produced by irregular waves'. Proc. Ist

Offshore Technology Conf., Houston. 72.

WOLFRAM DOC



PAPER 6

Modelling DB3 wave spectra

E.G. Pitt (Applied Wave Research)

EGEMT

Modelling DB3 Wave Spectra.

E G Pitt

Applied Wave Research

Synopsis

The work described was undertaken in collaboration with Paras Ltd as part of a designstudy for BP in relation to their oil production facility for the West of Shetland. Theimmediate objective was to define a number of sea-states for use in model testing ofthe production system.

The facilities available at the test installation required that each sea-state be describedin terms of the sum of at most two JONSWAP spectra. In order to meet thisrequirement a large subset of the directional spectra measured by the UKOOA DB3data buoy were fitted to one or tow JONSWAP spectra using a least squares criterion.Statistics of the fitting parameters. particularly 7 and fin, as functions of Hs werepresented. These. in conjunction with the statistics of the directional differencebetween the peaks in bi-modal sea-states allowed the selection of a number of'extreme' and 'interesting" test cases.

The fitting method will be described and the main results will be discussed.

"WAVES and MODELLING the MARINE ENVIRONMENr'Wednesday 11th September 1996


PAPER 7

The development of response-based criteria for the design of FPSO's westof Shetland

R.G. Standing (BMT Fluid Mechanics Ltd)

EGEMT

BMT Fluid Mechanics Limited

Workshop on Waves and Modelling the Marine EnvironmentHeriot-Watt University, II September 1996

"The Development of Response-Based Criteria for the Designof FPSOs West of Shetlands"

by R.G. Standing, BMT Fluid Mechanics Ltd., Teddington, Middlesex.

Synopsis

BMT are investigating the feasibility of developing response-based environmentalcriteria for the design of moorings for FPSOs operating West of Shetlands. Theobjective is to obtain a set of environmental parameters which are consistent with100-year and 1.000-year maximum vessel excursions, and which take account ofphysical relationships between the wind. waves and current. BMT undertook a pilotstudy for BP in 1995. based on a computer simulation of maximum excursions of theSchiehallion FPSO. This simulation was based on wind and wave parameters takenfrom the NESS data set and on a simulated current time-history. together with asimplified generic model of the Schiehallion vessel and mooring system.

This pilot study showed that the response-based approach has considerable potentialfor reducing the conservatism in mooring design. when compared with aconventional combination of 100-year wind. 100-year waves and 100-year current.There are many possible ways in which to select combinations of environmentalparameters. however, and the results were found to be very sensitive to the directionsof the environment, to the vessel's heading direction, and to the direction associatedwith the N-year excursion.

BMT are now enhancing the simulation model, and will then seek relationshipsbetween the maximum simulated excursions and the associated environmentalparameters.

44128 15 1



PAPER 8

Modelling the behaviour of a semi-submersible in an extremeenvironment

J. Bowers, I. Morton. G. Mould, (University of Stirling) A. Incecik, (University ofNewcastle upon Tyne) 0. Yilmaz (University of Glasgow)

WAMGET

MODELLING THE BEHAVIOUR OF A SEMI-SUBMERSIBLE IN AN

EXTREME ENVIRONMENT

John BowNcrs. Ian Morten. Gill MouldDcpartment ,•"Managcment and Organisatjin. LUnix erýit\ , t Stirllng

Atilla IncecikDepartment of Marine Technology. Universitx of Ne•k castle upon Tyne

Oguz YilmazDepartment of Naval Architecture and Ocean Engineering, University of Glasgow

Floating systems are critical to the development of the new. deeper fields west of Shetland.

The design of such systems requires an understanding of their behaviour in extreme conditions.

However, the response of floating systems is complex and dependent on both the magnitude

and direction of wind. wave and current. In such a multidimensional, directional environment

it is no longer possible to specify a simple return period wave as the basis for the system's

desisn. A more subtle approach is needed, combining a model of the floating system's

response in the range of possible environmental conditions and a statistical model to determine

the probabilities of the various combinations of conditions that might be experienced.

As an illustration of the techniques that have been developed, the behaviour of' a semi-

submersible west of Shetland is explored. The initial phase involves a time domain simulation

of the semi-submersible and the use of this model in a series of' parametric experiments to

identity its dependency on both the magnitude and directions of wind wxave and current. The

time domain simulation of the semi-submersible is carried out by taking into account steady and

dynamic wind. first and second order wave and current forces. The time domain simulation

tools have been validated with experimental measurements, The output from the time domain

analysis provides the basis for the construction of a response f'unction which captures the

essential characteristics ol the system's behaviour. The response function is then used to

transform the environmental data into a univariate time series of mooring forces. Conventional

cxtremc value techniques are then employed to extrapolate the semi-submersible's behaviour to

estimate the 50 year return period mooring lorces.

This example of an application of the structure variable approach to a directionally sensitive

system demonstrates the practicality of combining the time domain simulation and statistical

models to provide succinct guidance for design engineers. How.ever. the approach offers less

insight into the offshore environmentL An alternative methodology based on the explicit

analysis of the extreme environmental events using a point process model has also been

explored. The output from this method is contrasted wvith that of the structure variable

approach. In particular. it can provide a deeper understanding of the offshore environment and

the underlying causes of the extreme loadings.



PAPER 9

An investigation of the wave behaviour around a TLP in extreme seas

A. Amott, A. McLeary, C. Greated, (University of Edinburgh) A. Incecik (Universityof Newcastle upon Tyne)

WEAGT

An Investigation of the Wave Behaviour Around a Tension Leg

Platform in Extreme Seas

by

Arnott AD, Greated CA,Physics Dept. Edinburgh University.

Incecik ADept of Marine Tech, Newcastle University.

McLearyDept of Naval Architecture & Ocean Engineering. Glasgow University.

Abstract

This paper presents some results from an investigation into the dynamic response of aTension Leg Platform (TLP) in extreme waves. Using an approximately 1:100 scalemodel of the Heidrun TLP. a programme of testing has been carried out at the

Universities of Edinburgh and Glasgow. This involved force. velocity and wave

height measurements. results from the latter 2 sets of measurements being presentedhere. These measurements are to be used in order to refine predictive methods of 2nd

order transient and resonance forces acting on TLPs. Wave height measurementswere performed in both regular and irregular waves using wave gauges positionedaround the platform and video footage of the wave runup on the legs. Velocitymeasurements in the waves were performed in a plane parallel to the still water

surface in regular waves, using Particle Image Velocimetry, and in irregular wavesusing an Ultrasonic Velocity Probe.

In steep waves, in both regular and random seas. considerable amplification of the

water surface was evident. including the existence of water spouts and splashingbetween the 2 forward legs of the model. Between the legs of the model, harmonicsof the wave frequency were generated by reflected waves interactin2 with incidentwaves. In the more extreme wave cases, these waterspouts were found to impactagainst the underside of the deck.

In regular waves, as the wave crests reached the forward legs. the horizontal velocity

component approaching the centreline of a leg was found to diminish as the leg was

approached. In infinitely long-crested, random seas. the velocity component in the

direction of travel of the waves was found to be lower approaching a forward leg than

approaching the centreline of the model. The effect of adding a spreading component

to the wave fronts was to reduce this velocity component further in both cases.

"WAVES and MODELLING the MARINE ENVIRONMENr'Wednesday 11th September 1996


PAPER 10

Joint probabilities of extreme waves, wind and current: one way forward

J. Wolfram (Heriot-Watt University)

EGEMT

"Joint Probability of Extreme Waves, Wind and Current: One Way Forward"

Julian Wolfram BSc PhD CEng FRINA MSaRSTotal Oil Marine Professor of Offshore Research and Development

Department of Civil and Offshore EngineeringHeriot-Watt University, Edinburgh EHI4 4AS

Abstract

Current approaches to the joint probability of waves, wind and current are based onstatistics (derived from oceanographic data) that characterise, typically, a 3-hourinterval during which sea conditions are assumed to be "stationary". Data on waves,wind and current are being collected at Total Oil Marine's North Alwyn platform in thenorthern North Sea continuously at 5Hz allowing investigation ofjoint probabilitycharacteristics within a 3-hour interval. Thus permitting the joint probabilities ofindividual waveheights and periods and the associated wind and current, together withtheir directions to be investigated. The presentation describes the approach beingdeveloped by the research group at Heriot-Watt to analyse these data, the perceivedmerits and some of issues that need to be resolved.

In essence the approach involves developing short-term joint probability models todescribe what happens within nominally "stationary" 3-hour intervals of givensignificant wave height (Hs) average wave period (Tz), average wind speed andrelative direction and average current speed and direction. Such models can becombined with existing models, such as the NESS model which is based on manyyears, that allow the long-term joint probability combinations of Hs, Tz, etc to bepredicted. The combination then allows joint probability predictions for combinationsof individual extreme waves and periods and associated wind and current etc.

The form of environmental loading models required for various purposes are outlinedand one way to develop some of these are discussed. The questions that need to beaddressed in such developments are presented and discussion is invited concerningtheir solution.

Documents

AND MD•IWN6 - Wegemt...2019/04/02 · 1. Overview Measurements have been made of the velocity field and wave parameters for large waves on a moderately sheared current in a wave