RECOMMENDED PRACTICEDNV-RP-C205

ENVIRONMENTAL CONDITIONS AND ENVIRONMENTAL LOADS

APRIL 2007

Since issued in print (April 2007), this booklet has been amended, latest in October 2008. See the reference to Amendments and Corrections on the next page. DET NORSKE VERITAS

FOREWORDDET NORSKE VERITAS (DNV) is an autonomous and independent foundation with the objectives of safeguarding life, prop-erty and the environment, at sea and onshore. DNV undertakes classification, certification, and other verification and consultancyservices relating to quality of ships, offshore units and installations, and onshore industries worldwide, and carries out researchin relation to these functions.DNV Offshore Codes consist of a three level hierarchy of documents: Offshore Service Specifications. Provide principles and procedures of DNV classification, certification, verification and con-

sultancy services. Offshore Standards. Provide technical provisions and acceptance criteria for general use by the offshore industry as well as

the technical basis for DNV offshore services. Recommended Practices. Provide proven technology and sound engineering practice as well as guidance for the higher level

Offshore Service Specifications and Offshore Standards.DNV Offshore Codes are offered within the following areas:

A) Qualification, Quality and Safety MethodologyB) Materials TechnologyC) StructuresD) SystemsE) Special FacilitiesF) Pipelines and RisersG) Asset OperationH) Marine OperationsJ) Wind Turbines

Amendments and Corrections This document is valid until superseded by a new revision. Minor amendments and corrections will be published in a separatedocument normally updated twice per year (April and October). For a complete listing of the changes, see the Amendments and Corrections document located at: http://webshop.dnv.com/global/, under category Offshore Codes.The electronic web-versions of the DNV Offshore Codes will be regularly updated to include these amendments and corrections.Comments may be sent by e-mail to rules@dnv.comFor subscription orders or information about subscription terms, please use distribution@dnv.comComprehensive information about DNV services, research and publications can be found at http://www.dnv.com, or can be obtained from DNV, Veritas-veien 1, NO-1322 Hvik, Norway; Tel +47 67 57 99 00, Fax +47 67 57 99 11.

Det Norske Veritas. All rights reserved. No part of this publication may be reproduced or transmitted in any form or by any means, including pho-tocopying and recording, without the prior written consent of Det Norske Veritas.

Computer Typesetting (FM+SGML) by Det Norske Veritas.Printed in Norway

If any person suffers loss or damage which is proved to have been caused by any negligent act or omission of Det Norske Veritas, then Det Norske Veritas shall pay compensation to such personfor his proved direct loss or damage. However, the compensation shall not exceed an amount equal to ten times the fee charged for the service in question, provided that the maximum compen-sation shall never exceed USD 2 million.In this provision "Det Norske Veritas" shall mean the Foundation Det Norske Veritas as well as all its subsidiaries, directors, officers, employees, agents and any other acting on behalf of DetNorske Veritas.

Recommended Practice DNV-RP-C205, April 2007 Introduction Page 3INTRODUCTION

BackgroundThis Recommended Practice (RP) is based on the previousDNV Classification Notes 30.5 Environmental Conditions andEnvironmental Loads and has been developed within a JointIndustry Project (JIP), Phase I (2004-2005) and Phase II(2006).

AcknowledgementThe following companies have provided funding for this JIP:

Statoil, Norway Norsk Hydro, Norway BP, UK (Phase I).

In addition, the following companies and authorities haveattended project meetings as observers, providing useful com-ments to this new RP.

Aker Kvrner, Norway Moss Maritime, Norway Petroleum Safety Authority, Norway Petroleum Geo-Services, Norway.

DNV is grateful for the valuable cooperation and discussionswith these partners. Their individuals are hereby acknowl-edged for their contribution.Marintek, Norway provided valuable input to the developmentof Ch.10 Model Testing. Their contribution is highly appreci-ated.DET NORSKE VERITAS

Recommended Practice DNV-RP-C205, April 2007Page 4 IntroductionDET NORSKE VERITAS

Recommended Practice DNV-RP-C205, April 2007 Contents Page 5CONTENTS

1. GENERAL .............................................................. 91.1 Introduction .............................................................91.2 Objective...................................................................91.3 Scope and application .............................................91.3.1 Environmental conditions................................................... 91.3.2 Environmental loads ........................................................... 91.4 Relationship to other codes.....................................91.5 References ................................................................91.6 Abbreviations.........................................................101.7 Symbols...................................................................101.7.1 Latin symbols.................................................................... 101.7.2 Greek symbols .................................................................. 12

2. WIND CONDITIONS.......................................... 142.1 Introduction to wind climate ...............................142.1.1 General.............................................................................. 142.1.2 Wind parameters............................................................... 142.2 Wind data ..............................................................142.2.1 Wind speed statistics......................................................... 142.3 Wind modelling .....................................................142.3.1 Mean wind speed .............................................................. 142.3.2 Wind speed profiles .......................................................... 152.3.3 Turbulence ........................................................................ 172.3.4 Wind spectra ..................................................................... 192.3.5 Wind speed process and wind speed field ........................ 202.3.6 Wind profile and atmospheric stability............................. 222.4 Transient wind conditions ....................................232.4.1 General.............................................................................. 232.4.2 Gusts ................................................................................. 232.4.3 Squalls............................................................................... 23

3. WAVE CONDITIONS......................................... 243.1 General ...................................................................243.1.1 Introduction....................................................................... 243.1.2 General characteristics of waves ...................................... 243.2 Regular wave theories ...........................................243.2.1 Applicability of wave theories.......................................... 243.2.2 Linear wave theory ........................................................... 253.2.3 Stokes wave theory ........................................................... 263.2.4 Cnoidal wave theory ......................................................... 273.2.5 Solitary wave theory ......................................................... 273.2.6 Stream function wave theory ............................................ 273.3 Wave kinematics....................................................273.3.1 Regular wave kinematics.................................................. 273.3.2 Modelling of irregular waves............................................ 273.3.3 Kinematics in irregular waves .......................................... 283.3.4 Wave kinematics factor .................................................... 293.4 Wave transformation ............................................293.4.1 General.............................................................................. 293.4.2 Shoaling ............................................................................ 293.4.3 Refraction ......................................................................... 293.4.4 Wave reflection................................................................. 303.4.5 Standing waves in shallow basin ...................................... 303.4.6 Maximum wave height and breaking waves .................... 303.5 Short term wave conditions ..................................313.5.1 General.............................................................................. 313.5.2 Wave spectrum - general .................................................. 313.5.3 Sea state parameters ......................................................... 333.5.4 Steepness criteria .............................................................. 333.5.5 The Pierson-Moskowitz and JONSWAP spectra ............. 333.5.6 TMA spectrum.................................................................. 343.5.7 Two-peak spectra ............................................................. 343.5.8 Directional distribution of wind sea and swell ................. 353.5.9 Short term distribution of wave height ............................. 353.5.10 Short term distribution of wave crest

above still water level ....................................................... 36

stationary sea state ............................................................ 363.5.12 Joint wave height and wave period................................... 373.5.13 Freak waves ...................................................................... 373.6 Long term wave statistics ..................................... 373.6.1 Analysis strategies ............................................................ 373.6.2 Marginal distribution of significant wave height ............. 383.6.3 Joint distribution of significant wave height and period .. 383.6.4 Joint distribution of significant wave height

and wind speed ................................................................. 393.6.5 Directional effects............................................................. 393.6.6 Joint statistics of wind sea and swell ................................ 393.6.7 Long term distribution of individual wave height ............ 393.7 Extreme value distribution .................................. 403.7.1 Design sea state ................................................................ 403.7.2 Environmental contours.................................................... 403.7.3 Extreme individual wave height

and extreme crest height ................................................... 403.7.4 Wave period for extreme individual wave height ............ 413.7.5 Temporal evolution of storms........................................... 41

4. CURRENT AND TIDE CONDITIONS............. 444.1 Current conditions ................................................ 444.1.1 General.............................................................................. 444.1.2 Types of current................................................................ 444.1.3 Current velocity ................................................................ 444.1.4 Design current profiles ..................................................... 444.1.5 Stretching of current to wave surface ............................... 454.1.6 Numerical simulation of current flows............................. 454.1.7 Current measurements ...................................................... 454.2 Tide conditions ...................................................... 464.2.1 Water depth....................................................................... 464.2.2 Tidal levels ....................................................................... 464.2.3 Mean still water level ....................................................... 464.2.4 Storm surge....................................................................... 464.2.5 Maximum still water level ................................................ 46

5. WIND LOADS...................................................... 475.1 General ................................................................... 475.2 Wind pressure ....................................................... 475.2.1 Basic wind pressure .......................................................... 475.2.2 Wind pressure coefficient ................................................. 475.3 Wind forces............................................................ 475.3.1 Wind force - general ......................................................... 475.3.2 Solidification effect .......................................................... 475.3.3 Shielding effects ............................................................... 475.4 The shape coefficient............................................. 485.4.1 Circular cylinders ............................................................. 485.4.2 Rectangular cross-section ................................................. 485.4.3 Finite length effects .......................................................... 485.4.4 Spherical and parabolical structures ................................. 485.4.5 Deck houses on horizontal surface ................................... 485.4.6 Global wind loads on ships and platforms........................ 495.4.7 Effective shape coefficients.............................................. 495.5 Wind effects on helidecks ..................................... 505.6 Dynamic analysis .................................................. 505.6.1 Dynamic wind analysis..................................................... 505.7 Model tests ............................................................. 515.8 Computational Fluid Dynamics........................... 51

6. WAVE AND CURRENT INDUCED LOADS ON SLENDER MEMBERS ................................ 52

6.1 General ................................................................... 526.1.1 Sectional force on slender structure.................................. 526.1.2 Morisons load formula .................................................... 526.1.3 Definition of force coefficients......................................... 526.2 Normal force .......................................................... 526.2.1 Fixed structure in waves and current ................................ 52DET NORSKE VERITAS

3.5.11 Maximum wave height and maximum crest height in a 6.2.2 Moving structure in still water.......................................... 52

Recommended Practice DNV-RP-C205, April 2007Page 6 Contents6.2.3 Moving structure in waves and current.............................526.2.4 Relative velocity formulation ...........................................536.2.5 Applicability of relative velocity formulation ..................536.2.6 Normal drag force on inclined cylinder ............................536.3 Tangential force on inclined cylinder.................. 536.3.1 General ..............................................................................536.4 Lift force................................................................. 546.4.1 General ..............................................................................546.5 Torsion moment .................................................... 546.6 Hydrodynamic coefficients for normal flow....... 546.6.1 Governing parameters .......................................................546.6.2 Wall interaction effects .....................................................556.7 Drag coefficients for circular cylinders............... 556.7.1 Effect of Reynolds number and roughness .......................556.7.2 Effect of Keulegan Carpenter number ..............................566.7.3 Wall interaction effects ....................................................566.7.4 Marine growth...................................................................576.7.5 Drag amplification due to VIV .........................................576.7.6 Drag coefficients for non-circular cross-section...............576.8 Reduction factor due to finite length................... 576.9 Added mass coefficients........................................ 576.9.1 Effect of KC-number and roughness .................................576.9.2 Wall interaction effects .....................................................576.9.3 Effect of free surface.........................................................586.10 Shielding and amplification effects...................... 586.10.1 Wake effects......................................................................586.10.2 Shielding from multiple cylinders ....................................596.10.3 Effects of large volume structures ....................................596.11 Risers with buoyancy elements ............................ 596.11.1 General ..............................................................................596.11.2 Morison load formula for riser section with buoyancy

elements ............................................................................596.11.3 Added mass of riser section with buoyancy element........596.11.4 Drag on riser section with buoyancy elements .................606.12 Loads on jack-up leg chords ................................ 606.12.1 Split tube chords ...............................................................606.12.2 Triangular chords ..............................................................616.13 Small volume 3D objects....................................... 616.13.1 General ..............................................................................61

7. WAVE AND CURRENT INDUCED LOADS ON LARGE VOLUME STRUCTURES............ 63

7.1 General ................................................................... 637.1.1 Introduction.......................................................................637.1.2 Motion time scales ............................................................637.1.3 Natural periods..................................................................637.1.4 Coupled response of moored floaters ...............................647.1.5 Frequency domain analysis...............................................647.1.6 Time domain analysis .......................................................647.1.7 Forward speed effects .......................................................657.1.8 Numerical methods ...........................................................657.2 Hydrostatic and inertia loads............................... 657.2.1 General ..............................................................................657.3 Wave frequency loads ........................................... 667.3.1 General ..............................................................................667.3.2 Wave loads in a random sea..............................................677.3.3 Equivalent linearization ....................................................677.3.4 Frequency and panel mesh requirements ..........................677.3.5 Irregular frequencies .........................................................687.3.6 Multi-body hydrodynamic interaction ..............................687.3.7 Generalized body modes...................................................687.3.8 Shallow water and restricted areas....................................687.3.9 Moonpool effects ..............................................................697.3.10 Fluid sloshing in tanks ......................................................697.4 Mean and slowly varying loads............................ 707.4.1 Difference frequency QTFs .............................................707.4.2 Mean drift force ................................................................707.4.3 Newmans approximation.................................................717.4.4 Viscous effect on drift forces ............................................717.4.5 Damping of low frequency motions .................................71

7.5.1 General ..............................................................................737.5.2 Second order wave loads ..................................................737.5.3 Higher order wave loads ...................................................737.6 Steady current loads ............................................. 737.6.1 General ..............................................................................737.6.2 Column based structures ...................................................737.6.3 Ships and FPSOs...............................................................74

8. AIRGAP AND WAVE SLAMMING................. 768.1 General................................................................... 768.2 Airgap ................................................................... 768.2.1 Definitions.........................................................................768.2.2 Surface elevation...............................................................768.2.3 Local run-up .....................................................................768.2.4 Vertical displacement........................................................768.2.5 Numerical free surface prediction.....................................768.2.6 Simplified analysis............................................................778.2.7 Wave current interaction...................................................778.2.8 Airgap extreme estimates..................................................778.3 Wave-in-deck......................................................... 778.3.1 Horizontal wave-in-deck force .........................................778.3.2 Vertical wave-in-deck force..............................................778.3.3 Simplified approach for horizontal wave-in-deck force ...788.3.4 Momentum method for horizontal wave-in-deck force ....798.3.5 Simplified approach for vertical wave impact force.........798.3.6 Momentum method for vertical wave-in-deck force ........808.3.7 Diffraction effect from large volume structures ...............808.4 Wave-in-deck loads on floating structure........... 818.4.1 General ..............................................................................818.5 Computational Fluid Dynamics........................... 818.5.1 General ..............................................................................818.6 Wave impact loads on slender structures........... 818.6.1 Simplified method.............................................................818.6.2 Slamming on horizontal slender structure ........................818.6.3 Slamming on vertical slender structure.............................828.7 Wave impact loads on plates................................ 828.7.1 Slamming loads on a rigid body .......................................828.7.2 Space averaged slamming pressure ..................................828.7.3 Hydroelastic effects ..........................................................848.8 Breaking wave impact .......................................... 848.8.1 Shock pressures.................................................................848.9 Fatigue damage due to wave impact ................... 848.9.1 General ..............................................................................84

9. VORTEX INDUCED OSCILLATIONS ........... 869.1 Basic concepts and definitions ............................. 869.1.1 General ..............................................................................869.1.2 Reynolds number dependence ..........................................869.1.3 Vortex shedding frequency ...............................................869.1.4 Lock-in..............................................................................889.1.5 Cross flow and in-line motion...........................................889.1.6 Reduced velocity...............................................................889.1.7 Mass ratio..........................................................................889.1.8 Stability parameter ............................................................889.1.9 Structural damping............................................................899.1.10 Hydrodynamic damping....................................................899.1.11 Effective mass...................................................................899.1.12 Added mass variation........................................................899.2 Implications of VIV .............................................. 899.2.1 General ..............................................................................899.2.2 Drag amplification due to VIV .........................................909.3 Principles for prediction of VIV.......................... 909.3.1 General ..............................................................................909.3.2 Response based models.....................................................909.3.3 Force based models ..........................................................909.3.4 Flow based models............................................................919.4 Vortex induced hull motions................................ 919.4.1 General ..............................................................................919.5 Wind induced vortex shedding ............................ 929.5.1 General ..............................................................................92DET NORSKE VERITAS

7.5 High frequency loads ............................................ 73 9.5.2 In-line oscillations.............................................................92

Recommended Practice DNV-RP-C205, April 2007 Contents Page 79.5.3 Cross flow oscillations...................................................... 929.6 Current induced vortex shedding ........................929.6.1 General.............................................................................. 929.6.2 Multiple cylinders and pipe bundles................................. 939.6.3 In-line VIV response model.............................................. 939.6.4 Cross flow VIV response model....................................... 949.6.5 Multimode response.......................................................... 949.7 Wave induced vortex shedding ............................959.7.1 General.............................................................................. 959.7.2 Regular and irregular wave motion .................................. 959.7.3 Vortex shedding for KC > 40............................................ 959.7.4 Response amplitude .......................................................... 969.7.5 Vortex shedding for KC < 40 ........................................... 969.8 Methods for reducing VIO ...................................969.8.1 General.............................................................................. 969.8.2 Spoiling devices................................................................ 979.8.3 Bumpers............................................................................ 979.8.4 Guy wires.......................................................................... 97

10. HYDRODYNAMIC MODEL TESTING .......... 9910.1 Introduction ...........................................................9910.1.1 General.............................................................................. 9910.1.2 Types and general purpose of model testing ................... 9910.1.3 Extreme loads and responses ............................................ 9910.1.4 Test methods and procedures............................................ 9910.2 When is model testing recommended .................9910.2.1 General.............................................................................. 9910.2.2 Hydrodynamic load characteristics .................................. 9910.2.3 Global system concept and design verification .............. 10010.2.4 Individual structure component testing .......................... 10110.2.5 Marine operations, demonstration of functionality ........ 10110.2.6 Validation of nonlinear numerical models ..................... 10110.2.7 Extreme loads and responses .......................................... 10110.3 Modelling and calibration of the environment .10110.3.1 General ........................................................................... 10110.3.2 Wave modelling.............................................................. 10110.3.3 Current modelling........................................................... 10210.3.4 Wind modelling .............................................................. 10210.3.5 Combined wave, current and wind conditions ............... 10210.4 Restrictions and simplifications

in physical model .................................................10310.4.1 General............................................................................ 10310.4.2 Complete mooring modelling vs. simple springs ........... 10310.4.3 Equivalent riser models .................................................. 10310.4.4 Truncation of ultra deepwater floating systems

in a limited basin............................................................. 10310.4.5 Thruster modelling / DP ................................................. 10310.4.6 Topside model ................................................................ 10310.4.7 Weight restrictions.......................................................... 103

10.5 Calibration of physical model set-up................. 10310.5.1 Bottom-fixed models ...................................................... 10310.5.2 Floating models .............................................................. 10410.6 Measurements of physical parameters and

phenomena........................................................... 10410.6.1 Global wave forces and moments .................................. 10410.6.2 Motion damping and added mass ................................... 10410.6.3 Wave-induced motion response characteristics ............. 10410.6.4 Wave-induced slow-drift forces and damping................ 10410.6.5 Current drag forces ......................................................... 10410.6.6 Vortex-induced vibrations and motions (VIV; VIM)..... 10510.6.7 Relative waves; green water; air-gap.............................. 10510.6.8 Slamming loads .............................................................. 10510.6.9 Particle Imaging Velocimetry (PIV)............................... 10510.7 Nonlinear extreme loads and responses ............ 10510.7.1 Extremes of a random process........................................ 10510.7.2 Extreme estimate from a given realisation ..................... 10610.7.3 Multiple realisations ....................................................... 10610.7.4 Testing in single wave groups ........................................ 10610.8 Data acquisition, analysis and interpretation... 10610.8.1 Data acquisition .............................................................. 10610.8.2 Regular wave tests .......................................................... 10610.8.3 Irregular wave tests......................................................... 10610.8.4 Accuracy level; repeatability .......................................... 10610.8.5 Photo and video .............................................................. 10610.9 Scaling effects ...................................................... 10710.9.1 General............................................................................ 10710.9.2 Viscous problems ........................................................... 10710.9.3 Choice of scale................................................................ 10710.9.4 Scaling of slamming load measurements ....................... 10710.9.5 Other scaling effects ....................................................... 107

APP. A TORSETHAUGEN TWO-PEAK SPECTRUM.............................................. 109

APP. B NAUTIC ZONES FOR ESTIMATION OF LONG-TERM WAVE DISTRIBUTION PARAMETERS .............................................................. 111

APP. C SCATTER DIAGRAMS ................................. 112

APP. D ADDED MASS COEFFICIENTS .................. 115

APP. E DRAG COEFFICIENTS ................................ 119

APP. F PHYSICAL CONSTANTS.............................. 122DET NORSKE VERITAS

Recommended Practice DNV-RP-C205, April 2007Page 8 ContentsDET NORSKE VERITAS

Amended October 2008 Recommended Practice DNV-RP-C205, April 2007see note on front cover Page 91. General1.1 IntroductionThis new Recommended Practice (RP) gives guidance formodelling, analysis and prediction of environmental condi-tions as well guidance for calculating environmental loads act-ing on structures. The loads are limited to those due to wind,wave and current. The RP is based on state of the art withinmodelling and analysis of environmental conditions and loadsand technical developments in recent R&D projects, as well asdesign experience from recent and ongoing projects.The basic principles applied in this RP are in agreement withthe most recognized rules and reflect industry practice and lat-est research.Guidance on environmental conditions is given in Ch.2, 3 and4, while guidance on the calculation of environmental loads isgiven in Ch.5, 6, 7, 8 and 9. Hydrodynamic model testing iscovered in Ch.10.

1.2 ObjectiveThe objective of this RP is to provide rational design criteriaand guidance for assessment of loads on marine structures sub-jected to wind, wave and current loading.

1.3 Scope and application

1.3.1 Environmental conditions

1.3.1.1 Environmental conditions cover natural phenomena,which may contribute to structural damage, operation distur-bances or navigation failures. The most important phenomenafor marine structures are:

wind waves current tides.

These phenomena are covered in this RP.

1.3.1.2 Phenomena, which may be important in specific cases,but not covered by this RP include:

ice earthquake soil conditions temperature fouling visibility.

1.3.1.3 The environmental phenomena are usually describedby physical variables of statistical nature. The statisticaldescription should reveal the extreme conditions as well as the

long- and short-term variations. If a reliable simultaneous data-base exists, the environmental phenomena can be described byjoint probabilities.

1.3.1.4 The environmental design data should be representa-tive for the geographical areas where the structure will be situ-ated, or where the operation will take place. For ships and othermobile units which operate world-wide, environmental datafor particularly hostile areas, such as the North Atlantic Ocean,may be considered.

1.3.1.5 Empirical, statistical data used as a basis for evalua-tion of operation and design must cover a sufficiently longtime period. For operations of a limited duration, seasonal var-iations must be taken into account. For meteorological andoceanographical data 20 years of recordings should be availa-ble. If the data record is shorter the climatic uncertainty shouldbe included in the analysis.

1.3.2 Environmental loads

1.3.2.1 Environmental loads are loads caused by environmen-tal phenomena.

1.3.2.2 Environmental loads to be used for design shall bebased on environmental data for the specific location and oper-ation in question, and are to be determined by use of relevantmethods applicable for the location/operation taking intoaccount type of structure, size, shape and response characteris-tics.

1.4 Relationship to other codesThis RP provides the basic background for environmental con-ditions and environmental loads applied in DNVs OffshoreCodes and is considered to be a supplement to relevant national(i.e. NORSOK) and international (i.e. ISO) rules and regula-tions.Other DNV Recommended Practices give specific informationon environmental loading for specific marine structures. Suchcodes include:

DNV-RP-C102 Structural Design of Offshore Ships Recommended Practice DNV-RP-C103 Column Stabi-

lized Units DNV-RP-C206 Fatigue Methodology of Offshore Ships DNV-RP-F105 Free Spanning Pipelines DNV-RP-F204 Riser Fatigue DNV-RP-F205 Global Performance Analysis of Deep-

water Floating Structures.

1.5 ReferencesReferences are given at the end of each of Ch.2 to Ch.10. Theseare referred to in the text.DET NORSKE VERITAS

Recommended Practice DNV-RP-C205, April 2007 Amended October 2008Page 10 see note on front cover1.6 Abbreviations

1.7 Symbols

1.7.1 Latin symbols

ALS Accidental Limit StateBEM Boundary Element MethodCF Cross FlowCMA Conditional Modelling ApproachCQC Complete Quadratic CombinationDVM Discrete Vortex MethodFD Finite DifferenceFEM Finite Element MethodFLS Fatigue Limit StateFPSO Floating Production and Storage and OffloadingFV Finite VolumeGBS Gravity Based StructureHAT Highest Astronomical TideHF High FrequencyIL In-lineLAT Lowest Astronomical TideLF Low FrequencyLNG Liquified natural GasLS Least SquaresLTF Linear Transfer FunctionMHWN Mean High Water NeapsMHWS Mean High Water SpringsMLE Maximum Likelihood EstimationMLM Maximum Likelihood ModelMLWN Mean Low Water NeapsMLWS Mean Low Water SpringsMOM Method Of MomentsPM Pierson-MoskowitzPOT Peak Over ThresholdQTF Quadratic Transfer FunctionRAO Response Amplitude OperatorSRSS Square Root of Sum of SquaresSWL Still Water LevelTLP Tension Leg PlatformULS Ultimate Limit StateVIC Vortex In CellVIM Vortex Induced MotionVIV Vortex Induced VibrationsWF Wave Frequency

a0 Still water air gapa Instantaneous air gapA Dynamic amplification factorA Cross-sectional areaA(z) Moonpool cross-sectional areaA1 V/L, reference cross-sectional area for riser with

buoyancy elementsAC Charnock's constantAC Wave crest heightACF Cross flow VIV amplitudeAkj Added mass matrix elements

ar Relative accelerationAR Reference area for 2D added mass coefficientAT Wave trough depthB Bowen ratioB1 Linear damping coefficientBkj Wave damping matrix elementsBxx, Bxy Wave drift damping coefficientsc Wetted length during slammingc Wave phase velocityC Wind force shape coefficientCA Added mass coefficientCA0 Added mass coefficient for KC = 0CD Drag coefficientCd Hydrodynamic damping coefficientCDn Normal drag coefficient for inclined structural

memberCDS Drag coefficient for steady flowCDt Axial drag coefficient for inclined structural

memberCe Wind force effective shape coefficientcg Wave group velocityCh Horizontal wave-in-deck force coefficientCkj Hydrostatic restoring elementsCL Lift coefficientCM Mass coefficientCoh(r,f) Coherence spectrumCp Wind pressure coefficientCp Pressure coefficientCpa Space average slamming pressure coefficientCv Vertical wave-in-deck force coefficientd Water depthD Diameter or typical cross-sectional dimensionD() Directionality functiond(z/r) Instantaneous cross-sectional horizontal length

during slammingD(,) Directionality functionD[ ] Standard deviationDb Diameter of buoyancy elementDC Diameter of clean cylinder (without marine

growth)Di Diameter of element i in group of cylindersDp Width of cluster of cylinderE Wave energy densitye Gap ratio (= H/D)E Modulus of elasticityE(-) Quadratic free surface transfer functionE(+) Quadratic free surface transfer functionE[ ] Mean valueEI Bending stiffnessf Wave frequencyFc Current induced drag force Fd() Mean drift forcefdrag Sectional drag force on slender memberDET NORSKE VERITAS

Amended October 2008 Recommended Practice DNV-RP-C205, April 2007see note on front cover Page 11Fdx, Fdy Wave drift damping forcesFh Horizontal wave-in-deck forceFH(h) Cumulative probability function FHT(H,T) Joint probability distribution flift Sectional lift force on slender memberfN Sectional normal drag force on slender memberfn Natural frequencyFs Slamming forcefs Sectional slamming forcefT Sectional axial drag force on slender memberFv Vertical wave-in-deck forceg Acceleration of gravityg Wind response peak factorGM Metacentric heightH Wind reference heightH Clearance between structure and fixed boundaryH Wave heightH(1) First order force transfer functionH(2-) Second order difference frequency force transfer

functionH(2+) Second order sum frequency force transfer

functionh(z/r) Vertical reference height during slammingHb Breaking wave heightHm0 Significant wave heightHs Significant wave heightI Interaction factor for buoyancy elementsIkj Mass moments of inertiaJn Bessel functionk Wave numberk Roughness heightka Von Karman's constantKC Keulegan-Carpenter number = vmT/D

(KC = H/D in wave zone)Kkj Mooring stiffness elementsKn Modified Bessel function of order Ks Shoaling coefficientKS Stability parameter (Scrouton number) l Length of buoyancy elementL() Linear structural operatorlc Correlation lengthLMO Monin-Obukhov lengthLu Integral length scale in wind spectrumm Beach slopeM Mass of structurem* Mass ratiom66 Added moment of inertia for cross-sectionMa 3D added massma 2D added mass (per unit length)

Tangential added massMc Current induced moment due to dragMd() Mean drift momentM Wave drift yaw moment

Tam

me Effective massMeq Equivalent moonpool massMkj Global mass matrix elementsmn, Mn Spectral momentsmt Torsional moment on slender structural membern Number of propeller revolutions per unit timen Exponent for wave spreadingnx,ny,nz Components of normal vectorP Wave energy fluxp Pressureps Space average slamming pressureq Basic wind pressure

Sum frequency wave induced forceDifference frequency wave induced force

R Richardson numberR Reflection coefficientr Ratio between modal frequenciesr Displacement of structural memberr44 Roll radius of gyrationr55 Pitch radius of gyrationRe Reynolds number = uD/S Projected area of structural member normal to the

direction of forceS Wave steepnesss Exponent for wave spreadingS Distance between buoyancy elementsS Waterplane areaS(f), S() Wave spectrumS1 Average wave steepnessSi, i = 1,2 First moments of water plane areaSij Second moments of water plane areaSm02 Estimate of significant wave steepnessSmax Maximum wave steepnessSp Average wave steepnessSR() Response spectrumSs Significant wave steepnessSt Strouhal numberSU(f) Wind speed spectrumT Wave period T Transmission coefficientt Thickness of marine growthT0 Propeller thrust at zero speedT0 One-hour wind reference periodT1 Mean wave periodT10 10-minute wind reference periodTc Mean crest periodTm01 Spectral estimate of mean wave periodTm02 Spectral estimate of zero-up-crossing periodTm24 Spectral estimate of mean crest periodTn Natural periodTp Peak periodTR Return period

)(2WAq

+

)(2WAq

DET NORSKE VERITAS

dz Tz Zero-up-crossing period

Recommended Practice DNV-RP-C205, April 2007 Amended October 2008Page 12 see note on front cover1.7.2 Greek symbols

U Forward speed of structure/vesselu(1) First order horizontal velocityu(2-) Second-order difference-frequency horizontal

velocityu(2+) Second-order sum-frequency horizontal velocityu* Friction velocityu,v,w Wave velocity components in x,y,z-directionU0 One hour mean wind speedU10 10-minute mean wind speedUG, AG Parameters of Gumbel distributionUR, Ur Ursell numbers for regular waveUrs Ursell number for irregular waveUT,z Wind velocity averaged over a time interval T at

a height z meterV Volume displacementvc Current velocityVc Volume of air cushionvc() Far field currentvc,circ Circulational current velocityvc,tide Tidal current velocityvc,wind Wind induced current velocityvd Wake deficit velocityvm Maximum wave orbital particle velocityvn Normal component of velocityvr Relative velocityVR Reduced velocity = vT/D or v/(fD)VR Reference area for 3D added mass coefficientvs Significant velocityvt Normal component of velocityW Projected diameter of split tube chordz(x,y,t) Vertical displacement of the structure zB Vertical position of centre of buoyancyzG Vertical position of centre of gravityzs Stretched z-coordinate

Velocity of structural memberAcceleration of structural member

Spacing ratio Angle between the direction of the wind and the

axis of the exposed member or surface Asymmetry factor Angle between wave ray and normal to the sea bed

depth contour Exponent in power law current profile Wave attenuation coefficient Spectral band widthc Current flow velocity ratio = vc/(vc+vm) H, c Scale parameters in Weibull distribution Breaking wave parameter Wave direction of propagation Deadrise angle during slamming Aerodynamic solidity ratio

r&r&&

Viscous frequency parameter = Re/KC = D2/T H, c Shape parameters in Weibull distribution Logarithmic decrement (= 2) Spectral band width Nondimensional roughness = k/DSS Spatial extent of slamming pressure Local wave slope Shallow water non-linearity parameter Spectral band widthk Random phase Velocity potential Solidity ratio () Depth function in TMA spectrum Peak shape parameter (Jonswap) Length scale of wind speed process Location parameter in 3-parameter Weibull distri-

bution Gas constant for air = 1.4( ) Gamma function Free surface elevation Shielding factorh Height of moonpool1 Linear (first order) free surface elevation2 Second order free surface elevationm Local crest heightR,D Radiation and diffraction free surface elevation Surface friction coefficient Finite length reduction factor Moonpool geometry factor Wave length Shallow water parameter Spectral band width Kinematic viscosity coefficienta Kinematic viscosity coefficient for airij Irregular wave numbers Mass density of water Autocorrelation for wind speed fielda Mass density of airnm Cross-modal coefficients(f) Standard deviation of dynamic structural responsea, b Spectral width parameters (Jonswap)b Stress due to net buoyancy forceslam Stress in element due to slam loadU Standard deviation of wind speedw Stress due to vertical wave forces Wave angular frequencye Wave angular frequency of encounterp Angular spectral peak frequencyi() Response transfer functionj Rigid body motion in degree of freedom j Damping ratio Aspect ratio = b/l Phase functionDET NORSKE VERITAS

Amended October 2008 Recommended Practice DNV-RP-C205, April 2007see note on front cover Page 13p Main wave direction Stability function for wind profiles Wave amplification factor( ) Standard Gaussian cumulative distribution

functionAngular acceleration of cross-section.&DET NORSKE VERITAS

Recommended Practice DNV-RP-C205, April 2007 Amended October 2008Page 14 see note on front cover2. Wind Conditions2.1 Introduction to wind climate

2.1.1 GeneralWind speed varies with time. It also varies with the heightabove the ground or the height above the sea surface. For thesereasons, the averaging time for wind speeds and the referenceheight must always be specified.A commonly used reference height is H = 10 m. Commonlyused averaging times are 1 minute, 10 minutes and 1 hour.Wind speed averaged over 1 minute is often referred to as sus-tained wind speed.

2.1.2 Wind parameters

2.1.2.1 The wind climate can be represented by the 10-minutemean wind speed U10 at height 10 m and the standard deviationU of the wind speed at height 10 m. In the short term, i.e. overa 10-minute period, stationary wind conditions with constantU10 and constant U can often be assumed to prevail. Thiswind climate representation is not intended to cover wind con-ditions experienced in tropical storms such as hurricanes,cyclones and typhoons. It is neither intended to cover windconditions experienced during small-scale events such as fastpropagating arctic low pressures of limited extension. Theassumption of stationary conditions over 10-minute periods isnot always valid. For example, front passages and unstableconditions can lead to extreme wind conditions like windgusts, which are transient in speed and direction, and for whichthe assumption of stationarity does not hold. Examples of suchnonstationary extreme wind conditions, which may be criticalfor design, are given in DNV-OS-J101 and IEC61400-1.

2.1.2.2 The 10-minute mean wind speed U10 is a measure ofthe intensity of the wind. The standard deviation U is a meas-ure of the variability of the wind speed about the mean. Whenspecial conditions are present, such as when hurricanes,cyclones and typhoons occur, a representation of the wind cli-mate in terms of U10 and U may be insufficient. The instanta-neous wind speed at an arbitrary point in time during 10-minute stationary conditions follows a probability distributionwith mean value U10 and standard deviation U.

2.1.2.3 The turbulence intensity is defined as the ratio U/U10.

2.1.2.4 The short term 10-minute stationary wind climate maybe represented by a wind spectrum, i.e. the power spectral den-sity of the wind speed process, SU(f). SU(f) is a function of U10and U and expresses how the energy of the wind speed in aspecific point in space is distributed between various frequen-cies.

2.2 Wind data

2.2.1 Wind speed statistics

2.2.1.1 Wind speed statistics are to be used as a basis for rep-resentation of the long-term and short-term wind conditions.Long-term wind conditions typically refer to 10 years or more,short-term conditions to 10 minutes. The 10-minute meanwind speed at 10 m height above the ground or the still waterlevel is to be used as the basic wind parameter to describe thelong-term wind climate and the short-term wind speed fluctu-ations. Empirical statistical data used as a basis for design mustcover a sufficiently long period of time.

2.2.1.2 Site-specific measured wind data over sufficientlylong periods with minimum or no gaps are to be sought. Fordesign, the wind climate data base should preferably cover a10-year period or more of continuous data with a sufficient

2.2.1.3 Wind speed data are height-dependent. The meanwind speed at 10 m height is often used as a reference. Whenwind speed data for other heights than the reference height arenot available, the wind speeds for the other heights can be cal-culated from the wind speeds in the reference height in con-junction with a wind speed profile above the ground or abovethe still water level.

2.2.1.4 The long-term distributions of U10 and U shouldpreferably be based on statistical data for the same averagingperiod for the wind speed as the averaging period which is usedfor the determination of loads. If a different averaging periodthan 10 minutes is used for the determination of loads, the winddata may be converted by application of appropriate gust fac-tors. The short-term distribution of the instantaneous windspeed itself is conditional on U10 and U.

2.2.1.5 An appropriate gust factor to convert wind statisticsfrom other averaging periods than 10 minutes depends on thefrequency location of a spectral gap, when such a gap ispresent. Application of a fixed gust factor, which is independ-ent of the frequency location of a spectral gap, can lead to erro-neous results. A spectral gap separates large-scale motionsfrom turbulent scale motions and refers to those spatial andtemporal scales that show little variation in wind speed.

2.2.1.6 The latest insights for wind profiles above watershould be considered for conversion of wind speed databetween different reference heights or different averaging peri-ods. Unless data indicate otherwise, the conversions may becarried out by means of the expressions given in 2.3.2.11.

2.2.1.7 The wind velocity climate at the location of the struc-ture shall be established on the basis of previous measurementsat the actual location and adjacent locations, hindcast winddata as well as theoretical models and other meteorologicalinformation. If the wind velocity is of significant importance tothe design and existing wind data are scarce and uncertain,wind velocity measurements should be carried out at the loca-tion in question. Characteristic values of the wind velocityshould be determined with due account of the inherent uncer-tainties.

2.2.1.8 When the wind velocity climate is based on hindcastwind data, it is recommended to use data based on reliable rec-ognised hindcast models with specified accuracy. WMO(1983) specifies minimum requirements to hindcast modelsand their accuracy. Hindcast models and theoretical modelscan be validated by benchmarking to measurement data.

2.3 Wind modelling

2.3.1 Mean wind speed

2.3.1.1 The long-term probability distributions for the wind cli-mate parameters U10 and U that are derived from available datacan be represented in terms of generic distributions or in termsof scatter diagrams. An example of a generic distribution repre-sentation consists of a Weibull distribution for the arbitrary 10-minute mean wind speed U10 in conjunction with a lognormaldistribution of U conditional on U10 (see 2.3.3.1). A scatter dia-gram provides the frequency of occurrence of given pairs (U10,U) in a given discretisation of the (U10, U) space.

2.3.1.2 Unless data indicate otherwise, a Weibull distributioncan be assumed for the arbitrary 10-minute mean wind speedU10 in a given height z above the ground or above the sea waterlevel,

in which the scale parameter A and the shape parameter k are

))(exp(1)(10

kU A

uuF =DET NORSKE VERITAS

time resolution. site- and height-dependent.

Amended October 2008 Recommended Practice DNV-RP-C205, April 2007see note on front cover Page 152.3.1.3 In areas where hurricanes occur, the Weibull distribu-tion as determined from available 10-minute wind speedrecords may not provide an adequate representation of theupper tail of the true distribution of U10. In such areas, theupper tail of the distribution of U10 needs to be determined onthe basis of hurricane data.

2.3.1.4 Data for U10 are usually obtained by measuring thewind speed over 10 minutes and calculating the mean windspeed based on the measurements from these 10 minutes. Var-ious sampling schemes are being used. According to someschemes, U10 is observed from every 10-minute period in aconsecutive series of 10-minute periods, such that there are sixU10 observations every hour. According to other schemes, U10is observed from only one 10-minute period every hour orevery third hour, such that there are only 24 or 8 U10 observa-tions per day.

2.3.1.5 Regardless of whether U10 is sampled every 10 min-utes, every hour or every third hour, the achieved samples usu-ally obtained over a time span of several years form a data setof U10 values which are representative as a basis for estimationof the cumulative distribution function FU10(u) for U10.

2.3.1.6 In areas where hurricanes do not occur, the distribu-tion of the annual maximum 10-minute mean wind speedU10,max can be approximated by

where N = 52 560 is the number of consecutive 10-minuteaveraging periods in one year. Note that N = 52 595 when leapyears are taken into account. The approximation is based on anassumption of independent 10-minute events. The approxima-tion is a good approximation in the upper tail of the distribu-tion, which is typically used for prediction of rare mean windspeeds such as those with return periods of 50 and 100 years.

2.3.1.7 Note that the value of N = 52 560 is determined on thebasis of the chosen averaging period of 10 minutes and is notinfluenced by the sampling procedure used to establish the datafor U10 and the distribution FU10(u); i.e. it does not depend onwhether U10 has been sampled every 10 minutes, every hour orevery third hour. Extreme value estimates such as the 99%quantile in the resulting distribution of the annual maximum10-minute mean wind speed shall thus always come out asindependent of the sampling frequency.

2.3.1.8 In areas where hurricanes occur, the distribution of theannual maximum 10-minute mean wind speed U10,max shall bebased on available hurricane data. This refers to hurricanes forwhich the 10-minute mean wind speed forms a sufficient rep-resentation of the wind climate.

2.3.1.9 The quoted power-law approximation to the distribu-tion of the annual maximum 10-minute mean wind speed is agood approximation to the upper tail of this distribution. Usu-ally only quantiles in the upper tail of the distribution are ofinterest, viz. the 98% quantile which defines the 50-year meanwind speed or the 99% quantile which defines the 100-yearmean wind speed. The upper tail of the distribution can be wellapproximated by a Gumbel distribution, whose expressionmay be more practical to use than the quoted power-lawexpression.

2.3.1.10 The annual maximum of the 10-minute mean windspeed U10,max can often be assumed to follow a Gumbel distri-bution,

in which a and b are site- and height-dependent distributionparameters.

2.3.1.11 Experience shows that in many cases the Gumbel dis-

of the square of the annual maximum of the 10-minute meanwind speed than of the distribution of the annual maximum ofthe mean wind speed itself. Wind loads are formed by windpressures, which are proportional to the square of the windspeed, so for estimation of characteristic loads defined as the98% or 99% quantile in the distribution of the annual maxi-mum wind load it is recommended to work with the distribu-tion of the square of the annual maximum of the 10-minutemean wind speed and extrapolate to 50- or 100-year values ofthis distribution.

2.3.1.12 The 10-minute mean wind speed with return periodTR in units of years is defined as the (11/TR) quantile in thedistribution of the annual maximum 10-minute mean windspeed, i.e. it is the 10-minute mean wind speed whose proba-bility of exceedance in one year is 1/TR. It is denoted andis expressed as

in which FU10,max,1 year denotes the cumulative distributionfunction of the annual maximum of the 10-minute mean windspeed.

2.3.1.13 The 10-minute mean wind speed with return periodone year is defined as the mode of the distribution of the annualmaximum 10-minute mean wind speed.

2.3.1.14 The 50-year 10-minute mean wind speed becomes

and the 100-year 10-minute mean wind speed becomes

Note that these values, calculated as specified, are to be con-sidered as central estimates of the respective 10-minute windspeeds when the underlying distribution function FU10,max isdetermined from limited data and is encumbered with statisti-cal uncertainty.

2.3.2 Wind speed profiles

2.3.2.1 The wind speed profile represents the variation of themean wind speed with height above the ground or above thestill water level, whichever is applicable. When terrain condi-tions and atmospheric stability conditions are not complex, thewind speed profile may be represented by an idealised modelprofile. The most commonly applied wind profile models arethe logarithmic profile model, the power law model and theFrya model, which are presented in 2.3.2.4 through 2.3.2.12.

2.3.2.2 Complex wind profiles, which are caused by inversionand which may not be well represented by any of the mostcommonly applied wind profile models, may prevail over landin the vicinity of ocean waters.

2.3.2.3 The friction velocity u* is defined as

where is the surface shear stress and a is the air density.The friction velocity u* can be calculated from the 10-minutemean wind speed U10 at the height H = 10 m as

where is a surface friction coefficient. The surface frictioncoefficient is defined in 2.3.2.6. Some sources refer to as asurface drag coefficient; however, it is important not to con-fuse with the drag coefficient used for calculations of wind

NUU uFuF ))(()( 10max,10 year 1, =

[ ]{ })(expexp)(year 1,max,10 buauFU =

RTU ,10

)11(1year 1,,10 max,10R

UT TFU

R=

; TR > 1 year

)98.0(1year 1,50,10 max,10= UFU

)99.0(1year 1,100,10 max,10= UFU

au =*

10* Uu = DET NORSKE VERITAS

tribution will provide a better representation of the distribution forces on structures.

Recommended Practice DNV-RP-C205, April 2007 Amended October 2008Page 16 see note on front cover2.3.2.4 A logarithmic wind speed profile may be assumed forneutral atmospheric conditions and can be expressed as

where ka = 0.4 is von Karmans constant, z is the height and z0is a terrain roughness parameter, which is also known as theroughness length. For locations on land, z0 depends on thetopography and the nature of the ground. For offshore loca-tions z0 depends on the wind speed, the upstream distance toland, the water depth and the wave field. Table 2-1 gives typi-cal values for z0 for various types of terrain.

Table 2-1 is based on Panofsky and Dutton (1984), Simiu andScanlan (1978), JCSS (2001) and Dyrbye and Hansen (1997).

2.3.2.5 For offshore locations, the roughness parameter z0typically varies between 0.0001 m in open sea without wavesand 0.01 m in coastal areas with onshore wind. The roughnessparameter for offshore locations may be solved implicitly fromthe following equation

where g is the acceleration of gravity and AC is Charnocks con-stant. AC is usually higher for young developing and rapidlygrowing waves than for old fully developed waves. For opensea with fully developed waves, AC = 0.011-0.014 is recom-mended. For near-coastal locations, AC is usually higher with val-ues of 0.018 or more. Expressions for AC, which include thedependency on the wave velocity and the available water fetch,are available in the literature, see Astrup et al. (1999).

2.3.2.6 An alternative formulation of the logarithmic profile,expressed in terms of the 10-minute mean wind speed U(H) inthe reference height H = 10 m, reads

in which

This implies that the logarithmic profile may be rewritten as

2.3.2.7 The logarithmic wind speed profile implies that thescale parameter A(z) at height z can be expressed in terms ofthe scale parameter A(H) at height H as follows

The scale parameter is defined in 2.3.2.1.

2.3.2.8 As an alternative to the logarithmic wind profile, apower law profile may be assumed,

where the exponent depends on the terrain roughness.

2.3.2.9 Note that if the logarithmic and power law wind pro-files are combined, then a height-dependent expression for theexponent results

2.3.2.10 Note also that the limiting value = 1/ln(z/z0) as zapproaches the reference height H has an interpretation as aturbulence intensity, cf. the definition given in 2.3.2.3. As analternative to the quoted expression for , values for tabu-lated in Table 2-1 may be used.

2.3.2.11 The following expression can be used for calculationof the mean wind speed U with averaging period T at height zabove sea level as

where H = 10 m and T10 = 10 minutes, and where U10 is the10-minute mean wind speed at height H. This expression con-verts mean wind speeds between different averaging periods.When T < T10, the expression provides the most likely largestmean wind speed over the specified averaging period T, giventhe original 10-minute averaging period with stationary condi-tions and given the specified 10-minute mean wind speed U10.The conversion does not preserve the return period associatedwith U10.

2.3.2.12 For offshore locations, the Frya wind profile model isrecommended unless data indicate otherwise. For extreme meanwind speeds corresponding to specified return periods in excessof approximately 50 years, the Frya model implies that the fol-lowing expression can be used for conversion of the one-hourmean wind speed U0 at height H above sea level to the mean windspeed U with averaging period T at height z above sea level

Table 2-1 Terrain roughness parameter z0 and power-law exponent Terrain type Roughness

parameter z0 (m)Power-law exponent

Plane ice 0.00001-0.0001Open sea without waves 0.0001Open sea with waves 0.0001-0.01 0.12Coastal areas with onshore wind

0.001-0.01

Snow surface 0.001-0.006Open country withoutsignificant buildings and vegetation

0.01

Mown grass 0.01Fallow field 0.02-0.03Long grass, rocky ground 0.05Cultivated land with scattered buildings

0.05 0.16

Pasture land 0.2Forests and suburbs 0.3 0.30City centres 1-10 0.40

0

ln*)(zz

kuzU

a

=

2

00 )/ln(

)(

=

zzzUk

gAz aC

)ln11()()(Hz

kHUzU

a

+=

2

0

2

)(lnzH

k a=

( ) ( )0

ln1

ln

zHU z U HHz

= +

0

0

ln

ln)()(

zHzz

HAzA =

=

HzHUzU )()(

=

HzzHzz

ln

ln

lnln

0

0

)ln047.0ln137.01(),(10

10 TT

HzUzTU +=

+= 0 ln)(41.01ln1),( TzIzCUzTU UDET NORSKE VERITAS

is the surface friction coefficient. 0TH

Amended October 2008 Recommended Practice DNV-RP-C205, April 2007see note on front cover Page 17where H = 10 m, T0 = 1 hour and T < T0, where

and

and where U will have the same return period as U0.

2.3.2.13 Note that the Frya wind speed profile includes agust factor which allows for conversion of mean wind speedsbetween different averaging periods. The Frya wind speedprofile is a special case of the logarithmic wind speed profilein 2.3.2.4. The Frya wind speed profile is the best docu-mented wind speed profile for offshore locations and maritimeconditions.

2.3.2.14 Over open sea, the coefficient C may tend to be about10% smaller than the value that results from the quoted expres-sion. In coastal zones, somewhat higher values for the coeffi-cient C should be used, viz. 15% higher for U0 = 10 m/s and30% higher for U0 = 40 m/s.

2.3.2.15 Both conversion expressions are based on winterstorm data from a Norwegian Sea location and may not neces-sarily lend themselves for use at other offshore locations. Theexpressions should not be extrapolated for use beyond theheight range for which they are calibrated, i.e. they should notbe used for heights above approximately 100 m. Possible influ-ences from geostrophic winds down to about 100 m heightemphasises the importance of observing this restriction.

2.3.2.16 Both conversion expressions are based on the appli-cation of a logarithmic wind profile. For locations where anexponential wind profile is used or prescribed, the expressionsshould be considered used only for conversions between dif-ferent averaging periods at a height equal to the referenceheight H = 10 m.

2.3.2.17 In the absence of information on tropical storm windsin the region of interest, the conversion expressions may alsobe applied to winds originating from tropical storms. Thisimplies in particular that the expressions can be applied towinds in hurricanes.

2.3.2.18 The conversion expressions are not valid for repre-sentation of squall winds, in particular because the duration ofsqualls is often less than one hour. The representation of squallwind statistics is a topic for ongoing research.

2.3.2.19 Once a wind profile model is selected, it is importantto use this model consistently throughout, i.e. the wind profilemodel used to transform wind speed measurements at someheight z to wind speeds at a reference height H has to beapplied for any subsequent calculation of wind speeds, both atthe height z and at other heights, on the basis of wind speeds atthe reference height H.

2.3.2.20 The wind profile models presented in 2.3.2.4 and2.3.2.8 and used for conversion to wind speeds in heights with-out wind observations are idealised characteristic model pro-files, which are assumed to be representative mean profiles inthe short term. There is model uncertainty associated with theprofiles and there is natural variability around them: The truemean profile may take a different form for some wind events,such as in the case of extreme wind or in the case of non-neu-tral wind conditions. This implies that conversion of wind datato heights without wind measurements will be encumbered

racy which can be expected when conversions of wind speedsto heights without wind data is carried out by means of windprofile models. It is recommended to account for uncertainty insuch wind speed conversions by adding a wind speed incre-ment to the wind speeds that result from the conversions.

2.3.2.21 The expressions in 2.3.2.11 and 2.3.2.12 contain gustfactors for conversion of wind speeds between different aver-aging periods. As for conversion of wind speeds between dif-ferent heights also conversion between different averagingperiods is encumbered with uncertainty, e.g. owing to the sim-plifications in the models used for the conversions. HSE(2002) gives an indication of the accuracy which can beexpected when conversions of wind speeds between differentaveraging periods is carried out by means of gust factors. It isrecommended to account for uncertainty in such wind speedconversions by adding a wind speed increment to the windspeeds that result from the conversions.

2.3.3 Turbulence

2.3.3.1 The natural variability of the wind speed about the meanwind speed U10 in a 10-minute period is known as turbulenceand is characterised by the standard deviation U. For givenvalue of U10, the standard deviation U of the wind speed exhib-its a natural variability from one 10-minute period to another.Measurements from several locations show that U conditionedon U10 can often be well represented by a lognormal distribution.

in which ( ) denotes the standard Gaussian cumulative distri-bution function

The coefficients b0 and b1 are site-dependent coefficientsdependent on U10.

2.3.3.2 The coefficient b0 can be interpreted as the mean valueof lnU, and b1 as the standard deviation of lnU. The follow-ing relationships can be used to calculate the mean value E[U]and the standard deviation D[U] of U from the values of b0and b1,

Reference is made to Guidelines for Design of Wind Turbines(2001).

2.3.3.3 E[U] and D[U] will, in addition to their dependencyon U10, also depend on local conditions, first of all the terrainroughness z0, which is also known as the roughness length.When different terrain roughnesses prevail in different direc-tions, i.e. the terrain is not homogeneous, E[U] and D[U]may vary with the direction. This will be the case for examplein the vicinity of a large building. Buildings and other disturb-ing elements will in general lead to more turbulence, i.e.,larger values of E[U] and D[U], than will be found insmoother terrain. Figure 2-1 and Figure 2-2 give examples ofthe variation of E[U] and D[U] with U10 for an onshore andan offshore location, respectively. The difference between thetwo figures mainly consists in a different shape of the meancurve. This reflects the effect of the increasing roughness

02 148.011073.5 UC +=

22.00 )()043.01(06.0

+=HzUIU

)ln

()(1

0| 10 b

bF UU

=

=x

dex

2/2

21)(

[ ] )21exp( 210 bbE U +=

[ ] [ ] 1)exp( 21 = bED UU DET NORSKE VERITAS

with uncertainty. HSE (2002) gives an indication of the accu- length for increasing U10 on the offshore location.

Recommended Practice DNV-RP-C205, April 2007 Amended October 2008Page 18 see note on front coverFigure 2-1Example of mean value and standard deviation of U as function of U10 onshore location.

Figure 2-2Example of mean value and standard deviation of U as function of U10 offshore location

2.3.3.4 In some cases, a lognormal distribution for U condi-tioned on U10 will underestimate the higher values of U. AFrechet distribution may form an attractive distribution modelfor U in such cases, hence

The distribution parameter k can be solved implicitly from

and the distribution parameter 0 then results as

where denotes the gamma function

2.3.3.5 Caution should be exercised when fitting a distributionmodel to data. Normally, the lognormal distribution provides agood fit to data, but use of a normal distribution, a Weibull dis-tribution or a Frechet distribution is also seen. The choice ofthe distribution model may depend on the application, i.e.,whether a good fit to data is required to the entire distributionor only in the body or the upper tail of the distribution. It isimportant to identify and remove data, which belong to 10-minute series for which the stationarity assumption for U10 isnot fulfilled. If this is not done, such data may confuse thedetermination of an appropriate distribution model for U con-ditioned on U10.

2.3.3.6 The following expression for the mean value of thestandard deviation U, conditioned on U10, can be applied

for homogeneous terrain, in which

Measurements from a number of locations with uniform andflat terrain indicate an average value of Ax equal to 2.4. In roll-ing terrain, Ax tends to be somewhat larger. Unless data indi-cate otherwise, the following approximation to Ax may be usedfor purely mechanical turbulence (neutral conditions) over uni-form and flat terrain

in which z0 is to be given in units of m. Reference is made toPanofsky and Dutton (1984), Dyrbye and Hansen (1997), andLungu and van Gelder (1997).

2.3.3.7 The 10-minute mean wind speed U10 and the standarddeviation U of the wind speed refer to the longitudinal windspeed, i.e. the wind speed in the constant direction of the meanwind during a considered 10-minute period of stationary con-ditions. During this period, in addition to the turbulence in thedirection of the mean wind, there will be turbulence also later-ally and vertically. The mean lateral wind speed will be zero,while the lateral standard deviation of the wind speed Uy canbe taken as a value between 0.75U and 0.80U. The meanvertical wind speed will be zero, while the vertical standarddeviation of the wind speed Uz can be taken as Uz = 0.5U.These values all refer to homogeneous terrain. For complexterrain, the wind speed field will be much more isotropic, andvalues for Uy and Uz very near the value of U can beexpected.

2.3.3.8 When the wind climate at a location cannot be docu-mented by site-specific measurements, the distribution of U10can still, usually, be represented well, for example on the basisof wind speed measurements from adjacent locations. How-ever, the distribution of U will usually be harder to obtain,because it will be very dependent on the particular local rough-ness conditions, and it can thus not necessarily be inferredfrom known wind speed conditions at adjacent locations. At alocation where wind speed measurements are not available, thedetermination of the distribution of the standard deviation Uof the wind speed is therefore often encumbered with ambigu-ity. It is common practice to account for this ambiguity by

0

0,5

1

1,5

2

2,5

3

0 5 10 15 20

U10 (m/sec)

D[

U]

E

[ U]

(m

/sec

) mean valuest. dev.

0

0,5

1

1,5

2

2,5

0 5 10 15 20 25

U 10 (m/sec)

D[

U]

E

[ U]

(m

/sec

) mean valuest. dev.

))(exp()( 0| 10k

UUF

=

[ ][ ] 1)11(

)21()(

2

2

=

k

kED

U

U

[ ])11(

0

k

E U

=

= 1)( dtetx tx

ka = 0.4 is von Karmans constantz = the height above terrainz0 = the roughness parameterAx = constant which depends on z0

[ ] *ln

1

0

10 uA

zz

kAUE xaxU ==

0ln856.05.4 zAx =DET NORSKE VERITAS

using conservatively high values for U for design purposes. 0

Amended October 2008 Recommended Practice DNV-RP-C205, April 2007see note on front cover Page 192.3.4 Wind spectra

2.3.4.1 Short-term stationary wind conditions may bedescribed by a wind spectrum, i.e. the power spectral densityof the wind speed. Site-specific spectral densities of the windspeed process can be determined from available measuredwind data.

2.3.4.2 When site-specific spectral densities based on meas-ured data are used, the following requirement to the energycontent in the high frequency range should be fulfilled, unlessdata indicate otherwise: The spectral density SU(f) shallasymptotically approach the following form as the frequency fin the high frequency range increases

in which Lu is the integral length scale of the wind speed process.

2.3.4.3 Unless data indicate otherwise, the spectral density ofthe wind speed process may be represented by a model spec-trum. Several model spectra exist. They generally agree in thehigh frequency range, whereas large differences exist in thelow frequency range. Most available model spectra are cali-brated to wind data obtained over land. Only a few are cali-brated to wind data obtained over water. Model spectra areoften expressed in terms of the integral length scale of the windspeed process. The most commonly used model spectra withlength scales are presented in 2.3.4.5 to 2.3.4.10.

2.3.4.4 Caution should be exercised when model spectra areused. In particular, it is important to be aware that the true inte-gral length scale of the wind speed process may deviate signif-icantly from the integral length scale of the model spectrum.

2.3.4.5 The Davenport spectrum expresses the spectral den-sity in terms of the 10-minute mean wind speed U10 irrespec-tive of the elevation. The Davenport spectrum gives thefollowing expression for the spectral density

in which f denotes the frequency and Lu is a length scale of thewind speed process. The Davenport spectrum is originallydeveloped for wind over land with Lu = 1200 m as the proposedvalue.

2.3.4.6 The Davenport spectrum is not recommended for usein the low frequency range, i.e. for f < 0.01 Hz. There is a gen-eral difficulty in matching the Davenport spectrum to data inthis range because of the sharp drop in the spectral densityvalue of the Davenport spectrum near zero frequency.

2.3.4.7 The Kaimal spectrum gives the following expressionfor the spectral density,

in which f denotes frequency and Lu is an integral length scale.Unless data indicate otherwise, the integral length scale Lu canbe calculated as

z denotes the height above the ground or above the sea waterlevel, whichever is applicable, and z0 is the terrain roughness.Both z and z0 need to be given in units of m.

2.3.4.8 An alternative specification of the integral length scaleis given in IEC61400-1 for design of wind turbine generatorsand is independent of the terrain roughness,

where z denotes the height above the ground or the sea waterlevel, whichever is applicable.

2.3.4.9 The Harris spectrum expresses the spectral density interms of the 10-minute mean wind speed U10 irrespective ofthe elevation. The Harris spectrum gives the following expres-sion for the spectral density

in which Lu is an integral length scale. The integral length scaleLu is in the range 60-400 m with a mean value of 180 m. Unlessdata indicate otherwise, the integral length scale Lu can be cal-culated as for the Kaimal spectrum, see 2.3.4.6. The Harrisspectrum is originally developed for wind over land and is notrecommended for use in the low frequency range, i.e. forf < 0.01 Hz.

2.3.4.10 For design of offshore structures, the empirical Simiuand Leigh spectrum may be applied. This model spectrum isdeveloped taking into account the wind energy over a seawayin the low frequency range. The Simiu and Leigh spectrum S(f)can be obtained from the following equations

where

f = frequencyz = height above the sea surfaceU10 = 10-minute mean wind speed at height z

353

2

10

214.0)(

= fUL

fS uUU

3/42

10

2

102

))(1(

)(32

)(

UfL

fUL

fSu

u

UU

+

=

3/5

10

102

)32.101(

868.6)(

UfL

UL

fSu

u

UU

+

=

0ln074.046.0)300

(300 zuzL +=

+

0

Nights where temperature stratification severely >>0

)(ln*)(0

=

zzuzU

0

10

20

30

40

50

60

6 7 8 9 10 11 12 13

wind speed (m/s)

heig

ht (m

)

neutral

stable

unstable

20

0

)(dzdUdz

dg

R

=

RzLMO = in unstable air

RRzLMO

51= in stable air

)07.01()(

22 Bzv

zuTg

Rd

+

+

=

zu / zv /u v

)()(

12

12

qqTT

Lc

BMO

p

1T 2TDET NORSKE VERITAS

denoted 1 and 2, respectively, and and are the averagesuppresses mechanical turbulence generation 1q 2q

Amended October 2008 Recommended Practice DNV-RP-C205, April 2007see note on front cover Page 23specific humidities at the same two levels. The specific humid-ity q is in this context calculated as the fraction of moisture bymass.

2.3.6.8 Application of the algorithm in 2.3.6.7 requires an ini-tial assumption to be made for LMO. An iterative approach isthen necessary for solution of the Richardson number R. Con-vergence is achieved when the calculated Richardson numberR leads to a Monin-Obukhov length LMO by the formulas in2.3.6.6 which equals the value of LMO. Further details aboutatmospheric stability and its representation can be found inPanofsky and Dutton (1984).

2.3.6.9 Topographic features such as hills, ridges and escarp-ments affect the wind speed. Certain layers of the flow willaccelerate near such features, and the wind profiles willbecome altered.

2.4 Transient wind conditions

2.4.1 General

2.4.1.1 When the wind speed changes or the direction of thewind changes, transient wind conditions may occur. Transientwind conditions are wind events which by nature fall outsideof what can normally be represented by stationary wind condi-tions. Examples of transient wind conditions are:

gusts squalls extremes of wind speed gradients, i.e. first of all extremes

of rise times of gust strong wind shears extreme changes in wind direction simultaneous changes in wind speed and wind direction

such as when fronts pass.

2.4.2 Gusts

2.4.2.1 Gusts are sudden brief increases in wind speed, char-acterised by a duration of less than 20 seconds, and followedby a lull or slackening in the wind speed. Gusts may be char-acterised by their rise time, their magnitude and their duration.

2.4.2.2 Gusts occurring as part of the natural fluctuations ofthe wind speed within a 10-minute period of stationary windconditions without implying a change in the mean windspeed level are not necessarily to be considered as transientwind conditions, but are rather just local maxima of the station-ary wind speed process.

2.4.3 Squalls

2.4.3.1 Squalls are strong winds characterised by a suddenonset, a duration of the order of 10-60 minutes, and then arather sudden decrease in speed. Squalls imply a change in themean wind speed level.

2.4.3.2 Squalls are caused by advancing cold air and are asso-ciated with active weather such as thunderstorms. Their forma-tion is related to atmospheric instability and is subject toseasonality. Squalls are usually accompanied by shifts in winddirection and drops in air temperature, and by rain and lightning.Air temperature change can be a more reliable indicator of pres-ence of a squall, as the wind may not always change direction.

2.4.3.3 Large uncertainties are associated with squalls andtheir vertical wind profile and lateral coherence. The verticalwind profile may deviate significantly from the model profilesgiven in 2.3.2.4 and 2.3.2.8. Assuming a model profile such asthe Frya wind speed profile for extreme mean wind speeds asgiven in 2.3.2.13 is a possibility. However, such an assumptionwill affect the wind load predictions and may or may not beconservative. References

1) Andersen, O.J., and J. Lvseth, The Maritime TurbulentWind Field. Measurements and Models, Final Report forTask 4 of the Statoil Joint Industry Project, Norwegian Insti-tute of Science and Technology, Trondheim, Norway, 1992.

2) Andersen, O.J., and J. Lvseth, The Frya database andmaritime boundary layer wind description, Marine Struc-tures, Vol. 19, pp. 173-192, 2006.

3) Astrup, P., S.E. Larsen, O. Rathmann, P.H. Madsen, and J.Hjstrup, WASP Engineering Wind Flow Modellingover Land and Sea, in Wind Engineering into the 21stCentury, eds. A.L.G.L. Larose and F.M. Livesey,Balkema, Rotterdam, The Netherlands, 1999.

4) Det Norske Veritas and RIS, Guidelines for Design ofWind Turbines, Copenhagen, Denmark, 2001.

5) Dyrbye, C., and S.O. Hansen, Wind Loads on Structures,John Wiley and Sons, Chichester, England, 1997.

6) HSE (Health & Safety Executive), Environmental consid-erations, Offshore Technology Report No. 2001/010, HSEBooks, Sudbury, Suffolk, England, 2002.

7) IEC (International Electrotechnical Commission), WindTurbines Part 1: Design Requirements, IEC61400-1, 3rdedition, 2005.

8) JCSS (Joint Committee on Structural Safety), Probabilis-tic Model Code, Part 2: Loads, 2001.

9) Lungu, D., and Van Gelder, P., Characteristics of WindTurbulence with Applications to Wind Codes, Proceed-ings of the 2nd European & African Conference on WindEngineering, pp. 1271-1277, Genova, Italy, 1997.

10) Mann, J., Wind field simulation, Journal of Prob.Engng. Mech., Vol. 13, No. 4, pp. 269-282, Elsevier, 1998.

11) Panofsky, H.A., and J.A. Dutton, Atmospheric Turbu-lence, Models and Methods for Engineering Applications,John Wiley and Sons, New York, N.Y., 1984.

12) Saranyansoontorn, K., L. Manuel, and P.S. Veers, AComparison of Standard Coherence Models for InflowTurbulence with Estimates from Field Measurements,Journal of Solar Energy Engineering, ASME, Vol. 126,pp. 1069-1082, 2004.

13) Simiu, E., and R.U. Scanlan, Wind Effects on Structures;An Introduction to Wind Engineering, John Wiley, NewYork, N.Y., 1978.

14) WMO (World Meteorological Organization), Guide toMeteorological Instruments and Methods of Observation,Publication No. 8, World Meteorological Organisation,Geneva, Switzerland, 1983.DET NORSKE VERITAS

Recommended Practice DNV-RP-C205, April 2007 Amended October 2008Page 24 see note on front cover3. Wave Conditions3.1 General

3.1.1 IntroductionOcean waves are irregular and random in shape, height, lengthand speed of propagation. A real sea state is best described bya random wave model.A linear random wave model is a sum of many small linearwave components with different amplitude, frequency anddirection. The phases are random with respect to each other.A non-linear random wave model allows for sum- and differ-ence frequency wave component caused by non-linear interac-tion between the individual wave components.Wave conditions which are to be considered for structuraldesign purposes, may be described either by deterministicdesign wave methods or by stochastic methods applying wavespectra.For quasi-static response of structures, it is sufficient to usedeterministic regular waves characterized by wave length andcorresponding wave period, wave height and crest height. Thedeterministic wave parameters may be predicted by statisticalmethods.Structures with significant dynamic response require stochas-tic modelling of the sea surface and its kinematics by timeseries. A sea state is specified by a wave frequency spectrumwith a given significant wave height, a representative fre-quency, a mean propagation direction and a spreading func-tion. In applications the sea state is usually assumed to be astationary random process. Three hours has been introduced asa standard time between registrations of sea states when meas-uring waves, but the period of stationarity can range from 30minutes to 10 hours.The wave conditions in a sea state can be divided into twoclasses: wind seas and swell. Wind seas are generated by localwind, while swell have no relationship to the local wind.Swells are waves that have travelled out of the areas wherethey were generated. Note that several swell components maybe present at a given location.

3.1.2 General characteristics of wavesA regular travelling wave is propagating with permanent form.It has a distinct wave length, wave period, wave height.Wave length: The wave length is the distance between suc-cessive crests.Wave period: The wave period T is the time interval betweensuccessive crests passing a particular point. Phase velocity: The propagation velocity of the wave form iscalled phase velocity, wave speed or wave celerity and isdenoted by c = / T.Wave frequency is the inverse of wave period: f = 1/T.Wave angular