Offshore and Coastal Modelling

The papers contained in this volume were presented orally at the seventh POLYMODEL conference, held at Sunderland Polytechnic in the United King­ dom in May 1984 and sponsored by Barclays Bank PLC and Imperial Chemical Industries Ltd. The conferences are organised annually by the North East of England Polytechnic's Mathematical Modelling and Computer Simulation Group - POLYMODEL. The Group is a non-profit making organisation based on the mathematics department of the three polytechnics in the region and has membership drawn from those educational institutions and from regional industry. Its objective is to promote research and collaboration in mathematical and computer-based modelling. After a short introductory chapter, the volume may be considered as dividing naturally into four parts. Chapters 2 to 5 constitute the first part on Tides, Storm Surges and Coastal Circulations which deals with the hydrodynamics of coastal seas. Chapters 6 to 11 concern Coastal Engine­ ering Modelling and discuss such coastal phenomena as beach erosion, sediment transport, and non-linear waves. The third part (Chapters 12 to 16) on Offshore Structures considers sea structures in general and the connections between the structures (hoses, moorings, pipelines) in particular. The last two chapters focus on Offshore Corrosion problems.

1 Modelling in Offshore and Coastal Engineering.- 2 Tides, Storm Surges and Coastal Circulations.- 2.1 Bathymetry.- 2.2 Tides and Tidal Currents.- 2.3 North Sea Storm Surges.- 2.4 Two-dimensional Numerical Storm-surge Models.- 2.5 Surge Forecasting.- 2.6 Three-dimensional Models.- 2.7 Vertical Structure of Current.- 3 Modelling Storm Surge Current Structure.- 3.1 Introduction.- 3.2 Spectral Model Formulation.- 3.3 Form of Vertical Eddy Viscosity.- 3.4 A 3-D Simulation Model of Surge Currents on the North-West European Shelf.- 3.5 A Mechanistic Model of Wind Induced Current Profiles.- 3.6 Concluding Remarks.- 4 Optimally Controlled Hydrodynamics for Tidal Power from the Severn Estuary.- 4.1 Introduction.- 4.2 Hydrodynamics.- 4.3 Optimal Control.- 5 Numerical Modelling of Storm Surges in River Estuaries.- 5.1 Introduction.- 5.2 Points to note in Modelling.- 5.3 The Aims of a Mathematical Model of Storm Surges.- 5.4 The Differential Equations of the Model.- 5.5 Computational Aspects.- 5.6 Numerical Results: The Storm of 1953.- 5.7 Summary.- 6 Coastal Sediment Modelling.- 6.1 Introduction.- 6.2 Need for Computer Models.- 6.3 Model Types.- 6.4 Conclusions.- 7 The Application of Ray Methods to Wave Refraction Studies.- 7.1 Introduction.- 7.2 Ray Models.- 7.3 Application of the Ray Model, a Simple Case.- 7.4 A Study including Wave Breaking.- 7.5 A Study including Diffraction and Reflection.- 7.6 Future Developments.- 8 A Model for Surface Wave Growth.- 8.1 Introduction.- 8.2 Formulation of the Problem.- 8.3 First Order Solution.- 8.4 Second Order Solution.- 8.5 Third Order Solution.- 8.6 Wind Shear Stress.- 8.7 Conclusion.- 9 Power Take-Off and Output from the Sea-Lanchester Clam Wave Energy Device.- 9.1 Introduction.- 9.2 Experimental Tests.- 9.3 Power Take-off Simulation.- 10 Numerical Modelling of Ilfracombe Seawall.- 10.1 Introduction.- 10.2 Finite Element Modelling of Ilfracombe Seawall.- 10.3 Need for a Finite Element Model Approach.- 10.4 Conclusions.- 11 Modelling The Plan Shape of Shingle Beaches.- 11.1 Introduction.- 11.2 General Considerations when Modelling Beach Changes.- 11.3 Derivation of an Alongshore Transport Formula.- 11.4 Incipient Motion of Shingle.- 11.5 Discussion.- 11.6 Conclusions.- 12 Mathematical Modelling Applications for Offshore Structures.- 12.1 Introduction.- 12.2 Operational, Environmental and Foundation Condition.- 12.3 Structural Concepts.- 12.4 Fabrication.- 12.5 Construction.- 12.6 Load Out.- 12.7 Tow Out.- 12.8 Installation.- 12.9 Mathematical Modelling in Platform Design.- 12.10 Conclusions.- 13 Mathematical Model of A Marine Hose-String at a Buoy: Part 1, Static Problem.- 13.1 Introduction.- 13.2 Assumptions.- 13.3 Equations.- 13.4 Boundary Conditions.- 13.5 Hose Radius.- 13.6 The Load.- 13.7 Method of Solution.- 13.8 Analytical Solutions for Simplified Models.- 13.9 Results.- 13.10 Applications.- 13.11 Conclusions.- 14 Mathematical Model of a Marine Hose-String at a Buoy: Part 2, Dynamic Problem.- 14.1 Introduction.- 14.2 Equation of Motion.- 14.3 Boundary Conditions.- 14.4 Method of Solution.- 14.5 Flanges.- 14.6 Comparison of Analytical and Numerical Results.- 14.7 Numerical Results.- 14.8 Conclusions.- 15 The Design of Catenary Mooring Systems for Offshore Vessels.- 15.1 Introduction.- 15.2 Representation of the Environment.- 15.3 Mathematical Model of Moored Vessel.- 15.4 Calculations of Environmental Forces and Moments.- 15.5 Calculation of Mooring Forces and Moments.- 15.6 Static Analysis.- 15.7 Response of Vessel to Wind Gusting and Wave Drift Action.- 15.8 Conclusions.- 16 Some Problems Involving Umbilicals, Cables and Pipes.- 16.1 Introduction.- 16.2 The Statics of Cables and Pipes.- 16.3 Hydrodynamic Forces.- 16.4 Analytical Solutions.- 16.5 Typical Problems and Numerical Solutions.- 16.6 Final Comments.- 17 Mathematical Modelling in Offshore Corrosion.- 17.1 Introduction.- 17.2 General Mass Transport Theory.- 17.3 Mathematical Modelling of the Electrochemistry in Cracks.- 17.4 Mathematical Modelling in Cathodic Protection Offshore.- 17.5 Mathematical Modelling of Crevice Corrosion.- 17.6 Mathematical Modelling of Corrosion in Concrete.- 17.7 Conclusions.- 18 Fatigue Crack Growth Predictions in Tubular Welded Joints.- 18.1 Introduction.- 18.2 Fatigue Crack Growth Behaviour of Tubular Joints.- 18.3 Theoretical Analysis of Crack Growth.- 18.4 Conclusions.