Earlier models of random wave transformation are reviewed in the first section. Then the transformation of waves, including dissipation due to breaking and bottom friction, is described by an energy flux balance model. The wave height pdf of all waves (broken and unbroken) is shown by the field data to be well described by the Rayleigh distribution everywhere. The observed distributions of breaking and broken wave heights are fitted to simple analytical forms, and breaking wave dissipation is calculated by using a periodic bore formulation. The energy flux equation is integrated to yield local values of Hrms as a function of offshore wave conditions. Both analytical and numerical models are developed. In the last section the models are compared with results from random wave experiments in the laboratory and from an extensive set of field measurements.

/pdf/transformation-of-wave-height-distribution-2kl80xxt9b.pdf

Transformation of wave height distribution

Basic Ideas.- Systematic Descriptions.- Advanced Approaches.- Convergent Series For Divergent Taylor Series.- Nonlinear Initial Value Problems.- Nonlinear Eigenvalue Problems.- Nonlinear Problems In Heat Transfer.- Nonlinear Problems With Free Or Moving Boundary.- Steady-State Similarity Boundary-Layer Flows.- Unsteady Similarity Boundary-Layer Flows.- Non-Similarity Boundary-Layer Flows.- Applications In Numerical Methods.

Homotopy Analysis Method in Nonlinear Differential Equations

http://numericaltank.sjtu.edu.cn/KeyArticles/LIAO-Notes-2009.pdf

Notes on the homotopy analysis method: Some definitions and theorems

1. Introduction 2. Mathematical description of oscillations 3. Interaction between oscillations and waves 4. Gravity waves on water 5. Wave-body interactions 6. Wave-energy absorption by oscillating bodies 7. Wave interactions with oscillating water columns Bibliography Index.

https://assets.cambridge.org/97805217/82111/copyright/9780521782111_copyright.pdf

Ocean waves and oscillating systems : linear interactions including wave-energy extraction

This manuscript summarizes the feasibility study conducted for the WindFloat technology. The WindFloat is a three-legged floating foundation for multimegawatt offshore wind turbines. It is designed to accommodate a wind turbine, 5 MW or larger, on one of the columns of the hull with minimal modifications to the nacelle and rotor. Potential redesign of the tower and of the turbine control software can be expected. Technologies for floating foundations for offshore wind turbines are evolving. It is agreed by most experts that the offshore wind industry will see a significant increase in activity in the near future. Fixed offshore turbines are limited in water depth to ∼30–50 m. Market transition to deeper waters is inevitable, provided that suitable technologies can be developed. Despite the increase in complexity, a floating foundation offers the following distinct advantages: Flexibility in site location; access to superior wind resources further offshore; ability to locate in coastal regions with limited shallow continental shelf; ability to locate further offshore to eliminate visual impacts; an integrated hull, without a need to redesign the transition piece between the tower and the submerged structure for every project; simplified offshore installation procedures. Anchors are significantly cheaper to install than fixed foundations and large diameter towers. This paper focuses first on the design basis for wind turbine floating foundations and explores the requirements that must be addressed by design teams in this new field. It shows that the design of the hull for a large wind turbine must draw on the synergies with oil and gas offshore platform technology, while accounting for the different design requirements and functionality of the wind turbine. This paper describes next the hydrodynamic analysis of the hull, as well as ongoing work consisting of coupling hull hydrodynamics with wind turbine aerodynamic forces. Three main approaches are presented: The numerical hydrodynamic model of the platform and its mooring system; wave tank testing of a scale model of the platform with simplified aerodynamic simulation of the wind turbine; FAST, an aeroservoelastic software package for wind turbine analysis with the ability to be coupled to the hydrodynamic model. Finally, this paper focuses on the structural engineering that was performed as part of the feasibility study conducted for qualification of the technology. Specifically, the preliminary scantling is described and the strength and fatigue analysis methodologies are explained, focusing on the following aspects: The coupling between the wind turbine and the hull and the interface between the hydrodynamic loading and the structural response.

WindFloat: A floating foundation for offshore wind turbines

The subject of hydrodynamics applied to offshore structures is vast. The topics covered in this book aim to help the reader understand basic principles while at the same time giving the designer enough information for particular designs. Thus, results are given with derivations, and applications are discussed with the aid of examples, with an overview of the advantages and limitations of the method involved. This makes the book suitable as a text for undergraduate and graduate students specializing in offshore and ocean engineering. In addition, the final results, including tables and illustrations may be referenced directly without going through detailed derivations. They can therefore be used by design and applications engineers involved in offshore structure design. This title also introduces various types of offshore structures with reference to actual installations in various parts of the world. It describes wave mechanics and how to choose wave theories and design waves. After a choice of design wave is made, the author describes how this wave is used to obtain forces on a fixed offshore structure. If the structure is allowed to move, various methods of obtaining the motions of the structure are given. The short- and long-term responses are derived and different methods are described. The use of model tests to verify these methods at each step is shown.

Hydrodynamics of Offshore Structures

While existing literature on offshore structures does touch on model testing, a comprehensive text discussing the design, construction, instrumentation, testing and analysis of physical models is lacking. This book aims to fill that vacuum and provide, through its survey of the theoretical and practical aspects of physical modelling, an in-depth coverage of the technology of model testing. Although the main focus is on offshore construction, the text should prove of use to the entire field of engineering, and its breadth of scope should appeal not only to engineers and naval architects but to scientists interested in structural or hydraulic testing as well.

Offshore Structure Modeling

https://repository.tudelft.nl/islandora/object/uuid%3Ab9fc5609-f1b8-4a10-b622-a1e243f03b78/datastream/OBJ/download

Empirical calculation of roll damping for ships and barges

Review of riser analysis techniques

1. Introduction. Definition of nonlinear systems. Consistent methodology. Probability distributions. 2. Environments. Wave theories. Nonlinear waves. Random waves. Wave simulation. Waves plus current. Breaking waves. Wind spectra. 3. Wave Loading on Structures. Wave force formulations. Morison equation. Modified Morison equation. Four-term Morison equation. Transverse force. Random wave force. Wave breaking force. Steady drift force. 4. Offshore Structure Response. Nonlinear motion response. Response analysis of jacket structure. Single-degree of freedom system. Moorling line analysis. Time domain solution of moored systems. Low frequency oscillation. High frequency oscillation. Damping at low and high frequency responses. Riser deflection analysis. 5. Distribution of Short-Term Wave Parameters. Wave elevation distribution. Nonlinearity of sea waves. Wave height distribution. Distribution of wide-banded wave amplitudes. Nonlinear Gaussian waves. Nonlinear non-Gaussian waves. Wave group statistics. Wave period distribution. Non-stationary wave height distribution. Wave height-period distribution. Extreme wave height-steepness distribution. Review of nonlinear wave statistics. 6. Short Term Loading Distribution. Linear systems. Linearized systems. Loading spectra. Statistics of narrow-band Morison force. Statistics of wide-band Morison force. Statistics of wave-current force. Statistics of free surface structural response. Review of nonlinear excitation statistics. 7. Short Term Response Distribution. Structural response spectrum. Statistics of nonlinearly dampled system. Statistics of drift force. Statistics of low frequency motion. Discussion of nonlinear response statistics. 8. Long-Term Response Prediction. Long-term wave height distribution. Joint distribution of H s and T z . Extrapolation of wave scatter diagram to longer duration. Long-term wave load distribution. Prediction of extreme wave loads. Return periods of extreme events and non-encounter probabilities. Bivariate short- and long-term prediction. Time and frequency domain long-term predictions. Short and long-term response prediction for nonlinear systems. Review of extreme value prediction for linear and nonlinear systems. References at the end of each chapter. Author index. Subject index.

Subrata K. Chakrabarti

Papers

Hydrodynamics of Offshore Structures

Offshore Structure Modeling

Empirical calculation of roll damping for ships and barges

Review of riser analysis techniques

Nonlinear Methods in Offshore Engineering