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

In the present study, wave heights and dynamic pressures at the still-water level on half of a vertical cylinder surface are measured Since the height is measured only between 0° and 180°, the symmetry of the distribution cannot be shown However, Galvin and Hallermeier established in their study that symmetry existed in all cases tested The purpose of this study is to show further that the height distribution follows crest distribution and dynamic pressure distribution which, in turn, suggests that even the pressure transducers around the structure may be used to establish direction of the wave

Wave Height Distribution around Vertical Cylinder

Inline and transverse forces on a tube array in tandem with waves

Technical Note: On the formulation of Jonswap spectrum

An analytical method is developed to determine the transverse motions of a rigid articulated tower. In the theoretical analysis, the transverse forces are determined from the lift coefficients which are considered known. The transverse motions are then computed by solving a second order differential equation. A test was performed on a rigid articulated tower model. In the experimental analysis, lift coefficients are computed from the tower motions that were recorded. It is shown that the measured transverse motions and loads on the tower can be predicted well from the present theory.

Subrata K. Chakrabarti

Papers

Wave Height Distribution around Vertical Cylinder

Inline and transverse forces on a tube array in tandem with waves

Technical Note: On the formulation of Jonswap spectrum

Transverse Motion of Articulated Tower

Hydrodynamic coefficients of a harmonically oscillated tower