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With the development of floating wind turbines comes the need for mooring systems suitable for shallow water depths. Compliance becomes challenging for mooring systems composed of chain and wire rope. Polyester ropes can improve compliance, but the even lower stiffness of nylon may further reduce mooring line loads. However, fatigue lifetime of nylon ropes has been limiting. This paper presents results of stiffness and fatigue tests on long lay polyester and nylon ropes and evaluates the performance of two mooring systems for a floating wind turbine. The fibre ropes’ complex stiffness behaviour is modelled by the Syrope model, with mooring analyses based on fully coupled time-domain simulations. Nylon ropes reduce the dynamic loads in the mooring system, particularly wave frequency loads. This improves the fatigue lifetime of all components, allowing a reduction of the chain cross-section area by 40% compared to the polyester-based mooring system. The long lay nylon ropes show excellent fatigue properties. With the reduced loading, the lifetime is longer for the nylon ropes than the polyester ropes. Ultimate loads are also reduced when using nylon, allowing reduction of the breaking load by 30%. This gives a thinner and lighter rope than the equivalent polyester rope.

The wave induced motions and vertical bending moments induced by extreme seas on a Cruise Ship is investigated numerically and experimentally. Six sea states and extreme wave sequences, which could trigger modulation instability and induce high nonlinear ship responses, were chosen. The ship responses are simulated in the time domain with a body nonlinear seakeeping code based on strip theory. Two levels of complexity are used and compared: (a) the first assumes that the body nonlinear effects in the vertical responses are dominated by the hydrostatic and Froude-Krylov components, therefore the related forces are nonlinear, while radiation and diffraction is kept linear (partially body nonlinear method); (b) the second considers all forces as body nonlinear and they are updated at each time instant during the simulation depending on the hull wetted surface (fully body nonlinear method). The paper presents comparisons of direct time domain simulations with experimental records, as well as probability distribution of maxima. The fully body nonlinear code compares very well with the experiments in extreme wave conditions.

This paper investigates the experimental and numerical vertical bending moments induced by abnormal waves on two ships, namely, a bulk carrier and a Roll-on/Roll-off. The experimental data was obtained by seakeeping tests with scaled models in head waves at two Froude numbers. The wave traces were predefined and corresponding to wave records measured during storms in the North Sea. These wave records are particularly interesting because each of them includes one abnormal wave. The ship models, which are similar in length but different in their geometry, were tested in the same predefined wave conditions. The objective is to investigate the hull geometry influence on vertical bending moment under extreme sea conditions. Some conclusions are made by comparing directly the measured responses from the two models. The experimental data is also used as benchmark to validate the predictions by a partially nonlinear time domain seakeeping numerical model. The numerical model is then used to generalize the comparative analysis between the two ships.

The vertical response of an Ultra Large Containership in high seas is analysed by means of numerical methods, which are compared with experiments. The experiment was conducted in a wave tank on a free running model with aluminium back bone and the flexible response of the ship is measured. The ship was tested in regular waves of moderate amplitude to analyse springing, and in severe irregular seas for whipping response. It was found that the flexibility of the model increases the largest sagging peak by up to 32%. The hydroelastic response of the ship is numerically calculated using a body nonlinear time domain method based on strip theory. A practical engineering method is followed for calculating the dependency of the hydrodynamic forces on the geometrical nonlinearity of the wetted hull. The time domain code is coupled with a Finite Element Model and the ship hull is modelled as a non-uniform Timoshenko beam. The ship responses in moderate seas are very well calculated by the numerical method. Even though vertical motions in very high seas are slightly overestimated by the numerical results, the numerical vertical bending moments are reasonably in good agreement with the experimental results.

A body-nonlinear time domain code based on strip theory is used to calculate the vertical ship responses of a containership in extreme sea conditions. The numerical method calculates the radiation forces based on Cummins formulation. A practical engineering approach is followed for calculation of the radiation/diffraction forces for instantaneous wetted surface of the hull. The Froude–Krylov and hydro static forces are also calculated for instantaneous wetted surface area of the hull. The numerical method calculates the vertical responses of a container ship in abnormal waves embedded in a real deterministic sea and the results are compared with the model test data. Results obtained from the numerical code that uses body-nonlinear hydrodynamic and hydrostatic forces are compared with results from another code that uses linear radiation/diffraction force and body-nonlinear Froude–Krylov and hydrostatic force. Time series of the vertical ship motion, vertical bending moment at the midship, and the relative motion at the bow are calculated and compared. Additionally, short term distribution of peaks of the vertical motion and bending moment, and the largest vertical bending moment peaks are analyzed. It is observed that the body nonlinear radiation/diffraction forces significantly improve prediction of the ship responses in extreme waves.

The aim of this paper is to critically assess the methods used for the evaluation of wave-induced loads on ships examining analytical, numerical and experimental approaches. The paper will focus on conventional ocean going vessels and loads originating from steady state and transient excitations, namely slamming, sloshing and green water, for the latter, and including extreme or rogue waves, as well as the more occasional loads following damage. The advantages and disadvantages of the relatively simpler potential flow ap-proaches against the more time consuming CFD methods will be discussed with reference to accuracy, modelling nonlinear effects, ease of modelling and coupling, suitability for long term response evaluation and suitability for incorporation within design and operational decision making. The paper will also asses the uncertainties involved in predicting wave-induced loads and the probabilistic approaches used for the evaluation of long term response and fatigue analysis. The current design practice will be reviewed and the role of numerical prediction methods within the classification framework and goal based design approach will be discussed. Finally the suitability of current developments in prediction methods to meet the needs of the industry and future challenges will be discussed focusing on hybrid approaches, systems approach and data fusion.

The paper presents a numerical and experimental study of the wave induced motions of a Floating Production Storage and Offloading system for production of LNG (FLNG) and a shuttle tanker floating side by side in head seas. The objective is to investigate the side-by-side moored system first order (linear) wave frequency and second order low frequency responses. The focus is on the wave induced responses which might limit the system operability, namely, the relative motions and the loads on the mooring lines. A second objective is to validate a frequency domain numerical method for calculating second order responses to irregular wave excitations through comparisons with experimental data obtained in an offshore wave basin. A Green׳s function panel method is used for the hydrodynamic calculations. The second order calculations are performed with an approximate method where the second order velocity potential is calculated without considering the forcing function on the free surface boundary condition. The irregular seas calculations are performed in the frequency domain. It is shown that the second order low frequency loads cannot be neglected when calculating the tension on the side by side mooring system.

A subsystem of a large compliant floating hydrocarbon storage facility (FHSF) is established as a simplified model to validate its hydrodynamic performance. The subsystem is composed of two floating hydrocarbon storage tanks (floating tanks) placed in a large moonpool of a rigid barge frame. The barge frame is expected to serve as a breakwater as well as a protection to the floating tanks. The wave-induced responses of the subsystem with the existence of moonpool/gaps are investigated through experimental and numerical studies. The experimental studies followed a Froude scaling ratio 1:45 were conducted in an ocean basin under various wave conditions corresponding to nearshore environments. Both free surface elevations in the moonpool/gaps and the hydrodynamic responses of the three floating bodies were obtained. Besides, a numerical model based on linear potential flow theory is developed, and a dipole lid is introduced to incorporate the viscous effect on the resonant free surface motions. Comparable experimental and numerical results show that the free surface elevations in the moonpool/gaps can be reasonably predicted. Next, four different configurations of the subsystem were investigated, and different hydrodynamic coupling behaviors between the fluid resonant motions, the motions of the barge frame, and the floating tanks are revealed. It is demonstrated that the motions of the floating bodies and the resonant fluid motions in the narrow gaps are the smallest in the oblique sea. The present study provides a useful reference for the design and hydrodynamic analysis of floating multi-body systems for nearshore applications.

A strip theory based partially nonlinear time domain code is extended to include body nonlinearity in the calculation of radiation and diffraction forces, which expresses the dependence of hydrodynamic forces on the time changing underwater hull shape. The body nonlinear Froude–Krylov and hydrostatic forces are combined with the body nonlinear radiation and diffraction forces. The radiation forces are represented in terms of impulse response functions, infinite frequency added mass and radiation restoring coefficients. Additionally, a semi-empirical technique is employed to include the surge mode to overcome one of the strip theory two-dimensional simplifications. The method is used to calculate the wave induced vertical motions and bending moments on a modern Cruise Ship. Results from the time domain code in regular waves with different steepnesses, with and without nonlinear radiation and diffraction forces, are calculated and compared. Similarly, the analysis is carried out for design regular waves and is compared with model test experimental data obtained in a seakeeping tank.

The paper investigates the effects of the surge hydrodynamic forces and surge mode of motion on the vertical responses of a container ship and a chemical tanker in waves. A partially body nonlinear time domain code based on strip theory is modified to include the surge mode. The Froude–Krylov and hydrostatic forces are calculated for the exact wetted surface area of the hull for each time instant. Certain practical engineering techniques are used to overcome the 2D limitations imposed by strip theory in order to include the surge. Surge hydrodynamic coefficients are calculated using conformal mapping technique and surge Froude–Krylov forces are calculated for instantaneous wetted surface. Surge radiation forces are calculated based on Cummins formulation. The analysis is done for the S175 container ship and a chemical tanker in head seas for a range of wave steepness and Froude numbers. The effect of surge on the transfer functions and the peaks values of the vertical motions and vertical bending moment are analyzed. The numerical results are compared with the experimental results. It is observed that longitudinal forces reduce the vertical bending moment about the transverse axis at deck level for the wave frequencies of interest.

Most of the wave energy converters under development are planned for operation in shallow to intermediate water depths, typically 30 m to 70 m. However, the limited water depth reduces the wave energy resource as compared to offshore deep water. This paper presents an analysis of the water depth effects on the wave energy resource and on the energy absorbed by a floating device. The analysis is based on a procedure to modify the wave spectrum as the water depth reduces, namely the TMA method Bouws et al., 1985 . J. Geophys. Res. 90 (C1), 975–986. The method is based on the hypothesis that the similarity principle for the saturation range of shallow-water spectrum is not restricted to the equilibrium range, but is valid across the entire spectrum. A point absorber-type wave energy converter is modelled and the wave climatology of Figueira da Foz (Portugal) is used as a case study. Significant reduction has been identified for both the wave energy resource and wave energy converted as the water depth decreases. The presented methodology can be used for preliminary cost benefit analysis and decision making regarding the best water depth for installation of specific wave energy converters.

The paper presents an analysis of the radiation forces on a ship advancing with forced heave and pitch motions. This analysis is based on experimental data obtained with model tests and on numerical simulations with two codes, one based on 3D time domain Greens function method and the other is a 2D linear strip theory method. The case study consists of a hull shape from a Fast Ferry and several speeds are investigated between 0 and 40 knot. The objective is to quantify the forward speed effects on the radiation forces and to verify the skill of the conventional strip theory and of a time domain panel methods in dealing with large forward speeds.The consequences of applying simplifications on the linear boundary conditions of the common seakeeping codes are investigated. It is concluded that forward speed has a large effect on the radiation forces, especially on the coupling terms, and thus it is important to consider the full linear interactions between the steady and unsteady flows in the numerical calculations as the speed of the ship increases and the time domain panel code is able to represent these effects.

The paper presents an experimental and numerical investigation of the first order and slowly varying wave exciting forces on a body of simple geometry which is restrained from moving. Both monochromatic waves and three sets of bi-chromatic waves corresponding to three difference frequencies were tested. The depth effects on the second order forces are assessed by repeating the wave conditions for deep water, intermediate water depth and shallow water. The wave exciting mean drift forces and second order slowly varying forces were successfully measured and identified. However, since the magnitude of these forces is small compared to the global forces measured, there is some dispersion in the second order results. The experimental data is compared with three state of the art numerical methods which are able to compute the first and second order wave exciting forces. Two of the methods use Green's function panel methods (Wamit and HydroStar) and the third is based on an analytical solution (Diffrac-R). All methods compute the full second order solution, including the effects related to the quadratic interactions of first order quantities and to the second order diffraction potentials.

This paper presents a procedure to calculate the design pressure distributions on the hull of a wave energy converter (WEC). Design pressures are the maximum pressure values that the device is expected to experience during its operational life time. The procedure is applied to the prototype under development by Martifer Energy (FLOW—Future Life in Ocean Waves). A boundary integral method is used to solve the hydrodynamic problem. The hydrodynamic pressures are combined with the hydrostatic ones and the internal pressures of the large ballast tanks. The first step consists of validating the numerical results of motions by comparison with measured experimental data obtained with a scaled model of the WEC. The numerical model is tuned by adjusting the damping of the device rotational motions and the equivalent damping and stiffness of the power take-off system. The pressure distributions are calculated for all irregular sea states representative of the Portuguese Pilot Zone where the prototype will be installed and a long term distribution method is used to calculate the expected maximum pressures on the hull corresponding to the 100-year return period.