Exploitable results
Environmental contours represent an alternative method to the response surface method for the development of joint metocean design criteria. Uncertainties related to environmental contour plots have been examined. Both the environmental contour method and the response surface method give similar results for the West of Shetlands.
New insights are provided into the role of local and rapid spectral changes in the evolution of large ocean waves. Specific attention is paid to the importance of directional spreading. The physical mechanisms governing the evolution of the largest waves are investigated by applying both a fully non-linear wave model and the wave evolution equation first proposed by Zakharov. These two wave models are complementary; the former allowing the full non-linearity to be considered and the latter providing insights into the dominant physical processes. In all cases the third-order (three-wave) resonant interactions dominate changes to both the amplitude of the wave components and the dispersive properties of the wave group. However, the effects of directionality are shown to be critically important, highlighting those sea states in which freak or rogue waves are most likely to occur.
A method was developed to determine the structure reliability of an FPSO subjected to extreme loads under combined sea states. The method has application in reliability analyses of FPSO response to a particular marine environment, in which sea states are separated into wind-sea and swell components.
The development of short-term distributions for the maximum individual wave heights and crest heights during storms has been studied. The work is a continuation of work previously reported in Skourup et. al. (1997) and Sterndorff & Grønbech (2000).
A large number of wave radar measurements from the Danish sector of the North Sea from the period 1981 to 2000 have been analysed in order to provide short-term distributions for maximum individual wave heights and crest heights for 1-hour stationary sea-states and for whole storms. Measurements from laboratory tests and numerical simulation by means of a hybrid second-order wave model have also been analysed.
The work has specifically been aiming at the maximum wave heights and crests heights. For each stationary sea-state (or storm) the maximum wave height and crest height has been detected and normalised by the significant wave height. The results have then be fitted by Gumbel distributions of (Cmax/Hs)2 and (Hmax/Hs)2.
A model-testing program was carried out for the dynamic response of a turret moored FPSO in design environmental conditions.
The tests were made in the DHI 3D deep-water wave basin. An FPSO model was designed and constructed according to detailed dimensions agreed upon among the REBASDO partners. A special mooring line system was selected for obtaining the correct mooring line characteristics of a turret moored FPSO in deep water.
The environmental conditions (waves and wind) were calibrated and documented.
During the model tests the motions of the FPSO, the loads in turret and mooring lines, the bending moment on the FPSO and the wave elevation around the perimeter of the FPSO was measured.
A method for deterministic reproduction of non-linear long-crested and short-crested waves based on Stokes second order wave theory has been implemented. The method takes into account the effects due to finite water depth in the reproduction and dispersion of long-crested and short-crested deterministic waves (surface elevations and kinematics). Reproduction and dispersion of measured waves from the laboratory was made, and comparisons between the numerical model and measurements showed good agreement.
A method to separate the current in various components with different periodicity in time and then applying empirical orthogonal functions to each one to explain the spatial variability. The method was applied to Acoustic Doppler Current Profile data, and tidal current profiles were modelled.
Based on the 5-year directional data from the Norwegian Continental Shelf the Poisson distribution has been proposed to describe swell directional spreading. The model was established by analysing swell sea states selected according to a set of criteria.
A method to determine the fatigue change based on stochastic spectral analysis and subsequently fatigue reliability based on a FORM. The method includes the effect of bimodal sea states, consisting of a wind-sea and swell. It has been applied to a converted FPSO Hull.
The interaction of steep waves with a vertical cylinder is both of practical importance in engineering design as well as being a suitable test case for general diffraction codes. This work studied the effect of wave directionality. Using a new and efficient approach for cylindrical geometries and a very fine frequency resolution suited for the analysis of compact wave groups, both surface elevation around and forces on the scattering body were predicted. These results were then used to validate developments for our general diffraction code DIFFRACT.
For relatively compact bodies, the significance of the size of the focus spot was highlighted. If the body fits within this region, then the response due to a directional spread wave group looks much like that for a slightly modified uni-directional wave group. If the body extends outside this region, then the diffracted field is more complex. Close to the body, the strong double-frequency scattered field shows important spatial structure with short crescent-shaped wave crests being locally generated and then advancing round the body.
The work also examined the adequacy of simple frequency-independent models for wave directional spreading compared to full frequency-directional spectral models. Again for compact bodies, a simple frequency independent model such as a wrapped Normal was shown to be adequate for engineering design.
The interaction of steep waves with the curved bow of a ship shaped body was studied both computationally using 2nd order diffraction theory and experimentally in a wave tank. As part of the project, the Oxford code DIFFRACT was enhanced to give predictions of surface elevation as well as forces. In contrast to wave scattering by a surface-piercing vertical cylinder where there are strong third-order effects, the measured wave run-up and subsequent scattering from the ship was reproduced remarkably well by the 2nd order computation. Thus, the main wave scattering process is fully captured by the latest generation of engineering design tools.
The diffraction of directionally spread waves in a random sea poses severe computational problems using standard 2nd order theory because of the requirement to have discrete components in both frequency and direction. A new method was developed such that extreme events are built from discrete frequency components - as for uni-directional waves - but these single frequency components are now themselves directionally spread. This permits the incorporation of wave directional information into design calculations practical in a manner not possible before.
A new formula for the directional spreading of ocean swell has been established. This will allow more accurate description of swell spectra, reflecting in better-optimised design of offshore facilities sensitive to low-frequency waves, such as FPSO systems.
This work has involved the development of new modelling procedures capable of describing the non-linear interaction between waves and co-existing currents, particularly where the latter involves some depth-variation, typically arising due to the effects of the wind shear. Such problems are very difficult to model since the presence of depth-varying vorticity, associated with the current profile, leads to the wave motion itself becoming rotational. In this case the commonly applied design wave solutions, based on the assumption of irrationality, become inappropriate. A new approach based on the theory of fluid sheets has been developed and validated against a wide range of available data.
Reliability based design of moorings and risers in both long and short crested waves has been conducted which showed that in the absence of large current, traditional design predict extremes well whilst in the presence of large currents, significant reduction to design values may be obtained.
A method for specifying a multi-peaked wave spectrum has been established. The method allows up to 6 swell components and a wind-sea to be established for an arbitrary directional wave spectrum. Each component is described in terms of frequency spectrum function and a frequency-dependent directional spreading function.
This work concerns the calculation of long-term responses and environmental design criteria for FPSO systems. The design criteria are for both extreme and operating situations. The spectral response surface method (for short-term response analysis) has been integrated into an established approach for long-term storm statistics. The result is a fast and efficient method of generating long-term statistics for reliability studies and response-based design criteria.
The results show that a response-based approach is essential in estimating environmental criteria for moored ships. This arises from the sensitivity of the FSPSO system to wave period and directionality of winds, waves and currents. Partitioning of the input spectrum into independent sea and swell components is important especially for extreme roll motions. In fact, extreme roll arises in environments that are quite different from those producing most other extreme responses. Effects of short-term variability are large for responses excited by slow drift forces.
Effects of wave spreading in the dynamic response of hull, moorings and risers have been systematically examined. This showed the importance of the interaction between wave directions and predicted higher mooring responses in weathervaning FPSOs. It is necessary to take account of wave spreading in FPSO design.
A method to identify components of a complex wave spectrum has been composed with other methods and it was demonstrated to be a reliable and practical approach to separate the different wave requirements. The method has application in identifying and separating wind-sea and swell wave components in a sea state.
A joint environmental description including possibility of environmental parameters approaching from different directions has been developed by DNV for three locations at the Norwegian Continental Shell and for the West of Shetland. The probabilistic models developed are tailor made for load and load effect analysis of floating structures, their mooring arrangement and riser systems. Both instrumental data and hindcast data have been considered.
The following parameters are included in the joint model: wind speed, main wind direction, significant wave height (sea and swell), spectral peak period (sea or swell), main wave direction (wind sea and swell), current speed and current direction. Two approaches for including wind-sea and swell are suggested. In the first approach the distribution of total significant wave height and spectral peak period is combined with the two-peak Torsethaugen wave spectrum, which includes a procedure for splitting wave energy between wind-sea and swell. The alternative joint model approximates wind-sea and swell by separate distributions. The latter approach requires a wave spectrum including contribution from wind-sea and swell as, e.g. the Jonswap-Glenn spectrum.
Long-term distributions of significant wave height established using 18-year and 26-year annual, storm and global wave field data have been compared. As expected the study shows that differences between extremes predicted by the three distributions decrease with increasing number of years considered. Statistical and model uncertainties related to the annual, storm and global model have been specified.
Effects of wave directional spreading and two-peak spectra on the second order wave statistics were investigated. Particular attention has been given to the wave crest. Different directional spreading functions for wind-sea and swell have been applied. The results for the Torsethaugen frequency spectrum have been compared with prediction given by the JONSWAP spectrum, the Pierson-Moskwitz spectrum and the 2nd order Forristall crest model. The study shows that for sea states that exhibit a pronounced secondary peak, e.g. due to the presence of swell, the commonly used Forristall crest distribution may be unconservative. Further, for these sea states more severe crest values have been obtained applying the two peaks Torsethaugen spectrum than using the commonly applied JONSWAP spectrum with peak enhancement factor 3.3.
Limitations of the second order wave model to predict extreme crests were investigated. Statistics for freak waves defined according to the criterion c/hs> ê (c=wave crest, hs=significant wave height) was studied. The analyses were based on second order time domain simulations, short-term distributions for crest statistics documented in the literature, and long term field data. Time series of wave elevations have been generated using the Pierson-Moskowitz, JONSWAP and two-peak Torsethaugen frequency spectrum for long-crested seas and deep water. The analysis confirms that wind dominated seas are generally more non-linear than swell dominated seas as they represent steeper sea states, and consequently higher number of freak events are expected in these seas.
This work concerns the calculation of the probability of exceedance of wave crest elevation. New statistics have been calculated for broad-banded, unidirectional, deep-water sea states by incorporating a fully non-linear wave-model into a spectral response surface method. This is a novel approach to the calculation of statistics, and, as all of the calculations are performed in the probability domain, avoids the need for long time-domain simulations. Furthermore, in contrast to theoretical distributions, the broad banded, fully non-linear, nature of the sea-state can be considered. The results have been compared to those of fully non-linear time-domain simulations and are shown to be in good agreement. The results indicated that in unidirectional seas the crest elevations of the largest waves could be much higher than would be predicted by linear or second-order theory. Hence, the occurrence of locally long-crested sea-sates offers a possible explanation for the formation of freak or rogue waves.
In contrast, with the inclusion of directional effects the non-linear increase in the maximum crest elevation rapidly reduces. Indeed, with realistic directional spreads the fully non-linear statistics are shown to lie between the linear and second order predictions. However, this result masks the fact that the non-linear wave profile may be significantly steeper, with implications for wave slamming and green-water inundation. Furthermore, by combining these short-term statistics with the long term statistics of storms, the return periods of a number of extreme field observations have been correctly estimated.
This work concerns the calculation of dynamic responses of FPSO systems excited by first and second order forcing in waves, winds and currents. The novel aspect is the use of a spectral response surface method, a method that is fast, yet includes most of the important non-linearity in the excitation. The results include the probability of exceedance of responses such as offset, line tension; heave at the turret, and roll of the hull. The combination of first and second order forcing (for example in line tension) is treated automatically without the introduction of empirical rules. The designer wave, the time series of surface elevation most likely to excite an extreme response, has been calculated.
The results have been compared to measurements from tests in the DHI model basin and are shown to be in reasonable agreement. The main limit in the method is the quality of input data. It provides a rapid and accurate approach for estimating statistics of FPSO system responses in realistic, directionally spread seas. Moreover, the results raise new possibilities for the model testing and design of these systems.
This work concerns the calculation of the probability of exceedance of wave crest elevation. Statistics have been calculated for broad-banded, random waves by incorporating a Sharma and Dean's second order wave-model into a spectral response surface method. This is a novel and extremely rapid approach to the calculation of statistics; all of the calculations are performed in the probability domain rather than by slow time-domain simulations. Moreover, in contrast to empirical distributions, the precise spectrum of the sea-state can be considered.
The results have been compared to measurements, second order time-domain and fully non-linear time-domain simulations and are shown to be in reasonable agreement. The method provides a rapid and accurate approach for crest statistics in many realistic, directionally spread seas. However, second order methods do not capture all aspects of the wave kinematics and, at least in uni-directional seas, underestimate crest elevations.
These short-term statistics can be combined with the long-term statistics of storms and the return periods of a number of extreme wave crests predicted.
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