Stochastic bivariate time series models of waves in the North Sea and their application in simulation-based design

In this paper, we present and evaluate three long-term wave models for application in simulation-based design of ships and marine structures. Designers and researchers often rely on historical weather data as a source for ocean area characteristics based on hindcast datasets or in-situ measurements. The limited access and size of historical datasets reduces repeatability of simulations and analyses, making it difficult to assess the sampling variability of performance and loads on marine vessels and structures. Markov, VAR and VARMA wave models, producing independent long-term time series of significant wave height (H_s) and spectral peak period (T_p), is presented as possible solutions to this problem. The models are tested and compared by addressing how the models affect interpretation of design concepts and the ability to replicate statistical and physical characteristics of the wave process. Our results show that the VAR and VARMA models perform sufficiently in describing design performance, but does not capture the physical process fully. The Markov model is found to perform worst of the tested models in the applied tests, especially for measures covering several consecutive sea states.     

Study of irregular wave run-up over fringing reefs based on a shock-capturing Boussinesq model

This paper presents the results of a parametric study of irregular wave run-up over fringing reefs using the shock-capturing Boussinesq wave model Funwave-TVD to better understand the role of fringing reefs in the mitigation of wave-driven flooding. Laboratory experiments were newly performed with a typical fringing reef profile and typical hydrodynamic conditions to validate the model. Experimental data shows irregular wave run-ups are dominated by the low-frequency motions and confirms the run-up resonant phenomenon over the back-reef slope, which has been revealed in previous numerical studies. It is demonstrated that irregular wave evolution and run-up over fringing reefs are reasonably reproduced by the present model with a proper grid size. However, the infragravity run-up height and highest 2% run-up height over the back-reef slope are under-predicted due to the underestimation of the infragravity wave height over the reef flat. The validated model was then utilized to model irregular wave transformations and run-ups under different conditions. Through a series of numerical experiments, the effects of key hydrodynamic and reef geometry parameters, including the reef flat width, water depth over the reef flat, fore-reef slope angle and back-reef slope angle, on the irregular wave run-up were investigated. Variations of spectral components of irregular wave run-ups were examined to better understand the physical process underlying the effect of each parameter.     

Temporal variation of modulated-wave-train geometries and their influence on vertical bending moments of a container ship

A towing experiment was conducted using a modulated wave train to investigate the vertical bending responses of a hydro-structural container ship model. In the experiment, a spatially periodic modulated wave train, as a model of a freak wave in successive high waves mimicking the so-called three sisters, was generated by the recently established higher-order spectral method wave generation (HOSM-WG) method. HOSM-WG enables us to control the location and timing of the maximum crest height in a wave tank. With precise control of the towing carriage, an experiment was conducted in which the timing of the encounters between the ship model and the modulated wave train was accurately determined. The maximum sagging moment (SM) was found to increase in proportion with the encounter wave height. However, because of differences in the relative depth of the fore and aft troughs, the maximum SM is highly variable for a given wave height. The temporal wave-geometry evolution caused the relative trough-depth to vary significantly within a wave period in the vicinity of the maximum crest height. As a result, depending on the encounter timing, the SM varied considerably for a given wave height. The temporal variation of the wave geometry is a robust feature of a modulated wave train and is common between the spatially periodic and temporally periodic modulated wave trains.     

Characteristics of breaking irregular wave forces on a monopile

The substructures of offshore wind turbines are subjected to extreme breaking irregular wave forces. The present study is focused on investigating breaking irregular wave forces on a monopile using a computational fluid dynamics (CFD) based numerical model. The breaking irregular wave forces on a monopile mounted on a slope are investigated with a numerical wave tank. The experimental and numerical irregular free surface elevations are compared in the frequency-domain for the different locations in the vicinity of the cylinder. A numerical analysis is performed for different wave steepness cases to understand the influence of wave steepness on the breaking irregular wave loads. The wave height transformation and energy level evolution during the wave shoaling and wave breaking processes is investigated. The higher-frequency components generated during the wave breaking process are observed to play a significant role in initiating the secondary force peaks. The free surface elevation skewness and spectral bandwidth during the wave transformation process are analysed and an investigation is performed to establish a correlation of these parameters with the breaking irregular wave forces. The role of the horizontal wave-induced water particle velocity at the free surface and free surface pressure in determining the breaking wave loads is highlighted. The higher-frequency components in the velocity and pressure spectrum are observed to be significant in influencing the secondary peaks in the breaking wave force spectrum.     

Effects of wave directionality on extreme response for a long end-anchored floating bridge

Reliable design codes are of great importance when constructing new civil engineering concepts such as floating bridges. Previously only a scarce number of floating bridges have been built in rough wave conditions and only limited knowledge of the extreme environmental conditions and the associated extreme response exists. To form a better design basis an increased understanding of the sensitivity in the structural response towards changes in short-crested sea parameters is needed. Furthermore, acquiring the necessary accuracy in simulated extreme response is often a computationally expensive endeavour and the number of simulations needed is often based on experience. The present study investigates the wave-induced short-term extreme response of a simplified end-anchored floating bridge concept for several wave environments with a return period of 100 years. The study includes convergence of the coefficient of variation for the extreme response for different realization lengths as well as number of realizations. The sensitivity in the structural response towards different main wave directions and spreading exponents is investigated and includes both transverse and vertical displacement response spectra and extreme Von Mises stress in the bridge girder cross-section. The extreme response is based on an accuracy of 2% in the coefficient of variation equivalent to 40 3-h realizations and a low sensitivity in the response is found for natural occurring spreading exponents and for main wave directions within 15° from beam sea.     

Obtaining the distribution of quiescent periods directly from the power spectral densities of Sea waves

There is a growing practical interest in the ability to increase the sea states at which marine operations can be safely undertaken by exploiting the quiescent periods that are well known to exist under a wide range of sea conditions. While the actual prediction of quiescent periods at sea for the control of operations is a deterministic process, the long term planning of future maritime tasks that rely on these quiescent periods is a statistical process involving the anticipated quiescence properties of the forecasted sea conditions in the geographical region of interest. It is in principle possible to obtain such data in tabular form either large scale simulation or from field data. However, such simulations are computationally intensive and libraries of appropriate field data are not common. Thus, it is clearly attractive to develop techniques that exploit standard wave spectral models for describing the quiescence statistics directly from such spectra. The present study focuses upon such techniques and is a first step towards the production of a computationally low-cost quiescence prediction tool and compares its efficacy against simulations. Two significant properties emerge for a large class of wave spectral models that encompasses the ubiquitous Neumann and Pierson Moskowitz or Bretschneider forms. Firstly, the auto-correlation function of the wave profile that are required to produce the quiescence property can be obtained analytically in terms of standard special functions. This considerably reduces the computational cost making desktop computer-based planning tools a reality. Secondly, for each class of these parametric spectra, the probability of a given number of consecutive wave heights (normalised to the significant wave heights) less than some critical value is in fact independent of absolute wave height. Thus, for a broad class of practically interesting wave spectra all that is required to obtain the statistical distribution of the quiescent periods is simple rescaling.     

Effect of wave nonlinearity on fatigue damage and extreme responses of a semi-submersible floating wind turbine

Floating wind turbine has been the highlight in offshore wind industry lately. There has been great effort on developing highly sophisticated numerical model to better understand its hydrodynamic behaviour. A engineering-practical method to study the nonlinear wave effects on floating wind turbine has been recently developed. Based on the method established, the focus of this paper is to quantify the wave nonlinearity effect due to nonlinear wave kinematics by comparing the structural responses of floating wind turbine when exposed to irregular linear Airy wave and fully nonlinear wave. Critical responses and fatigue damage are studied in operational conditions and short-term extreme values are predicted in extreme conditions respectively. In the operational condition, wind effects are dominating the mean value and standard deviation of most responses except floater heave motion. The fatigue damage at the tower base is dominated by wind effects. The fatigue damage for the mooring line is more influenced by wind effects for conditions with small wave and wave effects for conditions with large wave. The wave nonlinearity effect becomes significant for surge and mooring line tension for large waves while floater heave, pitch motion, tower base bending moment and pontoon axial force are less sensitive to the nonlinear wave effect. In the extreme condition, linear wave theory underestimates wave elevation, floater surge motion and mooring line tension compared with fully nonlinear wave theory while quite close results are predicted for other responses.     

Semi-analytical solution for the water wave diffraction by arrays of truncated circular cylinders in front of a vertical wall

The present study investigates the combined wave field that is induced by the continuous interaction of plane waves with an array of truncated circular cylinders in front of a rigid wall. The long-term goal of the study is the investigation of possible increase in the efficiency of cylindrical Wave Energy Converters (WECs) by putting in the vicinity of the array a barrier to propagation, a wall, that could assist the reflection of the incoming waves. The main task is to develop a generic solution method that is free of conceptual simplifications employed, e.g. by the method of images and the assumption of “pure” wave reflection. To cope with the set task, the proposed method relies on the semi-analytical formulation of the velocity potentials, while the solution is sought by combined expressions that involve polar and elliptical harmonics. The wall is represented as an elliptical cylinder with zero semi-minor axis. This assumption has eventually a beneficial effect to the underlying formulation given that it simplifies significantly the expansions of the involved diffraction potentials.     

Interaction mechanisms among waves,currents and a submerged plate

Wave-induced loads on a submerged plate, representative of submerged breakwater, coastal-bridge deck and a certain type of wave energy converter, in a uniform current are investigated in this study using fully nonlinear numerical wave tanks (NWTs) based on potential flow theory. The coupling effect of wave and current is explored, and the underlying interaction mechanisms of the hydrodynamic forces are described. The presence of a background current modifies the frequency dispersion. It produces changes of the water-surface elevation, and also has an effect on wave-induced loads. Depending on the nonlinearity, higher harmonic wave components are generated above the submerged plate. These contribute to the wave forces. It is found that the horizontal and the vertical force, hence the moment, are affected in the opposite way by the currents. The Doppler shifted effect dominates the vertical force and the moment on the plate. Whereas, the Doppler shifted effect and the generation of higher wave harmonics play opposite roles on the horizontal forces. The contribution of 2^nd order harmonics is found to be up to 30% of the linear component. The current-induced drag force, represented by the advection term ρU∂φ/∂x in the pressure equation, is found to lead to a decrease in the moment for the most range of wavelengths considered, and an increase in the moment for a small range of longer waves.