Estimation of breaking wave properties and their interaction with a jacket structure

Among different types of loads on jacket structures, wave loads, especially breaking wave loads, are the most likely to threat the stability of the structure; therefore, the correct estimation of the wave loading of an offshore jacket structure is crucial for the design of these structures. Despite the importance of the correct estimation of breaking wave induced forces on jacket structures, so far, no slamming formulae to predict these forces are available in the design standards and guidelines or in other publications. Moreover, the implications of such extreme wave load events and the associated uncertainties for the dynamic response of the entire jacket structure, including the response of the foundation piles, are still not fully clarified. This PhD study attempts to improve the understanding of processes associated with the interaction of waves and jacket structures and to develop reliable wave slamming formulae for the prediction of breaking wave-induced loads on jacket structures. First, the present knowledge is analysed to identify the processes involved in the interaction as well as the related knowledge gaps. Second, the data available from previous tests performed on a truss structure under breaking and non-breaking waves in the Large Wave Flume (GWK tests) in Hannover are analysed to identify the most relevant influencing parameters and to provide reliable slamming formulae for breaking waves on legs and braces of jacket structures. Third, using a CFD model set-up for the waves generated in the large wave flume GWK and a CSD model for the truss structure tested in GWK, the laboratory tests are reproduced and a methodology is proposed to predict total forces induced by near-breaking and breaking waves on jacket structures. Finally, the proposed methodological approach including the slamming force formulae developed in this study is implemented to calculate total forces by breaking waves on a full-scale jacket structure (OC4 jacket). The Finite Element FE model of the OC4 jacket is extended by pile foundation model and the structural performance of the entire structure was examined by comparing the results by those of the numerical models developed for the same jacket structure. Finally, the dynamic response of the jacket structure with pile foundation to breaking waves is systematically analysed to achieve a substantially improved understanding of the processes involved in the wave-jacket-pile foundation interaction.

The wave transfer function derived from the linear wavemaker theory has been widely applied to validate the accuracy of the regular wave. However, it is limited to analyze the waves with large wave steepness, short wavelength, or breaking wave generated right on the wave paddle. By introducing the piston stroke-to-water depth ratio, the empirical formula in the literature is modified to predict both regular and breaking waves according to the wave steepness. Using an experimental wave flume, regular and breaking waves are generated by manipulating the target wave steepness and stroke-to-water depth ratio. The proposed equation is verified in accordance with the experiment results, and optimal variables including energy loss coefficient and breaker index are presented by analyzing the root-mean-square errors. With the developed equation, wave heights and relative depths from any type of piston-type wavemaker can be predicted if the variables of the proposed equation are properly adjusted. Additionally, the numerical wave tank (NWT) is modeled by smoothed particle hydrodynamics (SPH), and the numerically calculated wave heights show good agreement with the proposed equation. The developed methodology can be employed as a guideline toward further studies including analyses of structural behavior under the breaking wave.

An experimental study has been carried out on the forces from breaking waves on a tripod structure located on a shoal. The main purpose was to investigate both horizontal and vertical forces as well as overturning moments due to waves acting on the tripod. In addition, horizontal water particle velocities and crest elevations directly over the shoal have been measured. Nondimensional relations between the maximum depth average particle velocities over the shoal, the wave height, wave period, water depth, and wave crest elevation have been obtained. Further nondimensional relations between the wave crest elevation, wave height, wave period, and water depth have also been obtained. Finally, a simple wave force calculation method was developed that may be used to obtain wave forces on similar structures on other shoals that do not deviate significantly from the conditions used during the present tests.

We examine the implementation of a wave-breaking mechanism into a nonlinear potential flow solver. The success of the mechanism will be studied by implementing it into the numerical model HOS-NWT, which is a computationally efficient, open source code that solves for the free surface in a numerical wave tank using the high-order spectral (HOS) method. Once the breaking mechanism is validated, it can be implemented into other nonlinear potential flow models. To solve for wave-breaking, first a wave-breaking onset parameter is identified, and then a method for computing wave-breaking associated energy loss is determined. Wave-breaking onset is calculated using a breaking criteria introduced by Barthelemy et al. (J Fluid Mech https://arxiv.org/pdf/1508.06002.pdf , submitted) and validated with the experiments of Saket et al. (J Fluid Mech 811:642–658, 2017). Wave-breaking energy dissipation is calculated by adding a viscous diffusion term computed using an eddy viscosity parameter introduced by Tian et al. (Phys Fluids 20(6): 066,604, 2008, Phys Fluids 24(3), 2012), which is estimated based on the pre-breaking wave geometry. A set of two-dimensional experiments is conducted to validate the implemented wave breaking mechanism at a large scale. Breaking waves are generated by using traditional methods of evolution of focused waves and modulational instability, as well as irregular breaking waves with a range of primary frequencies, providing a wide range of breaking conditions to validate the solver. Furthermore, adjustments are made to the method of application and coefficient of the viscous diffusion term with negligible difference, supporting the robustness of the eddy viscosity parameter. The model is able to accurately predict surface elevation and corresponding frequency/amplitude spectrum, as well as energy dissipation when compared with the experimental measurements. This suggests the model is capable of calculating wave-breaking onset and energy dissipation successfully for a wide range of breaking conditions. The model is also able to successfully calculate the transfer of energy between frequencies due to wave focusing and wave breaking. This study is limited to unidirectional waves but provides a valuable basis for future application of the wave-breaking model to a multidirectional wave field. By including parameters for removing energy due to wave-breaking into a nonlinear potential flow solver, the risk of developing numerical instabilities due to an overturning wave is decreased, thereby increasing the application range of the model, including calculating more extreme sea states. A computationally efficient and accurate model for the generation of a nonlinear random wave field is useful for predicting the dynamic response of offshore vessels and marine renewable energy devices, predicting loads on marine structures, and in the study of open ocean wave generation and propagation in a realistic environment.

3D numerical modelling of scour around a jacket structure with dynamic free surface capturing

Breaking waves generated by wave shoaling in coastal areas have a close relationship with various physical phenomena in coastal regions. Therefore, it is crucial to accurately predict breaker indexes such as breaking wave height and breaking depth when designing coastal structures. Many studies on wave breaking have been carried out, and many experimental data have been documented. Representative studies on wave breaking provide many empirical formulas for the prediction of breaking index, mainly through hydraulic model experiments. However, the existing empirical formulas for breaking index determine the coefficients of the assumed equation through statistical analysis of data under the assumption of a specific equation. This study presents an alternative method to estimate breaker index using representative linear-based supervised machine learning algorithms that show high predictive performance in various research fields related to regression or classification problems. Based on the used machine learning methods, a new simple linear equation for the prediction of breaker index is presented. The newly proposed breaker index formula showed similar predictive performance compared to the existing empirical formula, although it was a simple linear equation.

This paper presents new laboratory data on long-wave (surf-beat) forcing by the random breaking of shorter gravity water waves on a plane beach. The data include incident and outgoing wave amplitudes, together with shoreline oscillation amplitudes at long-wave frequencies, from which the correlation between forced long waves and short-wave groups is examined. A detailed analysis of the cross-shore structure of the long-wave motion is presented, and the observations are critically compared with existing theories for two-dimensional surf-beat generation. The surf beat shows a strong dependency on normalized surf-zone width, consistent with long-wave forcing by a time-varying breakpoint, with little evidence of the release and reflection of incident bound long waves for the random-wave simulations considered. The seaward-propagating long waves show a positive correlation with incident short-wave groups and are linearly dependent on short-wave amplitude. The phase relationship between the incident bound long waves and radiated free long waves is also consistent with breakpoint forcing. In combination with previous work, the present data suggest that the breakpoint variability may be the dominant forcing mechanism during conditions with steep incident short waves.

For the design of vertical hydraulic structures pulsating wave forces need to be calculated. The total wave force is a result of every wave component (long waves and short waves) within a wave field. The common formulae are derived for regular or unimodal narrow sea states and use one characteristic wave height and period. Broad-banded spectra like bimodal sea states are present at many locations. Moreover, new hydraulic structures like Panamax or post-Panamax locks do have a large vertical surface exposed to pulsating wave loads. Swell components within the wave spectrum are disproportionally contributing to the total wave force compared to short waves. This depth effect for broad-banded or bimodal wave spectra is not considered by the traditional wave formulae which could result in significant underestimations of wave forces on hydraulic structures. This paper aims to determine the wave loads of irregular non-breaking wave fields under any wave spectrum: narrow banded, broad-banded, or bimodal. Spectral linear wave theory (LWT) is used to transform any wave spectrum to a wave force spectrum. The wave force or wave pressure at any level can directly be evaluated from the wave force spectrum or wave pressure spectrum for any shape of the wave spectrum considered within this research. Spectral LWT is compared to the outcome of wave flume experiments with bimodal seas and other wave force formulae, like the Goda formula and quasi-regular LWT and the NewWave theory. This paper gives a description and evaluation of the spectral LWT applied for bimodal wave spectra and a comparison of the accuracy and validity of other wave force formulae. The peak forces and peak pressures distribution obtained by spectral wave theory compare well to the measurements. It appears that the use of a spectral LWT to obtain characteristic extreme forces improves the accuracy of the extreme load more than the use of a second order wave model with a quasi-regular assumption (i.e. where the spectral shape is not considered). For the typical conditions that occur at hydraulic structures (horizontal bed, intermediate to deep water, non-breaking, and uni- and bimodal seas) the often-used Goda formula can both under of overestimate the peak loads. Goda is well applicable for conditions with (breaking) waves narrow wave spectra and values of kph <0.5.

In this study, the wave energy dissipation over a horizontal slotted plate with a leeside vertical seawall was extensively investigated by analytical and numerical approaches. The analytical model was developed by using the matched eigenfunction expansion method and the energy dissipation model with a porosity-dependent drag coefficient estimated by computational fluid dynamics (CFD) results from the 2D channel flow with symmetric slats. The energy dissipation of a horizontal slotted plate was assessed by analyzing the variation of the reflection coefficient, wave run-up, vertical wave force on the plate, and horizontal wave force on the vertical wall for different submergence depths, porosities, plate lengths, and wave steepnesses. Results from the analytical model were compared extensively with those from CFD simulations. CFD computations were performed by using an incompressible turbulence model based on Reynolds averaged Navier–Stokes equations and volume of fluid method. Overall, a good agreement was observed between the analytical and CFD results. A qualitative numerical analysis showed that the wave dissipation over a horizontal slotted plate was caused by the generation of higher-harmonic waves, wave breaking, and vortices formation near the slotted plate. The presented analytical and numerical models would provide a mutually complementary tool for the accurate and efficient design of a horizontal slotted plate for reducing the reflection coefficients, wave forces, and wave run-up on seawalls.

An ocean wave-based piezoelectric energy harvesting system using breaking wave force

Prediction of breaking wave forces on vertical cylinders

Three-dimensional (3D) directional wave focusing is one of the mechanisms that contributes to the generation of extreme waves, also known as rogue waves, in the ocean. To simulate and analyze this phenomenon, we generate extreme waves in a 3D numerical wave tank (NWT), by specifying the motion of a snake wavemaker. The NWT solves fully non-linear potential flow equations with a free surface, using a high-order boundary element method and a mixed Eulerian–Lagrangian time updating. Some numerical aspects of the NWT were recently improved, such as the accurate computation of higher-order derivatives on the free surface and the implementation of a fast multipole algorithm in the spatial solver. The former has allowed the accurate simulation of 3D overturning waves and the latter has led to at least a one-order of magnitude increase in the NWT computational efficiency. This made it possible to generate finely resolved 3D focused overturning waves and analyze their geometry and kinematics. In this paper, we first summarize the NWT equations and numerical methods. We then introduce a typical simulation of an overturning rogue wave, and analyze the sensitivity of its geometry and kinematics to water depth and maximum angle of directional energy focusing. We find that an overturning rogue wave can have different properties depending on whether it is in the focusing or defocusing phase at breaking onset. The maximum focusing angle and the water depth largely control this situation, and therefore the main features of the rogue wave crest, such as its 3D shape and kinematics.

Simulation with computational fluid dynamics methods is a reliable and important tool for researchers and industry. The present thesis refers to the study of propagation of incident waves nearshore using the open-source software OpenFOAM. Specifically using waves2Foam toolbox and the relaxation zone method, it is possible to make wave generation and absorption zones to simulate a numerical wave tank. At first the linear and non-linear wave theory is referred, as well as the phenomena which are observed when water waves interact with shoaling effects until the surf zone. Subsequently, the basic equations of conservation and their discretization with the Finite Volume Method -FVM are analyzed. Also, the basic processes that must be done for the definition of the numerical wave tank in OpenFOAM are described. In this context, a sensitivity analysis on the parameters of the relaxation zone is performed to find the most efficient application. The numerical experiments, in this thesis, aimed at simulating wave propagation over a submerged shelf of different geometries and the modelling of wave breaking on a slopping beach.

1Determining the largest wave height H which can occur in water of depth d without breaking is a fundamental reference quantity for the design of coastal structures. The ratio of breaking height (Hb) to depth (Hb/d), is known as the breaker index and has been the subject of much research over the past 150 years. Current design guidelines are based on investigations which, predominantly used monochromatic waves, thereby neglecting group effects. Groupiness or height modulation in wave trains is inherent to the free propagation of waves in deep water. Whilst our understanding of the formation and propagation of wave groups remains limited, significant progress has recently been made in the prediction of the onset and strength of breaking of wave groups in deep water. Recent two-dimensional laboratory studies have also shown that wave group effects have a marked affect on wave shoaling and breaking, influencing both the position and form of the breaking waves. These studies have used idealised wave spectra to generate modulating wave groups which are repeatable on a characteristic wave group time scale. Some scenarios yielded breaker indices up to 35% systematically above current design guideline values. Due to limitations of conventional wave probes when used near and within the breaking zone, a laser induced fluorescence (LIF) technique has recently been developed at the Water Research Laboratory. The technique yields high spatial and temporal resolution measurements of propagating wave forms from deep water, through the breaking region and inner surf zone. This technique has been verified using conventional capacitance wave probes and high resolution digital video images with resolution of better than 0.05mm obtained giving errors less than ±0.1 mm. Extensive investigations using repeatable wave groups and incorporating the LIF technique have been completed for a uniform bed slope of 10:1 in which the location of a shoaling bed was incrementally adjusted along the wave tank. In this manner, the shoaling and breaking properties of individual waves within the group could be carefully examined. It was observed that, as a wave group encounters a sloping bed, the behavior of the shoaling wave group is critically affected by the spatial phasing of the group relative to the bed. A critical depth between L0/5 > d > L0/8, where L0 is the deepwater wavelength, has emerged as the primary factor delineating two types of group shoaling. When a wave crest is coincident with the group energy maximum at this critical location, wave breaking tends to occur earlier, in deeper water and in a more gentle manner. However, where there is coincidence of a wave trough with the group energy maximum at this depth, delayed shoaling is observed. Notably, delayed shoaling stabilises the waves within the group, delaying the initiation of breaking and can yield Hb/d ratios up to 38% greater than present design guidelines. Our results show that present design guidelines based primarily on monochromatic waves are not conservative when wave group effects are considered.

An experimental study on wave forces on a vertical cylinder due to spilling breaking and near-breaking wave groups