Higher Wave Steepness Research Articles

WAVE OVERTOPPING MITIGATION BY A VERTICAL WALL OR A WAVE RETURN WALL AT THE END OF A PITCHED ROCK SLOPE

This extended abstract contains two topics: stability of a pitched rock slope (in contrast to randomly placed rock) and mitigation of excessive wave overtopping at an existing rock slope. The stability of a single pitched rock layer could reasonably well be predicted by the Van der Meer formula. The criteria for start of damage and failure, however, become much stricter for a single armour layer. The commonly used EurOtop-equations for wave overtopping were used to fit influence factors for a vertical wall, with and without bullnose, and for a wave return wall. A vertical wall will increase the crest level, where the wave return wall replaces a part of the crest of the rock structure and has the same crest level as the original structure. Test conditions were focused on steep waves (high wave steepness) only, as this is the actual design situation for Singapore structures facing the sea directly.

Numerical analysis of the buoy design to extract the effective kinetic wave energy

In many countries, sea wave energy is becoming more widely recognized as a significant and hopeful resource. The objective of this research is to evaluate the impact of alterations in buoy shape on the efficacy of the wave model by utilizing Computational Fluid Dynamics (CFD) to assess modifications in the buoy's dynamic behavior. The buoy's behavior is simulated using ANSYS Fluent, the volume of fluid approach, the open channel flow module, and 5th order Stokes wave models. To further investigate the wave sensitivity in challenging circumstances, Stokes waves were applied in the shallow domain at high wave steepness. The validation process consisted of a comparative analysis between the practical and mathematical results. The outcomes of a numerical fluid dynamical computation were compared, and laboratory observations were modified. For various configurations of underwater buoyancy, the drag and lift characteristics of numerical results were analyzed. The aim of this study was to identify the optimum buoy shape. The selection of this shape was based on several factors, of which the most significant were the least entropy, as well as the maximum lift and drag coefficient. Ideal shape was determined to be a spherical shape (shape B).

Generation and Absorption of Periodic Waves Traveling on a Uniform Current in a Fully Nonlinear BEM-based Numerical Wave Tank

Accurate and efficient numerical wave generation and absorption of two-dimensional nonlinear periodic waves traveling on a steady, uniform current were carried out in a potential, fully nonlinear numerical wave tank. The solver is based on the Βoundary Εlement Μethod (ΒΕΜ) with linear singularity distributions and plane elements and on the mixed Eulerian–Lagrangian formulation of the free surface equations. Wave generation is implemented along the inflow boundary by imposing the stream function wave solution, while wave absorption at both end-boundaries is effectively treated by introducing absorbing layers. On the absorbing beach side, the outflow boundary condition is modified to ensure that the solution accurately satisfies the dispersion relation of the generated waves. The modification involves a free-parameter that depends on the mass flux through the domain and is determined through a feedback error-correction loop. The developed method provides accurate time domain wave solutions for shallow, intermediate, and deep water depths of high wave steepness (wave heights up to 80% of the maximum value) that remain stable for 150 wave periods. This also holds in case a coplanar or opposing uniform current of velocity up to 20% of the wave celerity interacts with the wave.

Modelling of wave generation in a numerical tank by SPH method

There have been many mathematical and physical modelling strategies to represent a numerical wave tank that can generate the desired wave spectrums. Presently, one of the recent methodologies that have certain intrinsic capabilities for the investigation of free-surface hydrodynamic problems, namely, Smoothed-Particle-Hydrodynamics (SPH) technique, has been utilized for the modelling of a numerical wave tank. The Navier–Stokes and continuity equations are utilized for governing the fluid motion through Weakly Compressible SPH (WCSPH) approach which couples pressure and density by an equation of state. As one of the major numerical treatments, kernel gradient normalization is included into the present SPH method together with the numerical treatments, namely, well-known density smoothing algorithm, hybrid velocity variance-based free surface (VFS), and artificial particle displacement (APD) algorithms. The generation of regular and irregular waves is performed by a moving boundary at the inlet where natural damping is targeted by utilizing a dissipative beach at the end of numerical wave tank. A wide range of test cases in terms of wave-lengths and steepness ratios have been investigated for the regular wave simulations. Although the wave-maker is forced linearly to oscillate sinusoidally at the inlet of the tank, due to the relatively high wave steepness ratios applied, the non-linear character of the free-surface has been clearly observed with the performed Fast Fourier Transform analyses. Wave energy densities of the SPH results have also been compared with the linear theory expectations per unit wave-length. To scrutinize the conditions for the wave-breaking inception, three additional wave steepness values have been simulated at a single wave-length value. As a further examination of the proposed SPH scheme, JONSWAP irregular wave spectrum has been utilized with both flap and piston type moving boundaries. In the light of performed simulations, the proposed SPH numerical scheme can provide robust and consistent results while generating regular and irregular wave systems in deep water conditions. Furthermore, it is observed that it has the capability of capturing the non-linear characteristics of generated waves with high sensitivity, including the wave-breaking phenomenon.

Large eddy simulations of a turbulent channel flow with a deforming wall undergoing high steepness traveling waves

Backward traveling waves over a wall of a fully developed turbulent channel are known to reduce the drag coefficient, flow separation, and turbulence intensity. Based on previous studies of traveling waves with a small steepness (s = a/λ < 0.0625, a: nondimensional amplitude, λ: nondimensional wavelength), it is thought that the nondimensional wave-speed (C = C*/U*, C*: dimensional wave-speed, U*: mean channel velocity) is required to be more than one to have a zero net drag and a high reduction in the turbulent kinetic energy (TKE). This idea is tested here for waves with higher wave steepness (0.05 < s < 0.15) at various wave-speeds using large eddy simulations of a fully developed turbulent channel in which one wall is undergoing a traveling wave. It is found that the increase in wave steepness decreases the wave-speed at which a net zero drag is obtained, e.g., for waves with steepness of s = 0.05, 0.075, and 0.15, the wave-speed is, approximately, C = 1.6 ± 0.1, 0.9 ± 0.1, and 0.7 ± 0.1, respectively. Similarly, the increase in wave steepness decreases the wave-speed at which TKE of the flow in the vicinity of the wave is highly reduced, e.g., qualitatively minimized. In fact, the wave-speeds at which the high reduction in TKE is observed in this study are C = 1.2, 1.2, and 0.6 for waves with wave steepness of 0.05, 0.075, and 0.15, respectively.

Assessment of oscillating water column performance: Influence of wave steepness at various chamber lengths and bottom slopes

In this research, the effect of wave steepness on the hydrodynamic efficiency of an oscillating water column is examined at different chamber lengths and bottom slope angles. Results show that the best device efficiency for low wave frequencies is obtained at high chamber length and for high wave frequencies, the best device performance is achieved at low chamber length. Numerical findings reveal that for high wave steepness, the change in the chamber length has a negligible effect on the device efficiency at low wave frequencies and at high wave frequencies, the best device performance is attained at low chamber length. Results indicate that for the shoreline oscillating water column, the change in the bottom slope angle away from the resonance condition has a negligible effect on the device efficiency and at resonance condition, high bottom slope angle is preferred in order to obtain the best device efficiency. It is found that at high wave steepness, the device efficiency decreases and no specific resonance condition could be observed. It is also shown that the sensitivity of the device efficiency around the optimal device performance to the damping produced by power take-off device decreases as the wave steepness increases.

Observations of Large-Amplitude Mode-2 Nonlinear Internal Waves on the Australian North West Shelf

AbstractLarge-amplitude mode-2 nonlinear internal waves were observed in 250-m-deep water on the Australian North West shelf. Wave amplitudes were derived from temperature measurements using three through-the-water-column moorings spaced 600 m apart in a triangular configuration. The moorings were deployed for 2 months during the transition period between the tropical monsoon and the dry season. The site had a 25–30-m-amplitude mode-1 internal tide that essentially followed the spring–neap tidal cycle. Regular mode-2 nonlinear wave trains with amplitudes exceeding 25 m, with the largest event exceeding 50 m, were also observed at the site. Overturning was observed during several mode-2 events, and the relatively high wave Froude number and steepness (0.15) suggested kinematic (convective) instability was likely to be the driving mechanism. The presence of the mode-2 waves was not correlated with the tidal forcing but rather occurred when the nonlinear steepening length scale was smaller than the distance from the generation region to the observation site. This steepening length scale is inversely proportional to the nonlinear parameter in the Korteweg–de Vries equation, and it varied by at least one order of magnitude under the evolving background thermal stratification over the observation period. Despite the complexity of the internal waves in the region, the nonlinear steepening length was shown to be a reliable indicator for the formation of large-amplitude mode-2 waves and the rarer occurrence of mode-1 large-amplitude waves. A local mode-2 generation mechanism caused by a beam interacting with a pycnocline is demonstrated using a fully nonlinear numerical solution.

The Dimensioning Sea Loads (DIMSELO) project

DIMSELO is a Competence Building for Industry project (KPN), granted by the Norwegian Research Council under the ENERGIX program, which ran from 2013 to 2017. The project’s objective was to quantify the consequences of using advanced sea loads modeling in integrated simulations of offshore wind turbines in shallow to intermediate waters. During the project, engineering hydrodynamics load and wave kinematics models of increasing complexity and fidelity were chosen from the literature and implemented. The effect of different model combinations on the substructure loads was was tested for three reference turbines: a DTU 10 MW rotor positioned on a monopile at a water depth of h = 25 m, on a second monopile at h = 35 m and on a jacket, also at h = 35 m. In this paper, the fatigue loads in a production case for the h = 25 m monopile was calculated via three different load models: the well-known Morison model, the Rainey nonlinear force model and the McCamy-Fuchs linear diffraction model. The models were coupled to kinematics coming both from linear irregular waves and second order irregular waves. The comparison showed that using the McCamy-Fuchs diffraction theory reduced the predicted fatigue damage by 15% with respect to a base case where the Morison load model was used. Nonlinear wave kinematics and nonlinear force models influenced the force calculations but did not alter the total fatigue damage, since the load cases with high wave steepness were less likely to happen.In parallel to the research on engineering models, detailed wave loads models were also developed during DIMSELO. By means of CFD, it was possible to reproduce experimental time series of wave loads on a cylinder induced by regular and irregular nearly-breaking waves. Also, a spectral solver for the fast resolution of the fully nonlinear diffraction problem was devised at DTU during DIMSELO. The solver, which showed encouraging results in the preliminary testing, can be coupled to any nonlinear kinematics solver to calculate the force on a cylinder retaining full nonlinearity and diffraction.

THE USE OF PERFORATED PILE BEAKWATERS TO ATTENUATE WAVES

A laboratory investigation was conducted to compare the transmission characteristics of one-row and two-row submerged perforated pile breakwater models. The laboratory tests were conducted in unidirectional waves with different wave conditions and pile porosity that varied from 0.0625 to 0.48. The influences of water depth, incident wave steepness and porosities were studied. From the experimental results obtained, it was found that when the number of rows tested was increased, more wave energy was dissipated. This resulted in the decrease in transmitted wave heights. When the pile porosity was increased, less wave energy was attenuated, resulting in higher wave transmission coefficient, Kt and the transmission coefficient, Kt decreases as the wave steepness increases for all porosity values. It was also found that lower water depth has a significant influence on the transmission coefficient at higher wave steepness with Kt being less than 0.45 at a water depth below 0.23 m for partially submerged condition compared to Kt being more than 0.50 at water depth above 0.35 m for the submerged condition, for both the one-row and two-row piles respectively.

Computation of Nonlinear Free-Surface Flows by a Meshless Numerical Method

A meshless numerical model for nonlinear free surface water waves is presented in this paper. Using the fundamental solution of the Laplace equation as the radial basis functions and locating the source points outside the computational domain, the problem is solved by collocation of boundary points. The present model is first applied to simulate the generation of periodic finite-amplitude waves with high wave steepness and then is employed to simulate the modulation of monochromatic waves passing over a submerged obstacle. Very good agreements are observed when comparing the present results with an analytical solution, experimental data, and other numerical results.

Control of vortex shedding-induced effects in a sectional bridge model by spanwise perturbation method

An experimental study was conducted to determine the effectiveness of the spanwise sinusoidal perturbation method (SPPM) in controlling vortex-induced vibrations (VIV) in a plate girder bridge section model. The geometric parameters of the plate girder section model were selected to give the maximum VIV response. A SPPM module was attached to both the leading and trailing edges of the section model. Two different SPPM configurations with two different wavelengths and the same amplitude were utilized. Vertical motion responses, surface pressure measurements, as well as hotwire measurements in the wake of the section model were taken. The results revealed that the SPPM with the higher wave steepness distinctively suppressed the VIV responses. The behavior of the model with the SPPM is remarkably different with a fixed section model. Generally, a reduction in the fluctuating surface pressure components is observed, indicating an increase in the degree of steadiness of the flow around the model with either of the two SPPM configurations. However, no qualitative difference could be observed between the effects of the low and high wave steepness configurations. Moreover, wake measurements did not show any distinctive effect for either configuration when compared to the base case.

Non-linear wave-induced transient response of soil around a trenched pipeline

Submarine pipelines are always trenched within a seabed for reducing wave loads and thereby enhancing their stability. Based on Biot's poroelastic theory, a two-dimensional finite element model is developed to investigate non-linear wave-induced responses of soil around a trenched pipeline, which is verified with the flume test results by Sudhan et al. [Sudhan, C.M., Sundar, V., Rao, S.N., 2002. Wave induced forces around buried pipeline. Ocean Engineering, 29, 533–544] and Turcotte et al. [Turcotte, B.R., Liu, P.L.F., Kulhawy, F.H., 1984. Laboratory evaluation of wave tank parameters for wave-sediment interaction. Joseph H. Defree Hydraulic Laboratory Report 84-1, School of Civil and Environmental Engineering, Cornell University]. Non-linear wave-induced transient pore pressure around pipeline at various phases of wave loading is examined firstly. Unlike most previous investigations, in which only a single sediment layer and linear wave loading were concerned, in this study, the influences of the non-linearity of wave loading, the physical properties of backfill materials and the geometry profile of trenches on the excess pore pressures within the soil around pipeline, respectively, were explored, taking into account the in situ conditions of buried pipeline in the shallow ocean zones. Based on the parametric study, it is concluded that the shear modulus and permeability of backfill soils significantly affect the wave-induced excess pore pressures around trenched pipeline, and that the effect of wave non-linearity becomes more pronounced and comparable with that of trench depth, especially at high wave steepness in shallow water.

Refraction—Diffraction of Irregular Waves over a Mound

The transformation of monochromatic and directionally-spread irregular waves passing over a submerged elliptical mound was studied in a controlled laboratory experiment. A directional spectral wave generation was used to generate waves with equal peak frequencies and spectral energy, along with monochromatic waves of equivalent significant height and period. Spectra with both narrow and broad frequency and directional spreads were generated. Results indicate that monochromatic waves provide a poor approximation of irregular wave conditions if there is directional spread or high wave steepness.