Values Of Wave Steepness Research Articles

Influence of Right Triangular Prism Rough Beds on Hydraulic Jumps

A hydraulic jump phenomenon is exciting in turbulent flow as it causes large-scale turbulence and high-energy loss. This paper investigates the hydraulic jump characteristics of right triangular prism rough beds. The renormalization group RNG k-ε turbulent model and the volume of fluid (VOF) method in a CFD model are utilized to simulate hydraulic jumps. A total of 210 numerical simulations of four new types of rough beds were performed with an initial Froude number (Fr1) ranging from 4.8 to 9.4, the non-dimensionless wave steepness values of 0.67 ≤ t/s ≤ 1.33, and the distances between roughness elements of 0 ≤ Ls/y1 ≤ 2.67. This study found that arranging the right triangular prism rough elements in a stilling basin increased bed shear stress and energy loss. At the same time, they reduced sequent depth and jump length by about 22% and 50% compared to a smooth bed, respectively. In addition, the entropy production rates are also used to analyze energy dissipation, which clearly shows that the characteristic shape of a rough bed significantly influences the hydraulic jump length. Equations and plots that specify the relationships between the hydraulic jumps and study parameters are helpful guidelines for defining the rough bed dimension when designing or repairing a stilling basin for low-head irrigation works and highway sewers.

Smoothed particle hydrodynamics study of a heaving point absorber in various waves using wave tank and calm-water models

In this research, the influence of wave parameters on the response of a tuned point absorber was evaluated using the smoothed particle hydrodynamics (SPH) wave tank and calm-water models. In the first model, the device response was obtained under the effect of waves generated by a wavemaker. In the calm-water model, the added mass and hydrodynamic damping coefficients of the device were calculated from a short-time SPH-free decaying test. Then, using the Runge–Kutta method, the governing equation of motion was solved in MATLAB. Both models were verified by previously published experimental tests. Considering the viscous damping makes calm-water model superior to potential-flow models. Meanwhile, the computation time of this model is very lower than wave tank model. For wave steepness values below 8.5% which is more than the upper limit of wave steepness for deep-water waves, both models predicted a direct relationship between wave height and device motion. However, wave tank simulations showed that for steeper waves, the device motion was not significantly affected by the wave height. Moreover, the device response decreased as the wave period moved away from the device's natural period. The predictions of the two models had an average difference below 10%. While in linear conditions, the calm-water model predicted a slightly larger response than the wave tank model; in nonlinear cases, wave tank model predicted slightly higher device motions. This research shows that using the SPH calm water model is an efficient way to investigate wave-point absorber interactions.

A study on ship performance in waves using a RANS solver, part 2: Comparison of added resistance performance in various regular and irregular waves

Commercial ships frequently operate under irregular sea conditions; hence, their performance must be estimated through simulations in a more realistic environment. To date, a number of experiments and numerical studies have been conducted using regular waves to estimate added resistance. In this study, the performance of the KVLCC2 hull considering the added resistance in various regular and irregular waves was evaluated using an unsteady Reynolds-averaged Navier–Stokes solver. Resistance and motion responses were observed for regular waves with various wavelengths, regular waves with various wave steepness, and bichromatic waves superposed with regular waves. The change in resistance performance and damping with respect to motion response based on wave height was analyzed. An irregular wave corresponding to the joint North Sea wave project spectrum under sea state 6 was derived; based on this derived wave, the added resistance in irregular waves was estimated. The added resistance was compared with the estimated value using the spectral method, which was also employed to derive the added resistance under the target sea state using regular wave results. The estimated values differ from the direct calculation results owing to the nonlinearity of resistance in the irregular wave. However, the motion responses showed a similar tendency to those of the regular wave (except for those in the proximity of natural frequency that were relatively large and could be influenced by the wave height), as observed when various wave steepness values were used.

Galilean-transformed solitons and supercontinuum generation in dispersive media

The Galilean transformation is a universal operation connecting the coordinates of a dynamical system, which move relative to each other with a constant speed. In the context of exact solutions of the universal nonlinear Schrödinger equation (NLSE), inducing a Galilean velocity (GV) to the pulse involves a frequency shift to satisfy the symmetry of the wave equation. As such, the Galilean transformation has been deemed to be not applicable to wave groups in nonlinear dispersive media. In this paper, we demonstrate that in a wave tank generated Galilean-transformed envelope and Peregrine solitons show clear variations from their respective pure dynamics on the water surface. The type of deviations depends on the sign of the GV and can be captured by the modified NLSE or the Euler equations. Moreover, we show that positive Galilean-translated envelope soliton pulses exhibit self-modulation. While designated GV and wave steepness values expedite multi-soliton dynamics, the strong focusing of such higher-order coherent waves inevitably lead to the generation of supercontinua as a result of soliton fission. We anticipate that kindred experimental and numerical studies might be implemented in other dispersive wave guides governed by nonlinearity.

WCSPH simulation of the forced response of an attenuator oscillating water column wave energy converter

In this study, a weakly compressible smoothed particle hydrodynamics (WCSPH) model was used to simulate the forced piston motion of water inside a fixed oscillating water column (OWC) wave energy converter. The considered device was a chamber with a complex entrance geometry attached to the rear wall of the wave flume. The effect of an impulse turbine on the chamber was modeled by an equivalent orifice damping force applied on a thin plate. This way, a balance is established between numerical accuracy and efficiency. The simulations were performed for two different wave steepness values of 0.025 and 0.04. To validate the model results, the experimental work performed in the Technical University of Denmark was used. Fourier Transform analysis was performed on the SPH model results and experimental data to obtain the first-harmonic amplitude of the desired parameters. In general, a good correspondence was found between the SPH calculations and the experimental results for the piston motion of the water inside the chamber. However, the SPH results were slightly larger, especially around the resonance period. A possible reason is the placing of the plate above the free surface which might reduce the small sloshing motions of water inside the chamber. Finally, from the heaving velocity of the plate, the flux and pressure drop through the orifice were evaluated. It is shown that all three parameters reach their maximum around the resonance period of the chamber.

THE INFLUENCE OF FORWARD SPEED AND NONLINEARITIES ON THE DYNAMIC BEHAVIOUR OF A CONTAINER SHIP IN REGULAR WAVES

The aim of this paper is to compare the heave and pitch motions for the S175 containership, travelling in head regular waves, obtained from frequency domain linear and time domain partly nonlinear potential flow analyses. The frequency domain methods comprise the pulsating and the translating, pulsating Green’s function methods, with the relevant source distribution over the mean wetted surface of the hull. The time domain method uses the radiation and diffraction potentials related to the mean wetted surface, implemented using Impulse Response Functions (IRF), whilst the incident wave and restoring actions are evaluated on the instantaneous wetted surface. The calculations are carried out for a range of Froude numbers, and in the case of the partly nonlinear method for different wave steepness values. Comparisons are made with available experimental measurements. The discussion focuses on the necessity for a nonlinear approach for predicting the radiation potential and the possible numerical methods for its formulation.

Influence of Following, Regular, and Irregular Long Waves on Wind-Wave Growth with Fetch: An Experimental Study

AbstractA series of experiments were conducted in a wind-wave tank facility in Marseilles (France) to study the effects of preexisting swell conditions (represented by long mechanically generated waves) on wind-wave growth with fetch. Both monochromatic and irregular (JONSWAP-type) long-wave conditions with different values of wave steepness have been generated in the presence of a constant wind forcing, for several wind velocities. A spectral analysis of temporal wave signals combined with airflow measurements allowed for the study of the evolution of both wave systems with the aim of identifying the interaction mechanisms transportable to prototype scale. In particular, a specific method is used to separate the two wave systems in the measured bimodal spectra. In fetch-limited conditions, pure wind-wave growth is in accordance with anterior experiments, but differs from the prototype scale in terms of energy and frequency variations with fetch. Monochromatic long waves are shown to reduce the energy of the wind-waves significantly, as it was observed in anterior laboratory experiments. The addition of JONSWAP-type long waves instead results in a downshift of the wind-wave peak frequency but no significant energy reduction. Overall, it is observed that the presence of long waves affects the wind-wave energy and frequency variations with fetch. Finally, in the presence of JONSWAP-type long waves, variations of wind-wave energy and peak frequency with fetch appear in close agreement with the wind-wave growth observed at prototype scale both in terms of variations and nondimensional magnitude.

Eco-Engineering of Seawalls—An Opportunity for Enhanced Climate Resilience From Increased Topographic Complexity

In the context of “green” approaches to coastal engineering, the term “eco-engineering” has emerged in recent years to describe the incorporation of ecological concepts (including artificially water-filled depressions and surface textured tiles on seawalls and drilled holes in sea structures) into the conventional design process for marine infrastructures. Limited studies have evaluated the potential increase in wave energy dissipation resulting from the increased hydraulic roughness of ecologically modified sea defences which could reduce wave overtopping and consequent coastal flood risks, while increasing biodiversity. This paper presents results of small-scale laboratory investigations of wave overtopping on artificially roughened seawalls. Impulsive and non-impulsive wave conditions with two deep-water wave steepness values (=0.015 and 0.06) are evaluated to simulate both swell and storm conditions in a two-dimensional wave flume with an impermeable 1:20 foreshore slope. Measurements from a plain vertical seawall are taken as the reference case. The seawall was subsequently modified to include 10 further test configurations where hydraulic effects, reflective of “eco-engineering” interventions, were simulated by progressively increasing seawall roughness with surface protrusions across three length scales and three surface densities. Measurements at the plain vertical seawall compared favorably to empirical predictions from the EurOtop II Design Manual and served as a validation of the experimental approach. Results from physical model experiments showed that increasing the length and/or density of surface protrusions reduced overtopping on seawalls. Benchmarking of test results from experiments with modified seawalls to reference conditions showed that the mean overtopping rate was reduced by up to 100% (test case where protrusion density and length were maximum) under impulsive wave conditions. Results of this study highlight the potential for eco-engineering interventions on seawalls to mitigate extreme wave overtopping hazards by dissipating additional wave energy through increased surface roughness on the structure.

Wave RUN-UP Measurements under very oblique wave incidence

Under the scope of the HYDRALAB+ transnational access project, the so-called RODBreak experiment was conducted in the multidirectional wave basin at the Marienwerden facilities of the Leibniz University Hannover (LUH). A stretch of a rubble-mound breakwater was built in the wave basin with a very gentle slope. Its armour layer was made of Antifer cubes, at the roundhead and adjoining trunk, and of rock, at the rest of the trunk. A set of tests was carried out to extend the range of wave steepness values analysed in wave run-up, overtopping and armour layer stability studies, focusing on oblique extreme wave conditions, with incident wave angles from 40º to 90º. The present study focuses on the analysis of measured wave run-up values obtained in the tests and on their on their variability as well as the influence of the wave obliquity and directional spreading. Keywords: rubble-mound breakwaters; run-up; oblique waves; physical modelling; RODbreak.

WAVE RUN-UP AND OVERTOPPING IN RUBBLE-MOUND BREAKWATERS UNDER OBLIQUE WAVE INCIDENCE

The existing data gaps triggered the interest in developing the present experimental work, whose main goal is to contribute to a new whole understanding of the phenomena to mitigate future sea level rise impacts in European coastal structures, including the run-up and overtopping characterization on rough and permeable slopes. The key point is to extend the range of wave steepness values in run-up, overtopping and armour layer stability studies, focusing on oblique extreme wave conditions and on their effects on a sloping breakwater's trunk armour and roundhead. Recorded Presentation from the vICCE (YouTube Link): https://youtu.be/sHxoaocYuL0

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.

Experimental reconstruction of extreme sea waves by time reversal principle

We report an experimental study of the reconstruction of real-ocean rogue waves in a laboratory environment using the time reversal (TR) methodology (Chabchoub & Fink, Phys. Rev. Lett. , vol. 112, 2014, 124101). Three different rogue wave measurements are used to validate the TR approach. The generation and accurate control of target free-surface profiles in a unidirectional wave flume using standard techniques, such as the New Wave theory (Tromans, Anaturk & Hagemeier, Proceedings of the First International Offshore and Polar Engineering Conference , 1991, pp. 64–71), are fairly challenging, especially for very steep and, thus, highly nonlinear extreme waves. The TR method, making use of the time reversibility of wave propagation and symmetry of the governing hydrodynamic equations of motion, leads to a simple two-step experimental procedure, the accuracy of which is investigated in this paper. The use of the TR procedure requires the appropriate Froude scaling in designing the model-scale experiments. The present study represents the first validation of the TR method to realistic irregular seas containing rogue waves. Three extreme wave profiles are tested to assess the applicability of the TR scheme to different wave configurations taking into account variable characteristics. This includes the famed New Year wave. The accuracy of the TR method is demonstrated with varying wave steepness values and propagation distances of the reverse reconstruction. It is demonstrated that the unidirectional TR reconstruction is robust, even in the presence of unavoidable wave breaking, known to be an irreversible process within the framework of any wave hydrodynamic evolution equation, and independently of complex environmental conditions or focusing mechanism at play in the sea.

Experimental investigations on the performance of a fixed-oscillating water column type wave energy converter

Oscillating water column (OWC) type wave energy converters are the most promising candidates to harvest untapped ocean wave energy. OWC front wall opening and power take-off (PTO) damping optimization are very significant for feasible energy extraction. A comprehensive experimental investigation was performed for a bottom-fixed oscillating water column to determine the influence of the underwater opening height of the chamber, power take-off damping and wave steepness on the energy converter efficiency. A broad range of opening heights and power take-off dampings was utilized in physical experiments under various wave steepness values. Water column displacements, velocities and motion behaviors were also examined. Optimal orifice ratios were determined to obtain maximum efficiency under different wave steepness values. Based on the results, the key finding of this study is, for a certain range of wave steepness, optimal damping that should be applied on the system does not only depend on the wave characteristics, but also opening height of the chamber. The motion of water column surface behavior also affects the performance of the converter considerably.

3-D Scale Model Study of Wave Run-Up, Overtopping and Damage in a Rubble-Mound Breakwater Subject to Oblique Extreme Wave Conditions

A set of scale-model tests carried out to enlarge the range of wave steepness values analysed in run-up, overtopping and armour layer stability studies, focusing on oblique extreme wave conditions and on their effects on a gentler slope breakwater’s trunk armour and roundhead, is presented in this paper. A stretch of a rubble mound breakwater (head and part of the adjoining trunk, with a slope of 1(V):2(H)) was built in a wave basin at the Leibniz University Hannover to assess, under extreme wave conditions (wave steepness of 0.055) with different incident wave angles (from 40º to 90º), the structure behaviour in what concerns wave run-up, wave overtopping and damage progression of the armour layer. Two types of armour elements (rock and Antifer cubes) were tested. Non-intrusive methodologies including a new application of laser scanning technique for the assessment of both armour layer damage and wave run-up and overtopping were used. It is expected that such work will contribute also with data to improve empirical formulas as well as to validate complex numerical model for wave-structure interaction.

An entropy-viscosity large eddy simulation study of turbulent flow in a flexible pipe

We present a new approach – the entropy-viscosity method (EVM) – for numerical modelling of high Reynolds number flows and investigate its potential by simulating fully developed incompressible turbulent flow, first in a stationary pipe and subsequently in a flexible pipe. This method, which was first proposed by Guermondet al.(J. Comput. Phys., vol. 230 (11), 2011, pp. 4248–4267), introduces the concept of entropy viscosity, computed based on the nonlinear localized residual obtained from the energy equation. Specifically, this nonlinear viscosity based on the local size of entropy production is added to the spectral element discretization employed in our work for stabilization at insufficient resolution. Unlike its original formulation, which includes anad hoctuneable parameter$\unicode[STIX]{x1D6FC}$, here, we determine the value of$\unicode[STIX]{x1D6FC}$by assuming that the entropy viscosity is analogous to the eddy viscosity of the Smagorinsky model. However, the overall approach has the flavour of the implicit large eddy simulation (ILES) instead of the standard large eddy simulation (LES). Given the empiricism of our approach, we have performed systematic studies of homogeneous isotropic turbulence for validation (see appendix A). We have also carried out a more complete numerical simulation study to investigate incompressible turbulent flow in a stationary pipe at$Re_{D}=5300$and$Re_{D}=44\,000$, following the work of Wu & Moin (J. Fluid Mech., vol. 608, 2008, pp. 81–112) who performed very accurate direct numerical simulations (DNS) of these two cases. We found that the mean flow, turbulence fluctuations, and two-point correlations of the EVM-based LES are in good agreement with the DNS of Wu & Moin despite the fact that we employed grids with resolution two orders of magnitude smaller. If we instead use the standard Smagorinsky model in our simulations, the computations become unstable due to insufficient resolution of the smaller scales. Another important difference is that the entropy-viscosity model scales with the cube of the distance from the wall and approaches zero at the wall, which is theoretically correct, as shown by oura posterioritests. Based on the validated EVM approach, we then simulated fully developed turbulent flow at$Re_{D}=5300$in a flexible pipe subject to prescribed vibrations in the cross-flow plane corresponding to a standing wave of amplitude$A$and wavelength$\unicode[STIX]{x1D706}=3D$, where$D=2R$is the pipe diameter and$R$is the radius. We have simulated 11 cases corresponding to increasing values of wave steepness$s_{o}=2A/\unicode[STIX]{x1D706}$, with$s_{o}\in [0,0.067]$. We found a quadratic dependence of the friction factor on$s_{o}$with the minimum at approximately$s_{o}\approx 0.01$, so, surprisingly, we have a slight decrease in drag at first and then a substantial increase compared to the stationary pipe. To obtain the turbulence statistics, we averaged the simulated flow over twenty time periods at the nodes and anti-nodes separately. We found substantial changes in the mean velocity profile at distances$(1-r)^{+}>5$while the peaks of turbulent intensities were amplified by 50 % in the axial direction and by 200 % in the normal and azimuthal directions at$s_{o}=0.067$. The peak shear stress at the node increased by more than 200 % whereas at the anti-node it attained negative values. Turbulent budgets revealed large changes close to the wall at$(1-r)^{+}<50$while flow visualizations showed that many more strong worm-like vortices were generated in the near-wall regions compared to the stationary pipe. We have also computed various spatio-temporal correlations that show that the pressure fluctuations are very sensitive to the pipe vibration and scale quadratically with$s_{o}$. Both pressure and velocity correlations exhibit cellular patterns consistent with the standing-wave pipe motion.

Propagating Stationary Surface Potential Waves in a Deep Ideal Fluid

A new exact solution of the problem for propagating stationary potential wave of an arbitrary amplitude in a deep ideal homogeneous fluid was constructed. Calculated wavy surface is represented by transcendental Lambert’s complex functions. For a physical interpretation of the results real linear combinations of the solutions were formed. The range of the wave steepness values, in which the real sum of constructed comprehensive solutions describes waves with smooth crests, is defined. In the limiting case of waves with small but finite amplitude as well as infinitesimal amplitude, the real combinations of the solutions are transferred in classical nonlinear and linear asymptotic Stokes expressions. Another real combination of constructed complex solutions describing waves with cusped crests do not fall within the range of conditions for the existence of stationary waves.

Comparison of Artificial Neural Network and Regression Approaches for Evaluation of Hydrodynamic Performance of Quarter Circular Break Water

Quarter-circle Break Water (QBW) is a modified semi-circular breakwater, which are similar to caisson consists of a quarter circular surface facing incident waves, with horizontal bottom and a rear vertical wall and are generally placed on a rubble mound foundation. QBW may be constructed as emerged with and without perforations that may be one side or on either sides. By these perforations, the energy is dissipated owing to the formation of eddies and turbulence is created inside the hollow chamber. In this paper, the data collected from the experimental work carried out at National Institute of Technology, Surathkal is analysed by plotting the non-dimensional graphs of reflection coefficient, reflected wave height and incident wave height for various values of wave steepness. These values are used for prediction of QBW adopting Artificial Neural Network (ANN) and Regression (REG) approaches. In ANN, Multi-Layer Perceptron (MLP) and Radial Basis Function networks are considered for training the network data. Goodness-of-Fit (GoF) test viz., Kolmogorov-Smirnov test statistic and Model Performance Analysis (MPA) viz., correlation coefficient, mean absolute error and model efficiency are applied for checking the adequacy of ANN and REG approaches to the observed data. The results of GoF test and MPA indicates the MLP is better suited for evaluation of hydrodynamic performance of QBW.

The response of a semisubmersible model under focused wave groups: Experimental investigation

In recent years, extreme wave events have occurred more frequently than have been predicted using theoretical methods. It is, therefore, a requirement to investigate the impact of these events on coastal and offshore structures. This paper reports on results of an experimental investigation into the interaction between unidirectional waves and a horizontally moored semisubmersible model. The target crest height was created at a focal point and time using the focused wave technique. Different values of wave steepness were tested in order to ascertain the nonlinear effects on the quality of waves generated by a piston-type wavemaker. The measured crest height was in good agreement with the theoretical one within 4% relative error. The magnitudes of heave and pitch motions of the model were found to increase as the wave steepness increased. Overall, the paper contributes towards establishing the application of focused wave technique to floating offshore platforms.

A CFD model for simulating wave run-ups and wave loads in case of different wind turbine foundations influenced by nonlinear waves

A hydrodynamic simulation of wave run-up heights and wave loads on three types of wind turbine foundations, i.e. monopile, gravity-based and tripod support structures, was conducted using a RANS solver and employing k-ε turbulent closure. Due to the contribution of the present CFD model, a semi-empirical formula is calibrated based on velocity stagnation head theory for crest kinematics. Eventually, the results indicate that the difference among the maximum normalized run-up heights of these support structures is smaller for lower wave steepness than those for higher wave steepness. In contrast, it is shown that the difference among the wave loads of these foundations is larger for lower wave steepness than those for higher wave steepness. A calibrated run-up parameter is also obtained by means of numerical simulation and found that the value of calibrated run-up parameter becomes smaller accompanied with larger values of wave steepness and the maximum normalized run-up height. It is relevant that the tendency of run-up heights is positively correlated with higher nonlinearity, whereas an opposite trend is observed in the relationship between larger calibrated run-up parameter and lower nonlinearity.

An experimental study on deterministic freak waves: Generation, propagation and local energy

An experimental investigation on deterministic freak waves is presented here. Four similar freak wave sequences with different wave steepness values were used as the target waves in the experiments. A phase–amplitude iteration method was adopted to generate these deterministic freak wave sequences in the wave flume. The results demonstrate that the phase iteration considerably improves the modeling in the first optimization and becomes less effective for subsequent optimizations. The method is more likely to achieve well-matching results for small steepness target waves through phase iterations. Wave speeds and wave energy distributions of analyzed freak waves were also investigated. Reasonable estimates of wave speeds were achieved by adopting trough-to-trough periods and wave heights of freak waves according to third-order Stokes wave theory. The quadratic phase couplings between the first-harmonic component and higher-harmonic components were significant.