Kinematics of overturning solitary waves and their relations to breaker types

Numerical simulations using a full-nonlinear BIM (Boundary Integral Method) potential-theory wave model are carried out to study the internal velocity and acceleration fields of an solitary wave overturning on a reef with vertical face (submerged breakwater) and their relation to breaker type. The simulations make it clear that the jet size normalized by the incident wave height is uniquely governed by the crown height of the reef, while the jet shape is similar and independent of the size. Further, they reveal that the overall internal kinematics of overturning waves is clearly related to the jet size. As the jet size increases and the breaker type changes from spilling to plunging, the kinematics thus become increasingly different from those of steady waves. Water particles with the greatest velocities or accelerations within the wave converge towards the jet. After the breaking, both of the velocities and accelerations almost simultaneously reach extreme values near locations beneath the jet. Some of the extreme values are closely related to the breaker type and can be uniquely determined by substituting the breaker type index into the regression equations suggested here.     

Impulse modelling of wave impact pressures on vertical wall

Breaking waves on coastal structures cause high magnitude impact pressures which may be important for the structural stability. In estimating the impact pressure distribution on the wall, there have been a lot of theoretical and experimental work. The present study is concerned with a theoretical approach which is based on the pressure impulse, to find the impact pressures on vertical wall. The numerical solution of the governing equation is carried out using the boundary element method. The theoretical impact pressures are determined using the experimental values of impact pressure rising time. The computational results of the impact pressures from the pressure impulse model are found to agree well with the experimental data of an earlier study.     

A probability distribution for depth-limited extreme wave heights in a sea state

A model for the depth-limited distribution of the highest wave in a sea state is presented. The distribution for the extreme wave height is based on a probability density function (pdf) for depth-limited wave height distribution for individual waves [Méndez, F.J., Losada, I.J., Medina, R. 2004. Transformation model of wave height distribution. Coastal Eng, Vol. 50, 97:115.] and considers the correlation between consecutive waves. The model is validated using field data showing a good representation of the extreme wave heights in the surf zone. Some important statistical wave heights are parameterized obtaining useful expressions that can be used in further calculations.     

The influence of air and scale on wave impact pressures

Both laboratory and field tests that are described provide new information on the characteristics of wave impacts. Laboratory drop tests conducted using seawater and freshwater demonstrate that maximum impact pressures and rise times are influenced by both the level of aeration and the violence of the impact. A relationship is derived which enables the reduction in impact pressure caused by aeration to be estimated. This relationship is shown to provide a better means of predicting impact pressures in laboratory seawater wave tests from freshwater tests than either the Froude or Cauchy laws. Measurements are presented which show that, due to the different properties of seawater and freshwater, aeration levels are higher in seawater breakers than in freshwater breakers, even at a 1:25 model scale. The ways in which this affects the temporal variation in pressure and the scale relationships are discussed in some detail. Aeration and pressure measurements are also presented for full-scale wave impacts on a breakwater exposed to Atlantic waves. Attention is drawn to the likely role of expelled air and data included which indicate that the equivalent of up to 55% of entrained air does not necessarily prevent the occurrence of high impact pressures with short rise times.     

Laboratory study of wave and turbulence characteristics in narrow-band irregular breaking waves

Wave elevations and water particle velocities were measured in a laboratory surf zone created by the breaking of a narrow-band irregular wave train on a 1/35 plane slope. The incident waves form wave groups that are strongly modulated. It is found that the waves that break close to the shoreline generally have larger wave-height-to-water-depth ratios before breaking than the waves that break farther offshore. After breaking, the wave-height-to-water-depth ratio for the individual waves approaches a constant value in the inner surf zone, while the standard deviation of the wave period increases as the still water depth decreases. In the outer surf zone, the distribution of the period-averaged turbulent kinetic energy is closely correlated to the initial wave heights, and has a wider variation for narrow-band waves than for broad-band waves. In the inner surf zone, the distribution of the period-averaged turbulent kinetic energy is similar for narrow-band waves and broad-band waves. It is found that the wave elevation and turbulent kinetic energy time histories for the individual waves in a wave group are qualitatively similar to those found in a spilling regular wave. The time-averaged transport of turbulent kinetic energy by the ensemble-averaged velocity and turbulence velocity under the irregular breaking waves are also consistent with the measurements obtained in regular breaking waves. The experimental results indicate that the shape of the incident wave spectrum has a significant effect on the temporal and spatial variability of wave breaking and the distribution of turbulent kinetic energy in the outer surf zone. In the inner surf zone, however, the distribution of turbulent kinetic energy is relatively insensitive to the shape of the incident wave spectrum, and the important parameters are the significant wave height and period of the incident waves, and the beach slope.     

Dynamic analysis of a vertical plate exposed to breaking wave impact

From the experimental studies in recent years, it has become known that when a wave breaks directly on a vertical faced coastal structure, high magnitude impact pressures are produced. The theoretical and experimental studies show that the dynamic response of such structures under wave impact loading is closely dependent on the magnitude and duration of the load history. The dynamic analysis and design of a coastal structure can be succeeded provided the design load history for the wave impact is available. Since these types of data are very scarce, it is much more convenient to follow a method which is based on static analysis for the dynamic design procedure. Therefore, to facilitate the dynamic design of a vertical plate that is exposed to breaking wave impact, a multiplication factor called “dynamic magnification factor” is herein presented which is defined as the ratio of the maximum value of the dynamic response to that found by static analysis. The computational results of the present study show that the dynamic magnification factor is a useful ratio to transfer the results of static analysis to the dynamic design of a coastal plate for the maximum impact pressure conditions of p_max/γH₀≤18.     

An extension of the Airy theory for linear waves into shallow water

As a fully developed (Airy) wave propagates from deep into shallow water, its crest becomes more peaked while the trough flattens out. The median crest diameter MCD, defined as the distance between the wave flanks under the crest at a level halfway between the crest and trough, therefore decreases relative to the similarly defined median trough diameter MTD, which remains constant up to the breaking point. The MCD is directly related to other wave characteristics, which enables water particle velocities to be calculated for any water depth without having to recur to more complex, higher-order Stokes, cnoidal or Fenton theories. Over a nearly horizontal bottom, most fully developed wave characteristics can be expressed as functions of the wave period T_w. It is shown that the horizontal particle velocity at the bottom under the breaker crest is at least 9 times faster than under the breaker trough, which explains why sediment is transported landward under fair weather conditions. The proposed equations also shed new light on the formation of spilling, plunging and surging/collapsing breakers.     

An integrated three-dimensional model of wave-induced pore pressure and effective stresses in a porous seabed: II. Breaking waves

The evaluation of the wave-induced liquefaction potential is particularly important for coastal engineers involved in the design of marine structures. Most previous investigations of the wave-induced liquefaction have been limited to two-dimensional non-breaking waves. In this paper, the integrated three-dimensional poro-elastic model for the wave-seabed interaction proposed by [Zhang, H., Jeng, D.-S., 2005. An integrated three-dimensional model of wave-induced pore pressure and effective stresses in a porous seabed: I. A sloping seabed. Ocean Engineering 32(5/6), 701–729.] is further extended to simulate the seabed liquefaction potential with breaking wave loading. Based on the parametric study, we conclude: (1) the liquefaction depth due to breaking waves is smaller than that of due to non-breaking waves; (2) the degree of saturation significantly affects the wave-induced liquefaction depth, and no liquefaction occurs in full saturated seabed, and (3) soil permeability does not only significantly affect the pore pressure, but also the shear stresses distribution.     

Implementation and evaluation of alternative wave breaking formulas in a coastal spectral wave model

This paper describes methods and results of research for incorporating four different parameterized wave breaking and dissipation formulas in a coastal wave prediction model. Two formulations assume the breaking energy dissipation to be limited by the Rayleigh distribution, whereas the other two represent the breaking wave energy by a bore model. These four formulations have been implemented in WABED, a directional spectral wave model based on the wave action balance equation with diffraction, reflection, and wave–current interaction capabilities. Four parameterized wave breaking formulations are evaluated in the present study using two high-quality laboratory data sets. The first data set is from a wave transformation experiment at an idealized inlet entrance, representing four incident irregular waves in a slack tide and two steady-state ebb current conditions. The second data set is from a laboratory study of wave propagation over a complex bathymetry with strong wave-induced currents. Numerical simulation results show that with a proper breaking formulation the wave model can reproduce laboratory data for waves propagating over idealized or complicated bathymetries with ambient currents. The extended Goda wave breaking formulation with a truncated Rayleigh distribution, and the Battjes and Janssen formulation with a bore model produced the best agreement between model and data.     

Determination of wave energy dissipation factor and numerical simulation of wave height in the surf zone

Based on the time-dependent mild slope equation including the effect of wave energy dissipation, an expression for the energy dissipation factor is derived in conjunction with the wave energy balance equation. The wave height of regular and irregular waves is numerically simulated by use of the parabolic mild slope equation considering the energy dissipation due to wave breaking. Comparison of numerical results with experimental data shows that the expression for the energy dissipation factor is reasonable. The effects of the wave breaking coefficient on the breaking point and the distribution of wave height after breaking are discussed through the study of a specific experimental topography.     

Effects of wave age and air stability on whitecap coverage

The paper considers the effects of wave age and air stability on the whitecap coverage at sea. This is made by using the logarithmic mean wind velocity profile including a stability function as well as adopting a recent wave age dependent sea surface roughness formula. The results are valid for wind waves in local equilibrium with the steady wind. Examples of results demonstrate clear effects of wave age and air stability on the whitecap coverage. Comparisons are also made with field measurements by Sugihara et al. [Sugihara, Y., et al., 2007. Variation of whitecap coverage with wave-field conditions. J. Mar. Syst. 66, 47–60], representing unstable air stability conditions. Although the data basis is limited, the wave age independent Charnock sea roughness based predictions capture the main features of the observed whitecap coverage, suggesting a stronger dependence on air stability than on wave age in the data.     

Characteristics of developing waves as a function of atmospheric conditions,water properties,fetch and duration

For any specific wind speed, waves grow in period, height and length as a function of the wind duration and fetch until maximum values are reached, at which point the waves are considered to be fully developed. Although equations and nomograms exist to predict the parameters of developing waves for shorter fetch or duration conditions at different wind speeds, these either do not incorporate important variables such as the air and water temperature, or do not consider the combined effect of fetch and duration. Here, the wind conditions required for a fully developed sea are calculated from maximum wave heights as determined from the wind speed, together with a published growth law based on the friction velocity. This allows the parameters of developing waves to be estimated for any combination of wind velocity, fetch and duration, while also taking account of atmospheric conditions and water properties.     

An experimental study of the wave excitation in the gap between two closely spaced bodies,with implications for LNG offloading

The side-by-side offloading of liquid natural gas (LNG) at offshore terminals involves a fixed and a floating body in close proximity; the offshore terminal being the fixed body and the LNG tanker the floating body. The closeness of the two bodies leads to the formation of a long and relatively narrow gap, within which there is the potential for large amplifications of the water surface elevation. The present paper uses experimental results to characterise both the size and nature of the excitation within the gap. It also illustrates the effect of the vessel motion on this amplification by considering a 1:100 scaled model of an LNG tanker as well as its fixed approximation. It is found that the body's ability to move acts to increase the frequency at which resonant amplification within the gap occurs (the resonance frequency). The incident wave conditions considered include regular and irregular waves in both beam- and head-sea orientations; the latter leading to very different gap end conditions. The nature of the resonant amplification for the floating LNG tanker is shown to be similar for the two orientations, suggesting that the gap end conditions do not drive the resonant amplification. Consideration of the nonlinearity within the gap illustrates that resonant amplification occurs at the resonance frequency, irrespective of whether the fluid motion is first or second harmonic. The present paper provides data relevant to the safe offloading operations of an LNG tanker and demonstrates the importance of incorporating the vessel motion in numerical modelling procedures.     

Experimental and numerical investigation of non-predictive phase-control strategies for a point-absorbing wave energy converter

Phase control may substantially increase the power absorption in point-absorber wave energy converters. This study deals with validation of dynamic models and latching control algorithms for an oscillating water column (OWC) inside a fixed vertical tube of small circular cross-section by small-scale testing. The paper describes experimental and numerical results for the system's dynamics, using simple and practical latching control techniques that do not require the prediction of waves or wave forces, and which will be relevant to any type of point-absorbing devices.In the experimental set-up, the upper end of the tube was equipped with an outlet duct and a shut-off valve, which could be controlled to give a latching of the inner free surface movement. The pressure drop through the open valve is used as a simplified measure of the energy extraction. The control was realized by using the real-time measurement signals for the inner and outer surface displacement.A mathematical model of the system was established and applied in numerical simulation. In the case the OWC's diameter is much smaller than the wavelength and the wave amplitude much smaller than the draft, the free surface movement inside the tube can be described as an oscillating weightless piston. For this hydrodynamic problem an analytical solution is known. In addition, the mathematical model includes the effects of viscous flow losses, the air compressibility inside the chamber and the pressure drop across the valve. Experimental results were used to calibrate some of the model parameters, and the total model was formulated as a coupled system of six non-linear, first-order differential equations. Time-domain integration was used to simulate the system in order to test the control strategies and compare with experimental results.     

An investigation of the velocity field under regular and irregular waves over a sand beach

Near-bed horizontal (cross-shore) and vertical velocity measurements were acquired in a laboratory wave flume over a 1:8 sloping sand beach of finite depth. Data were acquired using a three-component acoustic Doppler velocimeter to measure the velocity field close to, but at a fixed distance from the bed. The near-bed velocity field is examined as close as 1.5 cm above a trough and crest of a ripple under three different types of wave forcing (Stokes waves, Stokes groups, and irregular waves). Although both horizontal and vertical velocity measurements were made, attention is focused primarily on the vertical velocity. The results clearly indicate that the measured near-bed vertical velocity (which was outside the wave-bottom boundary layer) is distinctly nonzero and not well predicted by linear theory. Spectral and bispectral analysis techniques indicate that the vertical velocity responds differently depending on the location over a ripple, and that ripple-induced effects on the velocity field are present as high as 4–8 cm above the bed (for vortex ripples with wavelengths on the order of 8 cm and amplitudes on the order of 2 cm). At greater heights above the bed, the observed wave-induced motion is adequately predicted by the linear theory.     

An experimental investigation of the characteristics of a cylinder interacting with waves and flow in the dominant-load regime

We describe in this paper the experimental investigations of the interaction of a bottom-pivoted vertical cylinder with water waves and flow, to determine the dominant-load-regime map by application of response step functions and response RAO. A rigid circular cylindrical mass-damper-spring oscillator system is investigated in regular waves and uniform flow to determine the response characteristics in the frequency domain. Interaction with waves dominates in the high frequency range f* = f_osc/ω_v = 0.862–1.547, with magnitude in the range of 0.1 rad. On the other hand, interaction with flow dominates at lower frequency range, f* = 0.442–0.862, with magnitude in the range of 0.01 rad. These are caused by the non-overlap peak positions of the magnitude response in waves and flow due to the change in added mass of the cylinder moving in different types of fluid loads. The frequency f* = 0.862 is the point where the dominant factors are transferred. The location of separation points determines the pressure distribution to induce the added mass changed. Separation positions determine the magnitude response, but do not determine the configuration of response RAO. That allows to enhance or reduce the magnitude response of the cylinder by taking advantage of the dominant-load-regime map in the frequency domain.     

An experimental model application of wavescreen: Dynamic pressure, water particle velocity, and wave measurements

This paper analyses the results of an application of a piled wavescreen. Experimental measurements were undertaken in the laboratory conditions for a given structural configuration under the attack of regular and irregular waves. Dynamic pressure distribution along and around the inclined piles was obtained employing pressure transducers. Using these data, in-line dynamic wave forces acting on piles were also determined. Water particle (orbital) velocities were measured at seaward and landward of the wavescreen using two acoustic Doppler velocimeters (ADV) simultaneously. Furthermore, wave data were collected using resistance type wave gauges at the seaward and landward of the structure. Based on those data, wave attenuation performance of the wavescreen was explored for two different depth values. Findings showed that piled wavescreen can provide effective shore protection as an environmentally friendly coastal structure.     

Pore pressures in marine sediments: An overview of measurement techniques and some geological and engineering applications

Pore pressures in the seabed are extremely sensitive to any imposed stress because of the low permeabilities commonly exhibited by marine sediments. Consequently, the measurement of sediment pore pressures can be used to infer either the nature of the imposed stress (if the sediment properties are known) or the physical properties of the sediment (if the imposed stresses are known). Stresses of many different types may be exerted on the seabed either through hydrostatic forces (e.g. tidal and wave effects), or directly by lithospheric forces (e.g. tectonic and thermal forces). Several techniques for measuring in situ pore pressures in the upper few metres of sediments have been developed, and one instrument, the PUPPI, will operate autonomously in water depths up to 6000 m. Basic sediment properties and processes can already be inferred from pore pressure responses using this technique. However, further application and development could greatly enhance its capability, especially for long-term monitoring of sediment conditions. In this Chapter, pore pressure measurement techniques are briefly reviewed and problems are highlighted. An outline is given of some of the many ways in which pore pressure measurements could be used to gain further insight into geological processes and to determine some of the pertinent sediment properties more accurately for engineering applications.     

Experimental study on wave transmission coefficient, mooring lines and module connector forces with different designs of floating breakwaters

This paper presents the results and conclusions obtained from the physical model tests carried out with four different designs of floating breakwaters. Changes from a basic design have been introduced in order to evaluate the improvement in the efficiency as a coastal protection structure. Incident and transmitted waves have been measured, as well as the efforts in the mooring lines and module connectors. It has been found that the width of the pontoons is one of the key design parameters, while small modifications in the floating breakwater's cross section shape are less determinant in its hydrodynamic behaviour and in mechanical loads in the discussed ranges. 2D and 3D tests were conducted, observing the great influence that the wave obliquity has in the module connector forces.     

A set of canonical problems in sloshing, Part I: Pressure field in forced roll—comparison between experimental results and SPH

In this article, impact pressure in the case of shallow water sloshing is investigated experimentally and numerically for forced rolling motion. The maximum values of impact pressures have been found for a frequency lower than the first sloshing frequency. Experimental results are compared with numerical ones obtained using smoothed particle hydrodynamics (SPH). The influence of viscosity and of density re-initialization on the SPH results are discussed. A new method for calculating the pressure on walls with SPH is presented.