Prediction of breaking wave forces on vertical cylinders

The variation of seawater level resulting from tidal fluctuations is usually neglected in regional groundwater flow studies. Although the tidal oscillation is damped near the shoreline, there is a quasi‐steady‐state rise in the mean water‐table position, which may have an influence on regional groundwater flow. In this paper the effects of tidal fluctuations on groundwater hydraulics are investigated using a variably saturated numerical model that includes the effects of a realistic mild beach slope, seepage face and the unsaturated zone. In particular the impact of these factors on the velocity field in the aquifer is assessed. Simulations show that the tidal fluctuation has substantial consequences for the local velocity field in the vicinity of the exit face, which affects the nearshore migration of contaminant in coastal aquifers. An overheight in the water table as a result of the tidal fluctuation is observed and this has a significant effect on groundwater discharge to the sea when the landward boundary condition is a constant water level. The effect of beach slope is very significant and simplifying the problem by considering a vertical beach face causes serious errors in predicting the water‐table position and the groundwater flux. For media with a high effective capillary fringe, the moisture retained above the water table is important in determining the effects of the tidal fluctuations. Copyright © 2001 John Wiley & Sons, Ltd.

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

INTRODUCTION The wave forces on an offshore structure are determined by a wave theory (e.g., Stokes or Stream Function) which relates the water kinematics (velocity and acceleration) to the wave parameters (height and period), and a theory which relates the resulting pressures on the structure to the predicted water kinematics (e.g., Morison Equation or Refraction Theory). Generally, the Morison Equation is used which incorporates two force coefficients-the drag and inertia coefficients. The wave parameters experienced by a structure during a storm are random. Also, inferred values of the force coefficients from field measurements indicate a random scatter from wave to wave due to the random nature of the processes involved and imperfect wave and hydrodynamic theories. Therefore, for offshore structures the prediction of wave forces and ultimately the selection of design criteria involve both the random nature of the wave parameters (e.g., height) and the uncertainty in the force coefficients. Procedures for selecting wave heights for design criteria have received considerable attention and are well established; however, the problem of considering the uncertainty in the force coefficients has received little attention. Currently there is no rational procedure to generally account for coefficient uncertainty except to use arbitrary, and potentially unrealistic, guidelines such as the mean value plus a multiple of the standard deviation. The purpose of this paper is to provide a rational framework for dealing with the uncertainty in force coefficients. This framework is statistical and incorporates into the force statistics the uncertainty of the force coefficients and the random occurrence of the wave parameters. BACKGROUND The wave forces on an offshore structure are generally determined by the Morison equation (Mathematical Equation Available in Full Paper) and QD and Qr are the drag and inertia forces (respectively) per unit length acting normal to a structural element; CD and Cr are the drag and inertia coefficients (i.e., the force coefficients), v and v are the water velocity and acceleration normal to the element, D is the element diameter and P is the mass density of water. As shown in Appendix I, the maximum total horizontal forces on a vertical cylinder during a wave cycle are (Mathematical Equation Available in Full Paper) which are obtained by integrating (1) over the water depth. FD is the total drag force; Fr is the total inertia force; H is the wave height and s is the wave steepness (height/wave length). The assumptions used to derive (2) are deepwater waves and linear wave theory. Similar expressions have been presented in Ref. 1. Except for the properties of the water and cylinder (p,D), (2) depends only on the force coefficients, CD and Cr, and wave height, H, if the steepness is small (exp(2ns)=1) or constant. It is noted that for these conditions the total forces are independent of wave period.

Numerical simulation of three-dimensional breaking waves and its interaction with a vertical circular cylinder

The main objective of the paper is to investigate wave impact forces from breaking waves on a monopile substructure for offshore wind turbine in shallow waters. This study examines the load assessment parameters relevant for breaking wave forces on a vertical circular cylinder subjected to breaking waves. Experiments are conducted in a shallow water flume and the wave generation is based on piston type wave maker. The experiments are performed with a vertical circular cylinder with diameter, D = 0.20m which represents a monopile substructure for offshore wind turbines with regular waves of frequencies around 0.8Hz. The experimental setup consists of a 1/10 slope followed by a horizontal bed portion with a water depth of 0.8m. Plunging breaking waves are generated and free surface elevations are measured at different locations along the wave tank from wave paddle to the cylinder in order to find the breaking characteristics. Wave impact pressures are measured on the cylinder at eight different vertical positions along the height of the cylinder under breaking waves for different environmental conditions. The wave impact pressures and wave surface elevations in the vicinity of the cylinder during the impact for three different wave conditions are presented and discussed.

In this paper the generation and evolution of an edge-wave packet are studied experimentally and numerically. In the laboratory an edge-wave packet is first generated on a sloping beach by a hinge-type wave-maker. Both the free surface displacement and velocity field are measured along several on-offshore cross sections. Numerical results are also obtained by solving the linear shallow-water wave equations and are compared with experimental data. Numerically predicted wave evolution characteristics are in good agreement with those shown by laboratory data. Analyses of the wave amplitude density spectra of both numerical solutions and experimental data show that wave packets are indeed trapped in the nearshore region and consist of a mixture of Stokes and higher-mode edge waves. Furthermore, the Stokes mode dominates in the low frequency range. Two additional wave-maker designs, i.e., the piston-type and the reverse hinge-type, are investigated numerically. Away from the wave-maker the wave forms (time histories) of the wave packets are insensitive to the details of wave-maker movements. The effects of beach slope on the evolution of wave packets are investigated. The behavior of the velocity field and the attenuation rates of runup amplitudes are also discussed.

In many design problems the sea state is specified as part of the design criteria. For offshore structures it is important to know the maximum probable wave and the maximum probable wave force which might be experienced during the life expectancy of the structure, for example the 50 yr or 100 yr wave and period and the 50 yr or 100 yr wave Based on previous analysis of wave and wave force measurements, practically no correlation was found between the measured apparent wave height and apparent wave force. Several authors have proposed statistical distribution of drag and mass coefficients, with recommendations for use in design. The statistical distribution of the calculated drag (or mass) coefficients has no relationship to the statistical distribution of the measured wave drag forces (or inertial forces). Borgman (1964) has considered the statistical distribution of wave forces. Methods are presented for predicting the probability distributions of peak wave drag and inertial forces, and a method is proposed which might be used to predict the most probable maximum wave force once the sea state is specified. It is found that there is a good correlation between the probability distributions of wave heights and the probability distributions of peak drag forces. For example, if the most probable maximum wave is given from a statistical distribution of wave height, then it is possible to predict the most probable maximum drag (or inertial) force, and the most probable maximum force (combined drag and inertial force).

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.

Little is known about wave forces caused by extreme breaking waves in deep water. This study presents certain results from simulation of the kinematics of plunging breakers in deep water obtained both from carefully controlled laboratory experiments and from numerical simulation. In the experiments extreme waves are generated in three ways:The dispersion properties of gravity waves are used to generate a transient situation in which the energy of the individual waves in a wave train concentrates towards a specified point in time and space, resulting in one extreme wave;Very steep Stokes waves of finite amplitude are forced to break at a selected point in deep water due to superposition of a subharmonic disturbance;Very steep Stokes waves are forced to break at a selected point due to superposition of' a superharmonic disturbance. In the numerical model, the development of the (breaking) wave profile, the particle velocities and the accelerations within the wave are simulated. We exact free-surface conditions. are satisfied, and good results are achieved up to the point where the overhanging crest hits the wave front. Comparison of the plunging breakers generated in the wave flume and calculated numerically, shows good agreement with respect to the wave geometry. The measured and calculated velocities also agree well at depths larger than approximately one wave amplitude below the mean water level. In the wave crest near the plunging jet, the measured velocities are, however, 1.5 times as large as the calculated velocities. This may be due to the difference in the method of generating the plunging breakers in the two cases. Experiments so far have now confirmed that transient, near breaking and breaking waves attain velocities up to 2.8 times the first order phase velocity. The results may be applied to the operation and evaluation of stability of ships under severe sea conditions. Further, they provide the basis for the estimation of wave drag and inertia forces from extreme breaking waves in deep water with many applications for the design and safety of offshore structures. INTRODUCTION In order to evaluate safety at sea, a basic need is a prediction of the characteristics of extreme sea states. There is an extensive literature on the subject of the' mysterious disappearances of ships, both large and small. A high percentage of these mysteries can be solved by even a cursory study of so-called "freak waves" (a freak being "capricious change"), which are more correctly termed episodic waves. By definition an episode is a recurring event, and so it is with huge waves on the continental shelves. Episodic waves occur in virtually all such areas during certain predictable times of the year. The origin of episodic waves is not fully understood. It is believed that a shoaling mechanism, unique to a certain geographic location as well as a particular random phase relationship between waves, can account for the phenomenon.

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

Recently, coastal erosion has been widely in progress and the erosion level becomes also serious in the world wide, espeically in East Sea in Korea. Since it would threaten the life, economics and security risk, it is necessary to much comprehend the reason why coastal erosion has occurred according to the geographical characteristics. Meanwhile, analysis about hydrodynamics of the solitary wave such as tunami in swash zone is needed for the best management practice of coastal erosion. Solitary wave is nonlinear wave and can be reproduced in the laboratoy scale by openning suddenly a sluice gate with water head difference, of which methodology was found in the literature, since it could be simply determined by a significant wave height. Thus, in this sutdy the generation of solitary wave was experimentalized using the sluice gate. Experimental conditions were classified by angles of a beach slope, a water level in a beach slope and a difference of water level between in a headtank and a channel bed. Two kinds of dimensionless analyses based from experimental results in this study were presented; the first analysis indicates nondimensionalization between the wave height and the water level in a beach slope in order to investigate characteristics of solitary wave approaching the beach. The second shows the other nondimensionalization between dynamic pressure and static pressure on a beach slope to investigate the relationship between wave breaking and wave pressure. Under the same conditions as laboratory experiments, the numerical results computed with a SWAN model embedded in FLOW 3D were compared in terms of wave height, and pressure on the beach slope, which shows good agreement with each other. Overall results from this study could provide fundamental hydraulic data for the reliabile verification of numerical simulation results about coastal erosion in swash zone caused by solitary waves.

In the present study, breaking focused wave groups were simulated using open-source Computational Fluid Dynamics model REEF3D in order to investigate the breaking wave impact on scaled (1:10) two-dimensional coastal deck structure with girder. The effect of environmental parameters, such as bottom slope and wave steepness on the breaking and geometric properties of high-crested spilling breakers, was investigated. The effect of the wave breaking location on the impact forces acting on the deck structure located at different airgap positions was studied for three wave impact scenarios: (i) when the wave breaking starts, (ii) when a slightly overturning crest is formed, and (iii) when the wave breaks and a fully overturning crest is formed just before hitting the preceding trough. The peak horizontal impact force was found to be higher when the wave breaks ahead of the structure and the overturning wave crest hits the deck positioned above the still water level. Additionally, the peak vertical impact force attains the peak when the deck is placed at the still water level for different stages of breaking. The peak horizontal impact force shows a parabolic trend, whereas the peak vertical impact forces show a decreasing linear trend with an increase in airgap. Finally, force coefficients are derived for calculating the peak impact force on deck with girders subjected to high-crested spilling breakers.

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.

Finite volume scheme for the solution of 2D extended Boussinesq equations in the surf zone

The combined action of environmental forcing (waves, coastal currents, sediment transport, e.t.c.), the continuously decreasing supply of coastal areas with sediment from rivers, as well as the intense anthropogenic activity, results in the appearance of severe erosion problems in coastal areas and constantly decreasing beach width. A frequently used coastal protection measure is the construction of detached breakwaters parallel to the coastline. Detached breakwaters have a direct effect on the incoming waves, which contributes to the control of coastal sediment transport, hence the morphodynamics of the coastal bed. There are many examples of such structures, the majority of which are emerged breakwaters. Recently, interest has been directed towards the construction of low-crested (LC) and submerged breakwaters due to the reduced construction cost and a more effective harmonization with the natural environment. These structures are characterized by wave overtopping and breaking over their crest in addition to all other coastal processes that are involved with emerged breakwaters. For the proper design of such structures, one critical aspect is the behavior of the induced flow in their vicinity due to their presence. To this purpose, several studies have been carried out in recent years. In particular, Petti et al. (1994) studied experimentally the large scale vortices developed by waves breaking above a submerged breakwater. Mory and Hamm (1997) performed measurements of wave height, surface elevation and wave generated currents around a detached breakwater for incoming regular and irregular waves. Kramer et al. (2005) performed a series of experimental measurements in order to study the waves - LC structure interaction, in terms of flow velocity and turbulence developing around such structures within the European Project DE.LO.S. Garcia et al. (2004), Losada et al. (2005), Johnson et al. (2005) e.t.c. used the database created within the DE.LO.S. project to develop and validate numerical codes for the simulation of wave-induced flow around LC breakwaters. The aim of the present study was the experimental study of the flow developed by waves in the vicinity of an LC rubble mound breakwater with crest level at the water line (zero freeboard). The geometrical scale of the physical model was 1/30. The breakwater was placed on a beach of constant slope 1/15, which is typical of steep beaches in Greece.