The limiting wave height in wind-induced wave trains

The vertical acceleration threshold concept has been applied to evaluate the limiting wave height in the train of wind-induced waves propagated over a horizontal bottom. This concept yields very simple computation of the probability of breaking for stochastic sea in deep and finite water depths. The computations confirmed the available field and laboratory observations that the limiting wave steepness in the deep water is lower than the steepness predicted by Stokes. For shallow water depth, the limiting wave height is smaller than 0.55h. This conclusion is consistent with field as well as wave tank observations.     

Run-up of surface waves on a sea wall built on a convex bottom profile

Wave run-up on a sea wall built on a convex bottom profile is studied in the framework of linear shallow water theory. When the wall is located in “deeper water,” a wave is reflected from the wall without changing its shape and phase, which is fully consistent with classical considerations. If the wall is shifted towards the shore, the shape of the wave changes in a complex way. Note that the wave phase changes to the opposite in the limiting case when the wall is located right on the shore. The role of nonlinear effects is studied by means of numerical simulations using nonlinear shallow water theory. It is shown that the contribution of nonlinear effects and breaking is high on a convex-shaped beach, which makes the structure of the wave field rather complicated.     

浅水极限波浪几何特征的实验研究

该文通过物理模型实验,对浅水区域内的波浪在破碎前极限状态下的几何特征进行了研究。实验基于JONSWAP谱对不规则波浪进行模拟,通过对波群中出现的单体极限波浪进行捕捉并对波形进行测量而得到研究样本。为了考察底坡因素对极限波浪几何特征的影响,实验共考虑了3组大小分别为β=1/15、1/30以及1/45的地形坡度。统计结果表明,在实验所采用的坡度范围内,当地波高与水深对近岸极限波浪的影响最为显著,随着水深与波高因素变化,极限波浪的几何特征也出现明显的改变。坡度因素对极限波陡和偏度的影响很小,可以被忽略,但是对不对称度参数的影响相对比较明显,坡度越陡,不对称程度越剧烈。最后,通过参数化,本文给出了极限波浪几何特征变化的经验公式。     

Hydrodynamic performance of a pile-supported OWC breakwater: An analytical study

A pile-supported OWC breakwater is a novel marine structure in which an oscillating water column (OWC) is integrated into a pile-supported breakwater, with a dual function: generating carbon-free energy and providing shelter for port activities by limiting wave transmission. In this work we investigate the hydrodynamics of this novel structure by means of an analytical model based on linear wave theory and matched eigenfunction expansion method. A local increase in the back-wall draft is adopted as an effective strategy to enhance wave power extraction and reduce wave transmission. The effects of chamber breadth, wall draft and air chamber volume on the hydrodynamic performance are examined in detail. We find that optimizing power take-off (PTO) damping for maximum power leads to both satisfactory power extraction and wave transmission, whereas optimizing for minimum wave transmission penalizes power extraction excessively; the former is, therefore, preferable. An appropriate large enough air chamber volume can enhance the bandwidth of high extraction efficiency through the air compressibility effect, with minimum repercussions for wave transmission. Meanwhile, the air chamber volume is found to be not large enough for the air compressibility effect to be relevant at engineering scales. Finally, a two-level practical optimization strategy on PTO damping is adopted. We prove that this strategy yields similar wave power extraction and wave transmission as the ideal optimization approach.     

Bow impact loading on FPSOs 1—Experimental investigation

Steep wave impact pressures and the structural dynamic response of floating production storage and offloading platform (FPSO) bows are studied using 1:80 scale segmented, instrumented models. The construction of these segmented models is discussed. The ‘new-wave’ theory is adopted and extended to generate steep waves and a limiting form of steep wave that might be found in deep water is proposed. A comparison between linear theoretical, experimental and suggested wave models is made. Experimental results with systemically varying parameters are presented.     

The impact of various methods of wave transfers from deep water to nearshore when determining extreme beach erosion

Several levels of increasing complexity of transferring wave information from offshore to nearshore have been studied to quantify their influence on extreme beach erosion estimates. Beach profiles which have been monitored since 1976 were used to estimate extreme beach erosion and compared to predictions. Examination of the wave propagation assumptions revolves around two types of offshore to nearshore transfer: excluding or including wave breaking and bottom friction. A second complication is whether still water level variations (ocean tide plus storm surge) are included.The inclusion of various combinations of wave propagation processes other than shoaling and refraction in the wave transfer function changes on the extreme erosion distribution tail through lowering estimates above one year return period. This brings the predicted tails closer to the observations, but does not capture the upper limit of storm demand implied by the extensive beach profile data set. Including wave breaking has a marked effect on probabilistic estimates of beach erosion. The inclusion of bottom friction is less significant. The inclusion of still water level variability in the wave transfer calculation had minimal impact on results for the case study site, where waves were transferred from offshore to water at 20 m depth. These changes were put into perspective by comparing them to changes resulting from limiting beach erosion by adjusting the statistical distributions of peak wave height and storm duration to have maximum limits. We conclude that the proposed improvements on wave transformation methods are as significant as limiting wave erosion potential and worth including.     

Forces and moment on a horizontal plate due to wave scattering

Wave reflection and transmission from a fixed horizontal plate have been widely studied but theoretical solutions are only available for certain limiting conditions. A general solution for this wave scattering problem is presented using the finite-element method, covering the whole range of relative depth ratio from shallow to deep water limits and submergence depth ratio from the water surface to the bed. Existing long-wave solutions for the surface plate and the submerged plate have been extended to obtain the hydrodynamic forces and overturning moment exerted on the plate. Results from the finite-element program compare well with these solutions. Variations of the reflection coefficient, wave forces and moment, with the plate width to wave length ratio, relative depth ratio and submergence depth ratio are discussed.     

On the form of crests in limiting gravity waves

Properties of surface singularities and the form of wave crests of limiting gravity waves in steady-state flows of an ideal liquid are considered by analyzing the kinematic boundary condition. It is shown that, for rotational waves, the angle at the crest can have any value from 0° to 180°, while it has the only value 90° in the case of irrotational waves. Two inferences are made from Bernoulli’s integral and the properties of singularities: (i) the Stokes wave is a rotational wave and (ii) no angular points can appear on the profiles of capillary-gravity and capillary waves.     

On the largest wave height in water of constant depth

Experimental evidence of the fact that, both in the laboratory and in the field, the largest wave height to water depth ratio realisable for oscillatory waves propagating in water of constant depth is about 0.55, has been published recently (Nelson, 1985); (Nelson, 1987); (Nelson, 1994). This paper presents various theoretical approaches to estimate this maximum value. In particular, the higher approximations of the Stokes and cnoidal theories give a much higher limiting wave height, close to 0.78 h, which is commonly used in engineering practice.However, the inclusion of higher harmonics, generated by a wave-maker paddle, into the analysis provides maximum wave height less than ≈ 0.6 h, which is in good agreement with observations.     

Wave interaction with a perforated wall breakwater with a submerged horizontal porous plate

This study examines the hydrodynamic performance of a new perforated-wall breakwater. The breakwater consists of a perforated front wall, a solid back wall and a submerged horizontal porous plate installed between them. The horizontal porous plate enhances the stability and wave-absorbing capacity of the structure. An analytical solution based on linear potential theory is developed for the interaction of water waves with the new proposed breakwater. According to the division of the structure, the whole fluid domain is divided into three sub-domains, and the velocity potential in each domain is obtained using the matched eigenfunction method. Then the reflection coefficient and the wave forces and moments on the perforated front wall and the submerged horizontal porous plate are calculated. The numerical results obtained for limiting cases are exactly the same as previous predictions for a perforated-wall breakwater with a submerged horizontal solid plate [Yip, T.L., Chwang, A.T., 2000. Perforated wall breakwater with internal horiontal plate. Journal of Engineering Mechanics ASCE 126 (5), 533–538] and a vertical wall with a submerged horizontal porous plate [Wu, J.H., Wan, Z.P., Fang, Y., 1998. Wave reflection by a vertical wall with a horizontal submerged porous plate. Ocean Engineering 25 (9), 767–779]. Numerical results show that with suitable geometric porosity of the front wall and horizontal plate, the reflection coefficient will be always rather small if the relative wave absorbing chamber width (distance between the front and back walls versus incident wavelength) exceeds a certain small value. In addition, the wave force and moment on the horizontal plate decrease significantly with the increase of the plate porosity.     

Wave interaction with a wave absorbing double curtain-wall breakwater

This study examines the hydrodynamic performance of a wave absorbing double curtain-wall breakwater. The breakwater consists of a seaward perforated wall and a shoreward impermeable wall. Both walls extend from above the seawater to some distance above the seabed. Then the below gap allows the seawater exchange, the sediment transport and the fish passage. By means of the eigenfunction expansion method and a least square approach, a linear analytical solution is developed for the interaction of water waves with the breakwater. Then the reflection coefficient, the transmission coefficient and the wave forces acting on the walls are calculated. The numerical results obtained for limiting cases agree very well with previous predictions for a single partially immersed impermeable wall, the double partially immersed impermeable walls and the bottom-standing Jarlan-type breakwater. The predicted reflection coefficients for the present breakwater also agree reasonable with previous experimental results. Numerical results show that with appropriate structure parameters, the reflection and transmission coefficients of the breakwater may be both below 0.5 at a wide range of the relative water depth. At the same time, the magnitude of wave force acting on each wall is small. This is significant for practical engineering.     

Improvements on Mean Free Wave Surface Modeling

Some new results of the modeling of mean free surface of waves or wave set-up are presented. The stream funetion wave theory is applied to incident short waves. The limiting wave steepness is adopted as the wave breaker indcx in the calculation of wave breaking dissipation. The model is based on Roelvink (1993), but the numerical techniques used in the solution are based on the Weighted-Average Flux (WAF) method (Watson et al. , 1992), with Time-Operator-Split-ting (TOS) used for the treatment of the source terms. This method allows a small number of eomputational points to be used, and is particularly efficient in modeling wave set-up. The short wave (or incident primary wave) energy equation is solved by use of a traditional Lax-Wendroff technique. The present model is found to be satisfactory compared with the measurements conducted by Stive (1983).     

Three-dimensional linear solution for wave propagation with slopingbottom

This paper presents a three-dimensional analytic linear wave solution for surface gravity wave propagation over a sloping bottom that is valid for small, but realistic, slopes. The sloping-bottom linear model is compared to published laboratory data and to predictions of two-dimensional, constant-bottom nonlinear theories. The model is shown to describe the measured wave-height growth in the wave transformation region up to a limiting local Ursell number U_r of 0.35-1.0, depending on the wave type, although, as a linear model, it does not predict the harmonics observed in that range. For U_r<0.35, the harmonics can generally be neglected and the sloping-bottom linear theory agrees closely with both the published wave-height data and third-order Stokes nonlinear theory. As a three-dimensional linear model, superposition can be invoked to synthesize and relate wave structure in the transformation region to complex incident ocean spectra with both wind wave and swell components that arrive with a range of incidence angles. As such, the sloping-bottom linear model presented here should be a convenient useful tool for ocean modeling through a significant portion of the wave transformation region     

Wave setup and setdown generated by obliquely incident waves

An analytical theory is developed for the wave setup and setdown induced by obliquely incident waves on an impermeable swell-built beach profile. The wave setup and setdown are found to decrease as wave obliquity increases. The incorporation of wave obliquity in wave setup and setdown formulation offers the physical reality in engineering applications. The general solutions presented in this paper yield the limiting case of normal wave incidence and the result is consistent with the classical theories published. The present theory is primarily applicable to the spilling and plunging breaker across the surf zone, within which wave amplitude is assumed to be linearly related to the local water depth. Experiments were conducted in a large-scale wave basin to compare with theoretical results and especially to investigate the applicability of this assumption to the case of obliquely incident waves. The dimensionless setup versus the distance offshore within the surf zone is found to depend on wave breaking angle and the shape of the beach profile; and it has a non-zero value at the original shoreline position. This implies that the original shoreline will advance landwards, and that the extent of this movement can be related to wave angle at breaking and the beach profile under consideration. The results of the present theory are in good agreement with experimental data and field measurements available.     

Padé coefficients for the solution of the wave dispersion equation under ice

The equations governing the propagation of linear gravity waves in ice-covered waters of finite depth is delineated for the linear elastic deformation of the ice plates that are modeled as elastically supported. The possible limiting condition for the validity of the assumptions involved in the formulation of the problem is discussed. A solution procedure for the solution of the wave dispersion equation under ice is discussed and a set of coefficients synthesized using the properties of infinite series and Padé approximants. Direct application of these coefficients for the calculation of wave characteristics in ice-covered sea will eliminate the need for iterative procedure, and hence will reduce the computational time. The derived coefficients were used for the computation of the wave characteristics of laboratory simulated waves and compared with the values obtained through iteration and the error was found to be less than 2%.     

Linear analysis of air cushion vehicle seakeeping response

A linearized analysis of the response of an air cushion vehicle running in waves is described. The analysis uses the linear systems approach where the vehicle is considered to be a “black box”, i.e. the response characteristics are determined experimentally from input-output relationships. The wave forces and moments are expressed in a form that produces the proper limiting behavior for infinite wavelength. Predicted motion response is shown to compare well with experimental data.     

Heat and mass transport by weakly non-linear internal waves in the presence of turbulence

The method of asymptotic multiscale expansion is applied to determine the mean current velocity and density fields induced by a packet of internal waves. In the limiting case of a weakly non-linear plane wave, heat, salt, and impulse vertical transport is conditioned by the vertical component of the Stokes drift velocity, which is non-zero, when turbulent viscosity and diffusion are considered. As the wave period decreases, the wave fluxes of heat, salt, and impulse increase. In shallow waters, these fluxes become more vigorous and may be comparable to the respective turbulent flows or even to be more powerful. Translated by Vladimir A. Puchkin.     

Effect of mooring-line stiffness on the performance of a dual coaxial-cylinder Wave-Energy Converter

A point-absorber-type Wave-Energy Converter (WEC) consisting of a floating vertical inner cylinder and an annular outer cylinder that slides along the inner one is considered. The two cylinders heave differently under wave excitation, and wave energy can be harnessed from the relative heave motion between the two cylinders using a Permanent Magnet Linear Generator (PMLG) as the Power Take-Off unit. A mooring cable is attached to the bottom of the inner cylinder. This paper aims to examine the effect of the stiffness of the mooring cable on the performance of the coaxial-cylinder WEC system. The two limiting cases of no mooring cable (freely floating inner and outer cylinders) and an infinitely stiff mooring cable (fixed inner cylinder) were also considered. To perform the analysis, hydrodynamic and interference coefficients of the two heaving cylinders were computed semi-analytically using the method of matched eigenfunction expansions. Experimentally determined viscous corrections on damping were also included in the model in order to have more realistic predictions. The performance of the system in terms of motion responses and capture width were predicted and discussed for both regular and irregular waves. The results of the analysis indicate that both the freely floating design and the design with rigidly moored inner cylinder are viable. The two limiting cases show similar optimal performances, albeit with very different optimal generator damping. However, an ill-chosen mooring-cable stiffness may cause the inner and the outer cylinders to have the same resonance frequency, eliminating the relative heave motion and leading to almost no energy extraction. This situation needs to be avoided when designing the mooring system for a coaxial-cylinder WEC.     

The theoretical study on diagonal wave interaction with perforated-wall breakwater with rock fill

The interaction of diagonal waves with perforated-wall breakwater partially filled with rock fill is studied using the linear potential theory. By means of the matched eigenfunction expansion method, an analytical method is presented to calculate the reflection coefficient and the wave force coefficient of the breakwater. The calculated results of the reflection coefficient for limiting cases are the same to the existing results. The main effect factors of the reflection coefficient and the wave force coefficient are analyzed by numerical examples. With the increasing of thickness of rock fill, the wave force coefficient on the perforated wall generally decreases, while the reflection coefficient increases. With the increasing of the incident angle of the wave, the reflection coefficient of the breakwater first decreases, reaches its minimum, and then increases monotonously.     

Oblique wave diffraction by segmented offshore breakwaters

This paper presents a theoretical model to examine oblique wave diffraction by a detached breakwater system consisting of an infinite row of regularly-spaced thin, impermeable structures located in water of uniform depth. The fluid is assumed incompressible and inviscid and to undergo irrotational motion. Wave heights are assumed to be sufficiently small such that linear wave theory is applicable. The eigenfunction expansion solution of Dalrymple and Martin (1990) for normal wave incidence on this breakwater geometry is modified herein to study oblique wave effects. Numerical results, in the form of contour maps of the relative wave height behind the structure, or complex reflection coefficients, are presented for a range of wave and breakwater parameters. The accuracy of the present model is verified by a comparison with existing results for the limiting cases of an isolated detached breakwater, and a breakwater with a single gap. Also, for the multi-gap breakwater, the present solution is further verified for both normal and oblique wave incidence with results in the open literature.