Energy exchange between the spectral components of surface gravity waves and fourth-order spectra

An attempt is made to relate wave energy transfer in the model wave spectrum to the fourthorder spectra. Calculations were performed using Zakharov's equation for non-resonance energy transfer. It was found that the sign of the wave spectrum derivative (at maximum) always coincides in time with the sign of the fourth order, i.e. the latter may indicate the direction of energy transfer at the wave spectrum maximum observed or modelled at a given moment of time. The initial spectrum is modelled using the JONSWAP spectrum with random phases.Translated by V. Puchkin.     

Spectral evolution of surface waves in a deep sea due to the effect of wave-wave interactions

The wave-wave kinetic equation for surface gravity waves in a deep sea is solved numerically, using the Runge-Kutta technique. Spectral evolution of waves resulted only from their being non-linear, with no wave generation and decaying taking place. To perform computations the JONSWAP-type frequency spectra and a variety of angular wave spectra were used. The angular spectrum of waves turned out to be stable. The frequency spectrum differed from the JONSWAP spectrum in that it had a high-frequency part, which was not similar to the Phillips spectrum. The form of the high-frequency spectral slope was determined as a result of spectral evolution and proved to have the form of the ‘−6’ law. Translated by Vladimir A. Puchkin.     

Wave transmission by overtopping due to random waves

Experimental studies of wave transmission by overtopping for a smooth impermeable breakwater with 1:1.5 slope under both regular and random waves were conducted. A resulting relationship between the transmission coefficient (determined by wave height and wave period) and a breakwater height above mean water level normalized with the height of wave run-up measured directly by capacity wave meter is reported. Meanwhile, their discrepancies in both regular and random waves are also discussed in this study. The authors find also that the transmitted significant wave period by overtopping of random waves may be much longer than those of the incoming wave. This characteristic is especially prominent and probably creates the oscillation phenomenon in the wave basin at the back of breakwater when the breakwater height (above mean water level) to water depth ratio is greater than 0.23 and the incoming wave period is longer than 8 sec.     

高频表面波对定常Ekman流解的影响

基于Jenkins(1989)建立的包含Stokes漂流、风输入和波耗散影响的修正Ekman模型,采用Paskyabi等(2012)使用的推广的Donelan等(1987)中的谱和波耗散函数,并利用Paskyabi等(2012)中修正方法给出的包含高频波的风输入函数,在粘性不依赖于水深及粘性随深度线性变化的条件下,研究了包含高频毛细重力波的随机表面波对Stokes漂流和Song(2009)导出的波浪修正定常Ekman流解的影响。结果表明高频表面波使Stokes漂流在海表面剪切加强,对定常Ekamn流解的影响通常不能忽略,但对Ekman流场的角度偏转影响很小。最后,将考虑高频表面波尾谱影响所估算的定常Ekman流解与已有观测结果以及经典Ekman解进行了比对分析。     

Some applications of maximum entropy spectral estimation to ocean waves and linear systems response in waves

In traditional spectral analysis the use of windows is required because the assumption is made that the data outside the sample are zero. A data window is simply equal to unity inside, and zero outside the sample. This is equivalent to the truncation of the autocovariance function beyond some lag after which zeros are added. In Fast Fourier Transform spectral estimation a spectral window with smaller or greater negative side lobes is used. Any use of windows results in a smearing or spectral leakage that limits the spectral resolution. Maximum entropy spectral estimation (MEM) is equivalent to an extrapolation of the autocovariance function being consistent with some model assumptions. The result of the extrapolation is an increased spectral resolution in the frequency domain. In applications of MEM no kind of windows are used. MEM is applied to describe wind wave scalar spectra. The technique can also be used in the plane to estimate directional spectra. Our results show that MEM is a powerful tool for estimation of scalar spectra and simulation of the sea surface. There are also theoretical reasons for assuming that MEM are superior to traditional methods when only short samples are available. Our preliminary results verify this assumption. We propose a data acquisition system based on MEM, and also show that the response of linear systems can be calculated and simulated by MEM.     

Estimating global shelf sediment mobility due to swell waves

Global climate models (GCMs), such as those produced at the European Centre for Medium-Range Weather Forecasts (ECMWF), generate data that are relevant to the study of marine sedimentary processes. We used estimates of significant wave height and period, derived from an ECMWF GCM, to predict for the first time the area of continental shelves over which sediment is mobilised. The wave climatology was such that 0.1 mm diameter quartz sand had the potential to be mobilised on at least one occasion between July 1992 and July 1995 over 41.6% of the earth's continental shelves. The North Atlantic region has the most energetic global wave climate, strong enough to mobilise 0.1 mm diameter quartz sand to water depths of up to 234 m at least once over a 3-year period.     

Dynamic pressures on inclined cylinders due to freak waves

The dynamic pressure distribution around a cylinder tilted along and against the principal wave direction is measured. The cylinder was exposed to the action of random waves in the presence and absence of extreme waves. Six inclinations from the vertical plane, three along and three against the wave direction, were considered. The cylinder in upright position was also studied. The variation of dimensionless peak pressure (pressure maximum/average highest one-third wave height, H_1/3) with the relative wave height (maximum wave height/H_1/3) for locations facing the wave and at the rear of the cylinder for different angles of inclinations of the cylinder are reported for the two kinds of waves mentioned earlier. The statistical properties of the different asymmetries in the pressure traces are also discussed.     

Bragg reflection of sinusoidal waves due to trapezoidal submerged breakwaters

Numerical and laboratory experiments are performed to investigate characteristics of the Bragg reflection due to multi-arrayed trapezoidal submerged breakwaters. The numerical model is based on the Reynolds averaged Navier–Stokes equations with the VOF method and the k–ε turbulence closure model. As expected, the reflection coefficients increase as the array of submerged breakwaters increases in both laboratory measurements and numerical results. The resonant periods provide similar relative wave numbers regardless of the permeability and the number of arrays. The reflection coefficients due to porous breakwaters are smaller than those due to non-porous breakwaters. The velocity contours for two and three arrays are also described.     

Stem waves along vertical wall due to random wave incidence

This study investigates stem waves, propagating along a vertical wall, due to obliquely incident random waves through laboratory experiments and numerical simulations. Attention is paid to the difference or similarity between the stem waves due to periodic waves and random waves, the nonlinear and linear characteristics, and the effect of wave breaking on the evolution of stem waves. The following were found from this study: as the incident angle of waves become large or the nonlinearity of the incident waves become small, the significant stem wave height, normalized by the incident significant wave height, becomes large. This tendency is the same as that generated by the Stokes waves or cnoidal waves. However, regardless of the nonlinearity of incident waves, the width of stem waves is almost the same. This is a different point between the stem waves due to periodic and random waves. The wave breaking suppresses the growth of the stem waves.     

Pressures and forces on inclined cylinders due to regular waves

The variation of the dynamic pressures around a circular cylinder due to regular waves is studied in a wave basin of constant water depth of 3 m. The measuring segment consisted of 12 pressure transducers placed at an elevation of 0.8 m below the still water level. The tests were conducted with the cylinder axis inclined with respect to the vertical plane along and against wave direction. The results on the variation of dimensionless pressures with the non-dimensional input wave parameters are reported for different angles of orientation of the cylinder. The sectional normal force obtained by integrating the pressures is also presented as a function of wave steepness and the effect of angle of orientation of the cylinder is also reported.     

利用波浪频谱数值模拟畸形波的方法探究

畸形波是一种特殊的波浪,它的波高极高,波峰尖瘦,能量很集中[1].图1是一个比较典型的畸形波[1],这个波列的有效波高是5.65 m,而其中的畸形波波高是有效波高的3.19倍,达到了18.04 m,波峰的高度是13.90 m,波的周期是9.8 s,畸形程度很大.最有名的畸形波是图2给出的1995-01-01-15:20在北海Draupner石油平台记录的波高25.6m的“新年波”,1 200 s长的观测记录显示当时的有效波高是11.92 m,波峰的高度达到18.4 m.由水深70 m,畸形波的特征周期12 s,根据线性色散关系得出波长为220 m.     

On spectral and statistical characteristics of shallow water waves

Spectral, zero up-crossing and Tucker's methods of analysis are examined for shallow water wave records. Among the wave height parameters H_s and are most reliable and consistent irrespective of the analysis technique. Tucker analysis, though simple, seems versatile for estimating these wave height parameters. The standard period parameters are less consistent. For practical purposes every period that might reasonably occur has to be considered along with their corresponding height estimate. Joint distribution of heights and periods is in agreement with the function proposed by CNEXO.     

Dynamic pressures and run-up on semicircular breakwaters due to random waves

The dynamic pressures due to random waves of predefined spectral characteristics exerted on a semicircular breakwater model at five different elevations along the depth are measured. In addition, the wave run-up on the model and its reflection characteristics are measured. The results on the variation of the frequency pressure spectra along the depth and the run-up spectra are reported in this paper. The average spectral characteristics as well as statistical properties of the above two parameters are presented. The average reflection coefficient is reported as a function of the wave steepness, described as the ratio of the significant wave height to the square of the peak period.     

Model tree approach for prediction of pile groups scour due to waves

Scour around piles could endanger the stability of the structures placed on them. Hence, an accurate estimation of the scour depth around piles is very important in coastal and marine engineering. Due to the complex interaction between the wave, seabed and pile group; prediction of the scour depth is not an easy task and the available empirical formulas have limited accuracy. Recently, soft computing methods such as Artificial Neural Networks (ANNs) and Support Vector Machines (SVMs) have been used for the prediction of the scour depth. However, these methods do not give enough insight about the process and are not as easy to use as the empirical equations. In this study, new formulas are given that are easy to use, accurate and physically sound. Available empirical equations for estimating the pile group scour depth such as those of Sumer et al. (1992) and Bayram and Larson (2000), are less accurate compared to the given equations. These equations are as accurate as other soft computing methods such as ANN and SVM. Moreover, in this study, safety factors are given for different levels of acceptable risks, which can be so useful for engineers.     

Gravity torques for surface waves

The effects of the gravity torques acting on the angular momentum of surface gravity waves are calculated theoretically. For short crested waves the gravity torque is caused by the force of gravity on the orbiting fluid particles acting down the slopes of the crests and troughs and in the direction parallel to the crests and troughs. The gravity torque tries to rotate the angular momentum vectors, and thus the waves themselves, counterclockwise in the horizontal plane, as viewed from above, in both hemispheres. The amount of rotation per unit time is computed to be significant assuming reasonable values for the along-crest and trough slopes for waves in a storm area. The gravity torque has a frequency which is double the frequency of the waves. For long crested waves the gravity torque acts in the vertical plane of the orbit and tries to decelerate the particles when they rise and accelerate them when they fall. By disrupting the horizontal cyclostrophic balance of forces on the fluid particles (centrifugal force versus pressure force) the gravity torque accounts qualitatively for the three characteristics of breaking waves: that they break at the surface, that they break at the crest, and that the crest breaks in the direction of wave propagation.     

A fast convolution approach to the transformation of surface gravity waves: Linear waves in 1DH

The transformation of irrotational surface gravity waves in an inviscid fluid can be studied by time stepping the kinematic and dynamic surface boundary conditions. This requires a closure providing the normal surface particle velocity in terms of the surface velocity potential or its tangential derivative. A convolution integral giving this closure as an explicit expression is derived for linear 1D waves over a mildly sloping bottom. The model has exact linear dispersion and shoaling properties. A discrete numerical model is developed for a spatially staggered uniform grid. The model involves a spatial derivative which is discretized by an arbitrary-order finite-difference scheme. Error control is attained by solving the discrete dispersion relation a priori and model results make a perfect match to this prediction. A procedure is developed by which the computational effort is minimized for a specific physical problem while adapting the numerical parameters under the constraint of a predefined tolerance of damping and dispersion error. Two computational examples show that accurate irregular-wave transformation on the kilometre scale can be computed in seconds. Thus, the method makes up a highly efficient basis for a forthcoming extension that includes nonlinearity at arbitrary order. The relation to Boussinesq equations, mild-slope wave equations, boundary integral equations and spectral methods is briefly discussed.     

Seabed shear stress and bedload transport due to asymmetric and skewed waves

A simple conceptual formulation to compute seabed shear stress due to asymmetric and skewed waves is presented. This formulation generalizes the sinusoidal wave case and uses a variable friction factor to describe the physics of the boundary layer and to parameterize the effects of wave shape. Predictions of bed shear stresses agree with numerical computations using a standard boundary layer model with a k–ε turbulence closure. The bed shear stress formulation is combined with a Meyer-Peter and Müller-type formula to predict sheet flow bedload transport under asymmetric and skewed waves for a horizontal or sloping bed. The predictions agree with oscillatory water tunnel measurements from the literature.     

随机波浪中畸形波在三维岛礁地形上的试验研究

在试验水池中,开展了波浪在岛礁地形上演化问题的研究。首先在实验水池中建立了西太平洋某岛礁地形的模型,然后采用改进的JONSWAP谱,由造波机产生不同周期、波高的随机波浪。试验中观察到了不同类型畸形波生成的过程及不同波面形态的畸形波。对偏度、峰度及水深与畸形波要素H_m/H_s（H_m表示波列中的最大波高, H_s为有效波高）的关系进行了详细的分析,同时,对畸形波波高H_fr与偏度的关也进行了分析。通过对试验结果分析,发现峰度与畸形波要素i>H_m/H_s呈正相关, H_fr增大时相应的偏度也会呈现增大的趋势。此外,水深的变化剧烈时（如斜坡、海山位置）有助于畸形波的发生。     

Cyclostrophic balance in surface gravity waves

The cyclostrophic balance (pressure forcevs. force centrifugal force) is shown to be satisfied for all fluid particles in surface gravity waves with sinusoidal form and circular particle orbits. Consequences of the cyclostrophic balance are 1) that the normal dispersion relation for deep water hold and 2) that the orbital radius decrease with increasing depth at the usual exponential rate, from which it follows that the wave pressure and particle speed also decrease with depth exponentially. In addition, the cyclostrophic and hydrostatic balances together predict wave breaking at the crests for amplitudes exceeding one divided by the wave number. In contrast to the traditional perturbation method, based on irrotational flow, the cyclostrophic method does not demand that the amplitude be much less than a wave length and does not require an infinite wave train.     

Theoretical and experimental analysis of tethered buoy instability in gravity waves

The motion of a tethered spherical buoy subjected to incident regular waves was measured in a wave tank. Transverse instability was observed when the period of the wave generated was close to one-half of the natural period of the buoy. The transverse instability confirmed as Mathieu type was predominant at the surface but diminished with increase in the depth of submergence. The stable and unstable zones were determined on the Mathieu's instability diagram. Experimental results were in agreement with the predicted zone of instability for a two degree of freedom oscillation problem of Mathieu type which has a periodically varying spring constant.