Influence of processes of nonlinear transformations of waves in the coastal zone on the height of breaking waves

Using data from laboratory, field, and numerical experiments, we investigated regularities in changes in the relative limit height of breaking waves (the breaking index) from peculiarities of nonlinear wave transformations and type of wave breaking. It is shown that the value of the breaking index depends on the relative part of the wave energy in the frequency range of the second nonlinear harmonic. If this part is more than 35%, then the breaking index can be taken as a constant equal to 0.6. These waves are spilling breaking waves, asymmetric on the horizontal axis, and are almost symmetric on the vertical axis. If this part of the energy is less than 35%, then the breaking index increases with increasing energy in the frequency range of the second harmonic. These waves are plunging breaking waves, asymmetric on the vertical axis, and are almost symmetric on the horizontal axis. It is revealed that the breaking index depends on the asymmetry of waves on the vertical axis, determined by the phase shift between the first and second nonlinear harmonic (biphase). It is shown that the relation between the amplitudes of the second and first nonlinear harmonics for an Ursell number less than 1 corresponds to Stokes’ second-order wave theory. The empirical dependences of the breaking index on the parameters of nonlinear transformation of waves are proposed.     

Dispersal of droplets over breaking wind waves under the direct action of wind

This paper describes the dispersal of droplets over breaking wind waves under the direct action of wind, based on a comparison between the actual distribution of droplet velocity and the wind field measured in a wind-wave tank (reference wind speed 16 m sec^–1). The velocity distribution of droplets with a diameterd>0.81 mm over breaking wind waves was measured by Koga (1981). In this paper the wind field over breaking wind waves is measured by a flow visualization technique using styrofoam flakes as a tracer. The comparison allows a clear interpretation of droplet movement over the wave profile, and shows that the horizontal movement of the droplets ofd>0.81 mm is approximately determined by acceleration by the wind while their vertical movement is determined by acceleration due to gravity. These observations offer some support for the dispersion model proposed by Koga and Toba (1981).     

Probability distributions of peaks,troughs and heights of wind waves measured in the black sea coastal zone

The present paper examines the adequacy of different probability density functions to describe the peaks, troughs and peak-to-trough excursions of wind waves measured in the coastal zone of the Bulgarian part of the Black sea. For that purpose various theories for non-Gaussian random process are applied. Some theories depend on the mean, variance and coefficient of skewness γ₃ of the process. Others also take the coefficient of kurtosis γ₄ into consideration. The analyzed field data are gathered in the coastal zone of the Bulgarian part of the Black sea with depth decreasing from 18 to 1.3 m. The measurements are carried out simultaneously for 11 points with time series of 20 min duration. The coefficients of skewness and kurtosis in those time series are expressed as functions of depth and spectral peak frequency. Analogous dependencies on depth of other parameters are also found. As a result of the investigation it is concluded that the probabilities of occurrence of large wave crests and heights are underpredicted by all of the theories considered.     

Experimental investigation of breaking criteria of deepwater wind waves under strong wind action

The present study describes an experimental investigation of breaking criteria of deepwater wind waves under strong wind action. In a wind wave flume, waves were generated using different wind speeds and measured at different locations to obtain wave trains of no, intermittent, or frequent breaking. Water particle movement and free surface elevation were measured simultaneously using a PIV system and a wave gauge, respectively. For wind waves, not all the waves measured at a fixed location are breaking waves, and the breaking of a larger wave is not guaranteed. However, the larger the wave height, the larger the probability of breaking. In order to take as many breaking waves as possible for the cases of frequent breaking, we used the waves whose heights were close to the highest one-tenth wave height. The experimental results showed that the geometric or kinematic breaking criteria could not explain the occurrence of breaking of wind waves. On the other hand, the vertical acceleration beneath the wave crest was close to the previously suggested limit value, −0.5g, when frequent breaking of large waves occurred, indicating that the dynamic breaking criterion would be good for discriminating breaking waves under a strong wind action.     

Simplified method for the calculation of irregular waves in the coastal zone

A method applicable for the estimation of the wave parameters along a set bottom profile is suggested. It takes into account the principal processes having an influence on the waves in the coastal zone: the transformation, refraction, bottom friction, and breaking. The ability to use a constant mean value of the friction coefficient under conditions of sandy shores is implied. The wave breaking is interpreted from the viewpoint of the concept of the limiting wave height at a given depth. The mean and root-mean-square wave heights are determined by the height distribution function, which transforms under the effect of the breaking. The verification of the method on the basis of the natural data shows that the calculation results reproduce the observed variations of the wave heights in a wide range of conditions, including profiles with underwater bars. The deviations from the calculated values mostly do not exceed 25%, and the mean square error is 11%. The method does not require a preliminary setting and can be implemented in the form of a relatively simple calculator accessible even for an inexperienced user.     

Generation of internal waves by a barotropic tide in the coastal zone

Within the framework of the linear theory of long waves, we study internal waves generated by a barotropic tide in a two-layer ocean of variable depth taking into account the influence of the Coriolis force. Barotropic waves run over an extended unevenness of the bottom at an arbitrary angle. This unevenness is regarded as a model of the continental slope and shelf. We establish the dependences of the amplitudes of generated internal waves on the angle of incidence of the barotropic tide, topography of the bottom, and stratification. Translated by Peter V. Malyshev and Dmitry V. Malyshev     

Acoustic measurements of the velocity field beneath shoaling and breaking waves

An acoustic current meter attached to a servo-hydraulic surface-following device was used to obtain near-surface velocity measurements beneath breaking and near breaking surface gravity waves shoaling on a 1:40 beach. The data are compared to velocities predicted by two adaptations of linear theory: superposition and stretching. For unbroken and near breaking waves, the predictions are in close agreement with the measurements. For breaking and broken waves, near surface crest velocity measurements are influenced by air entrainment; trough velocities are relatively well predicted. The problems associated with the acoustic measurement of near-surface velocities are highlighted.     

A method for detecting the breaking of wind-generated waves in deep water

The breaking of wind-generated waves is an important phenomenon in the ocean, having close relation to many aspects of the ocean, such as air-sea interaction, ocean wave dynamics, oceanic remote sensing and ocean engineering. The first problem encountered in both its theoretical study and practical measurement is how to detect the breaking of waves.     

Features of wind field over the sea surface in the coastal area

In this paper we analyze SAR wind field features, in particular the effects of wind shadowing. These effects represent the dynamics of the internal atmospheric boundary layer, which is formed due to the transition of the air flow arriving from the rough land surface to the “smooth” water surface. In the wind-shadowed area, the flow accelerates, and a surface wind stress increases with fetch. The width of the shadow depends not only on the wind speed and atmospheric boundary layer stratification, but also on geographic features such as windflow multiple transformations over the complex surface land–Lake Chudskoe–land–Gulf of Finland. Measurements showed that, in the area of wind acceleration, the surface stress normalized by an equilibrium value (far from the coast) is a universal function of dimensionless fetch Xf/G. Surface wind stress reaches an equilibrium value at Xf/G ≈ 0.4, which is the scale of the planetary-boundary-layer relaxation.     

Turbulent structure in water under laboratory wind waves

The structure of the turbulent boundary layer underneath laboratory wind waves was studied by using a combination of a high-sensitivity thermometer array with a two-component sonic flowmeter. The temperature fluctuations are used to detect movements of water parcels, with temperature as a passive quantity. The turbulence energy was dominant in the frequency range (0.01 0.1 Hz), which was much smaller than the wind-wave frequency (2 5 Hz), and in which the turbulence was anisotropic. There was a frequency range (0.2 2 Hz for velocity, 0.2 5 Hz for temperature fluctuation) where the turbulence was isotropic and had a –5/3 slope in the energy spectrum. These points are the same as those in previous works. However, by analyses of the time series by using a variable-interval time-averaging technique (VITA), it has been found that conspicuous events in this main turbulence energy band are the downward bursting from the vicinity of the water surface. Thus the structure of the water layer underneath the wind waves has characters which are similar to the familiar turbulent boundary layer over a rough solid wall, as already conceived. It has been found that, at the same time, the turbulence energy can be related to quantities of the wind waves (the root mean squared water level fluctuation and the wave peak frequency), for different wind and wave conditions. That is, the turbulence underneath the wind waves develops under a close coupling with the wind waves.     

深水波浪破碎时波浪演化特征实验研究

采用能量聚焦的方式产生深水破碎波,并通过增加输入波陡使发生不同强度的波浪破碎现象。实验中,沿水槽中心位置布置22个浪高仪,分析波浪传播过程中的波面演化特征。对水槽不同位置处波面数据进行波能谱与小波能谱分析,发现在聚焦波传播过程中,低频能量部分保持相对稳定,而一次谐波高频部分先逐渐拓宽,经过破碎区域后又逐渐恢复。能量在高频部分有所损失,这种现象在破碎时更加明显,且破碎强度越大,越显著。波浪未破碎时,由于波浪传播过程中高频部分拓宽,导致聚焦前后特征频率略有增加,特征群速和特征周期略有减小;当波浪破碎时,由于破碎导致的能量损失比较明显,且卷破时更加明显,导致破碎后特征频率减小,特征群速和特征周期增大。     

Nonlinear interaction of internal waves in the coastal zone of the Sea of Japan

Nonlinear interactions of the internal waves of a tidal period with low-frequency synoptic-scale internal waves are studied using instrumental measurements of the current in the coastal zone of the Sea of Japan. In the course of spectral analysis of the data of instrumental measurements, it is found that a maximum in the spectrum of the kinetic energy of coastal waters in the vicinity of the semidiurnal frequency ω₀ is surrounded by satellite maxima whose frequencies obey the relation ω _s = ω₀ ± Ω, where Ω is the characteristic frequency of synoptic-scale internal waves. The spectrum of the anticyclonic current component has a similar structure in the vicinities of the frequency ω₀ and its first and second harmonics. The general theory of nonlinear interactions of weakly dispersive waves is used to solve the problem of modulation and the parametric amplification of tidal internal waves in the coastal zone using low-frequency narrow-band internal waviness. As can be judged from the literature, the effect of parametric modulation of tidal internal waves by low-frequency synoptic-scale internal waves has been recorded in the coastal zone of a tidal sea for the first time.     

Onshore/offshore wind influence on breaking waves: An empirical study

Beach based and in-situ observations of plunging and spilling breakers, with associated localised wind data, have isolated important characteristics regarding breaking waves in the surf zone. Offshore winds enhance the development of plunging breakers; onshore winds, the development of spilling breakers. Extremely strong offshore, or onshore winds, may re-introduce more spilling or plunging breaker-type characteristics, respectively.     

规则波在浅水中运动及破碎的数值计算

利用一维Boussinesq方程描述了在浅水中的波浪运动以及破碎情况。在方程中引入了表面翻滚的概念，认为翻滚的水体是以波速运动的，翻滚的作用表现在水平速度的垂直分布上，产生了附加迁移动量项。通过对Airy波在浅水中运动以及破碎情况的研究，得出的一些结论与Schaeffer和合田的成果吻合良好。     

Preferences of coastal zone user groups regarding the siting of offshore wind farms

Offshore wind power has a large potential as a vast resource for delivering clean and abundant energy on a global scale. However, the siting of offshore wind farms in the coastal zone has negative effects on the seascape. This might be particularly evident in the case if offshore wind farms are located close to areas with recreational activities in the coastal zone. Extending the analysis from a previous investigation of the preference for reducing visual impacts from offshore wind farms, the present paper utilises the same sample representing the Danish population. Based on the stated preferences from a Choice Experiment in a mail survey the preferences for reducing visual disamenities from offshore wind farms among different types of coastal zone users are compared to the preferences of less frequent users of the coastal zone. The results strongly indicate that in addition people who can see offshore wind farms from their residence, anglers and recreational boaters, i.e. users of the coastal zone, significantly perceive the visual impacts to be more negative compared to people who do not use the coastal area for those specific purposes. Furthermore, the results also indicate that respondents who visit the beach on a frequent basis also have stronger preferences for reducing the visual disamenities, when compared to less frequent visitors. As a consequence, the specific users and frequent visitors of the coastal zone are willing to pay approximately twice as much to have future offshore wind farms moved further away from the coast, when compared to less frequent users and visitors. These results display that, given the wind farms are not located at relative large distance from the shore, the recreational value of the coastal use is potentially jeopardised by visual impacts from offshore wind farms. From an energy planner's point of view, these results are noteworthy, as they – everything else being equal – point towards that potential gains in capital cost (investment, construction and running costs) by locating offshore wind farms at relative close distances from the shore might be outweighed by the visual disamenity costs in coastal areas with a large recreational activity. As such, the optimal location, i.e. distance from the shore, of offshore wind farms might be closer to the coast in areas with little recreational activities compared to coastal areas with a higher level of recreational activities.     

Improved coastal boundary condition for surface water waves

Surface water waves in coastal waters are commonly modeled using the mild slope equation. One of the parameters in the coastal boundary condition for this equation is the direction at which waves approach a coast. Three published methods of estimating this direction are examined, and it is demonstrated that the wave fields obtained using these estimates deviate significantly from the corresponding analytic solution. A new method of estimating the direction of approaching waves is presented and it is shown that this method correctly reproduces the analytic solution. The ability of these methods to simulate waves in a rectangular harbor is examined.     

Neotectonic dynamics of the marine coastal zone exemplified by the Antarctic Peninsula

The proposed concept of the “marine coastal zone” (MCZ) is substantiated with considering the role of the neotectonics in the formation and evolution of the corresponding morphologic system using the Antarctic Peninsula as an example. For this purpose, the results of the immediate geologic-geomorphologic observations are correlated with an original schematic neotectonic map compiled for the region in question. It is shown that neotectonic movements are responsible for the block structure of the coastal zone representing its most stable element, which is complicated by subsequent regional exogenic coast-forming processes with the glacial one being dominant. Other aspects of the marine coastal zone influenced by neotectonics are also considered. A new (near-polar) type of the marine coastal zone is defined.