Note on Salter's energy absorber in random waves

Salter's wave theory energy device has been the object of extensive theoretical and experimental studies during recent years. This paper describes the performance of the device in random waves by means of a numerical study. Different situations are considered.First, the cam is allowed to have one degree of freedom (the cam rolls about a rigid and fixed shaft) and is in a shallow sea where the waves are modeled by the JONSWAP spectrum. Power extraction, efficiency and dynamic response are presented in terms of wind characteristics for a cam radius of 3 m. In the open sea where typical waves are longer and higher, waves are represented by the P-M spectrum and the cam radius is taken to be 7 m. Finally, it is shown for a particular set of design parameters how the efficiency decays and the power extraction decreases with lack of rigidity in the support system.     

Tentative engineering approach to scour around breakwaters in random waves

An approach by which the scour depth and protection layer width around the head of vertical-wall breakwaters, the scour and deposition depths as well as the protection layer widths at the round head of rubble-mound breakwaters in random waves can be derived is presented. Here the formulas for scour depth by Sumer and Fredsøe (1997) for vertical-wall breakwaters for regular waves and Fredsøe and Sumer (1997) for rubble-mound breakwaters for irregular waves are used. They are combined with describing the waves as a stationary Gaussian narrow-band random process to derive the scour and deposition depths as well as protection layer widths in random waves. Comparisons are made between the present approach and the Fredsøe and Sumer (1997) random wave scour data for rubble-mound breakwaters.     

Separation of obliquely incident and reflected irregular waves by the Morlet wavelet transform

An existing 2D time-domain method for separating irregular incident and reflected waves by wavelet transform [Ma et al., 2010. A new method for separation of 2D incident and reflected waves by the Morlet wavelet transform. Coastal Eng., 57(6):597–603] is extended to account for obliquely incident irregular waves propagating over sloping bottoms. The linear shoaling and refraction coefficients are adopted to determine the amplitude and phase changes of waves. The optimal central frequency of the Morlet wavelet is determined by the minimum Shannon wavelet entropy. Numerical tests show that the present method can accurately separate waves over horizontal depths. For waves at sloping bottoms, however, the separation errors increase as bottom slope increases and are significant for waves with incident angle larger than π/3.     

Generalized Haurwitz waves

Waves which propagate along a vertical wall lying in an arbitrary direction on aβ-plane are derived as a generalization of Haurwitz waves (Haurwitz, 1940) whose direction of propagation is restricted to the east-west direction. The waves are classified into two types. One consists of neutral waves, which correspond to a generalization of Haurwitz waves. The other consists of waves with complex wavenumber and without energy flux. The phase of the waves also propagates in the direction normal to the coast in an envelope except for the case in which the coast lies in the east-west direction.     

Local balance in the air-sea boundary processes

A new growth equation for wind waves of simple spectrum is presented upon three basic concepts. The period and the wave height of significant waves in dimensionless forms, which are considered to correspond to the peak frequency and the energy level, respectively, are used as representative quantities of wind waves. One of the three basic concepts is the concept of local balance, and the other two concern the acquisition of wave energy and the dissipation of wave energy, respectively. It is shown from some actual data that the equation, together with two universal constants concerning the acquisition and the dissipation of wave energy (B=6.2×10^?2 andK=2.16×10^?5, respectively), is applied universally to wide ranges of wind waves from those in a wind-wave tunnel to fully developed sea in the open ocean. “The three-second power law for wind waves of simple spectrum”, and a few relations as the lemmas, are derived, such that the mean surface transport due to the orbital motion of wind waves is always proportional to the friction velocity in wind, and that the steepness is inversely proportional to the root of the wave age. It is also derived that the portion of wind stress which directly enters the wind waves decreases exponentially with increasing wave age and is 7.5 % of the total wind stress for very young waves. Also, equations are presented as to the increase of momentum of drift current, and as to the supply of turbulent energy by wind waves into the upper ocean.     

Wave power statistics for individual waves

The paper provides a bivariate distribution of wave power and wave height, as well as a bivariate distribution of wave power and wave period; both bivariate distributions are for individual waves within a sea state. This is relevant for e.g. making assessments of wave power devices and their potential for converting energy from waves. The results can be applied to compare systematically the wave power potential for individual waves in a given sea state at different locations.     

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.     

Internal wave excitation from a collapsing mixed region

The collapse of a uniform density fluid (a “mixed region”) into a surrounding ambient fluid with complex stratification is examined by way of laboratory experiments and fully nonlinear numerical simulations. The analysis focuses upon the consequent generation of internal gravity waves and their influence upon the evolution of the collapsing mixed region. In experiments and simulations for which the ambient fluid has uniform density over the vertical extent of the mixed region and is stratified below, we find the mixed region collapses to form an intrusive gravity current and internal waves are excited in the underlying stratified fluid. The amplitude of the waves is weak in the sense that the intrusion is not significantly affected by the waves. However, scaling the results to the surface mixed layer of the ocean we find that the momentum flux associated with the waves can be as large as 1 N/m². In simulations for which the ambient fluid is stratified everywhere, including over the vertical extent of the mixed region, we find that internal waves are excited with such large amplitude that the collapsing mixed region is distorted through strong interactions with the waves.     

Propagating tsunami wave and subsequent resonant response signals detected by HF radar in the Kii Channel,Japan

Signals from the tsunami waves induced by the March 11, 2011 moment magnitude (M_w) 9.0 Tohoku-Oki earthquake and from subsequent resonances were detected as radial velocity variability by a high-frequency ocean surface radar (HF radar) installed on the eastern coast of the Kii Channel, at a range of about 1000 km from the epicenter along the eastern to southern coasts of Honshu Island. A time–distance diagram of band-passed (9–200 min) radial velocity along the beam reveals that the tsunami waves propagated from the continental shelf slope to the inner channel as progressive waves for the first three waves, and then natural oscillations were excited by the waves; and that the direction of the tsunami wave propagation and the axis of the natural oscillations differed from that of the radar beam. In addition, spectral analyses of the radial velocities and sea surface heights obtained in the channel and on the continental shelf slope suggest complex natural oscillation modes excited by the tsunami waves.     

Sediment transport and beach morphodynamics induced by free long waves,bound long waves and wave groups

New laboratory data are presented on the influence of free long waves, bound long waves and wave groups on sediment transport in the surf and swash zones. As a result of the very significant difficulties in isolating and identifying the morphodynamic influences of long waves and wave groups in field conditions, a laboratory study was designed specifically to enable measurements of sediment transport that resolve these influences. The evolution of model sand beaches, each with the same initial plane slope, was measured for a range of wave conditions, firstly using monochromatic short waves. Subsequently, the monochromatic conditions were perturbed with free long waves and then substituted with bichromatic wave groups with the same mean energy flux. The beach profile changes and net cross-shore transport rates were extracted and compared for the different wave conditions, with and without long waves and wave groups. The experiments include a range of wave conditions, e.g. high-energy, moderate-energy, low-energy waves, which induce both spilling and plunging breakers and different turbulent intensities, and the beaches evolve to form classical accretive, erosive, and intermediate beach states. The data clearly demonstrate that free long waves influence surf zone morphodynamics and promote increased onshore sediment transport during accretive conditions and decreased offshore transport under erosive conditions. In contrast, wave groups, which can generate both forced and free long waves, generally reduce onshore transport during accretive conditions and increase offshore transport under erosive conditions. The influence of the free long waves and wave groups is consistent with the concept of the relative fall velocity, H/w_sT, as a dominant parameter controlling net beach erosion or accretion. Free long waves tend to reduce H/w_sT, promoting accretion, while wave groups tend to increase the effective H/w_sT, promoting erosion.     

Tentative engineering approach to scour around spherical bodies in random waves

An approach by which the scour depth around a spherical body and the self-burial depth of such a body in random waves can be derived is presented. Here the formulas for scour and self-burial depths of a spherical body by Truelsen et al. [Truelsen C, Sumer BM, Fredsøe J. Scour around spherical bodies and self- burial. ASCE J Waterway Port Coast Ocean Eng 2005;131(1):1–13] for regular waves are used. They are combined with describing the waves as a stationary Gaussian narrow-band random process to derive the scour and self-burial depths in random waves.     

Placement Effect on the Stability of Tetrapod Armor Unit on Breakwaters in Irregular Waves

Tetrapod, one of the well-known artificial concrete units, is frequently used as an armor unit on breakwaters. Two layers of tetrapod units are normmaly placed on the breakwaters with different placement methods. In this study, the stability of tetrapod units with two different regularly placement methods are investigated experimentally in irregular waves. Stability coefficients of tetrapod units for both placement methods are obtained. The important characteristic wave parameters of irregular waves causing the same damage ratio as those of the regular waves are also determined. It reveals that the average of one-tenth highest wave heights within the wave train (H_1/10) causes the similar damage as regular waves.     

Large amplitude, leaky, island-generated, internal waves around Palau, Micronesia

Three years of temperature data along two transects extending to 90 m depth, at Palau, Micronesia, show twice-a-day thermocline vertical displacements of commonly 50–100 m, and on one occasion 270 m. The internal wave occurred at a number of frequencies. There were a number of spectral peaks at diurnal and semi-diurnal frequencies, as well as intermediate and sub-inertial frequencies, less so at the inertial frequency. At Palau the waves generally did not travel around the island because there was no coherence between internal waves on either side of the island. The internal waves at a site 30 km offshore were out-of-phase with those on the island slopes, suggesting that the waves were generated on the island slope and then radiated away. Palau Island was thus a source of internal wave energy for the surrounding ocean. A numerical model suggests that the tidal and low-frequency currents flowing around the island form internal waves with maximum wave amplitude on the island slope and that these waves radiate away from the island. The model also suggests that the headland at the southern tip of Palau prevents the internal waves to rotate around the island. The large temperature fluctuations (commonly daily fluctuations ≈10 °C, peaking at 20 °C) appear responsible for generating a thermal stress responsible for a biologically depauperate biological community on the island slopes at depths between 60 and 120 m depth.     

Infra-gravity wave generation by the shoaling wave groups over beaches

A physical parameter, μb, which was used to meet the forcing of primary short waves to be off-resonant before wave breaking, has been considered as an applicable parameter in the infra-gravity wave generation. Since a series of modulating wave groups for different wave conditions are performed to proceed with the resonant mechanism of infra-gravity waves prior to wave breaking, the amplitude growth of incident bound long wave is assumed to be simply controlled by the normalized bed slope, βb. The results appear a large dependence of the growth rate, α, of incident bound long wave, separated by the three-array method, on the normalized bed slope, βb. High spatial resolution of wave records enables identification of the cross-correlation between squared short-wave envelopes and infra-gravity waves. The cross-shore structure of infra-gravity waves over beaches presents the mechanics of incident bound- and outgoing free long waves with the formation of free standing long waves in the nearshore region. The wave run-up and amplification of infra-gravity waves in the swash zone appear that the additional long waves generated by the breaking process would modify the cross-shore structure of free standing long waves. Finally, this paper would further discuss the contribution of long wave breaking and bottom friction to the energy dissipation of infra-gravity waves based on different slope conditions.     

Air-Sea Interactions under the Existence of Opposing Swell

Data of a comprehensive laboratory study on the coexistent system of wind waves and opposing swell (Mitsuyasu and Yoshida, 1989) have been reanalyzed to clarify the air-sea interaction phenomena under the coexistence of wind waves and swell. It is shown that the magnitude of the decay rate of swell due to an opposing wind is almost the same as that of the growth rate of swell caused by a following wind, as measured by Mitsuyasu and Honda (1982). The decay rate is much smaller than that obtained recently by Peirson et al. (2003), but the reason for the disagreement is not clear at present. The effect of an opposing swell on wind waves is very different from that of a following swell; wind waves are intensified by an opposing swell while they are attenuated by a following one. The phenomenon contradicts the model of Phillips and Banner (1974), but the reason for this is not clear at this time. The high-frequency spectrum of wind waves shows a small increase of the spectral density. Wind shear stress increases a little due to the effect of opposing swell. The intensification of wind waves by opposing swell and the small increase of the spectral density in a high-frequency region can be attributed to the increase of wind shear stress. Such organized phenomena lead to the conclusion that the hypothesis of local equilibrium for pure wind waves (Toba, 1972) can also be satisfied for wind waves that coexist with opposing swell. The recent finding of Hanson and Phillips (1999) can be explained by this mechanism.     

On the nonlinear interactions in triads of edge waves on the sea shelf

We study nonlinear three-wave interactions between edge waves propagating in the same direction over the shelf step. The conditions of synchronism are determined and the coefficient of interaction is computed for the cases where the waves of the five lowest modes participate in the interaction. The space-time dynamics is studied by analyzing, as an example, a single triad of edge waves. The possibility of interaction of edge waves in the regions with actual topography is demonstrated. __________ Translated from Morskoi Gidrofizicheskii Zhurnal, No. 3, pp. 3–19, May–June, 2008.     

南海灾害性波浪基本特征研究

本文基于1991-2016年全球卫星高度计融合数据对南海灾害性波浪基本特征进行了分析，根据灾害性波浪诱发天气类型不同，将其分为"台风浪"和"非台风浪"。依此主线，对两类波浪在南海不同海域的特征进行了研究，并提出了用于定量研究两类波浪强度关系的台风浪权重系数（W），得到了两类波浪在南海相对强弱关系的分布规律，量化研究了南海灾害性波浪的特征。本文以卫星高度计波高数据为样本进行了极值分析，得到了南海重现期波浪要素整体分布规律，研究发现W值大小与广义极值曲线类型显著相关。     

基于VMD对SAR海洋内波参数的自动反演

经验模态分解(empirical mode decomposition,简称EMD)是反演海洋内波参数的有效方法之一,但由于EMD存在模态混叠等问题,对海洋内波进行参数反演时会产生一定误差。相比较于EMD,变分模态分解(variational mode decomposition,简称VMD)能够有效地抑制模态混叠现象。为了更好地对海洋内波进行参数反演,提出了一种基于VMD对合成孔径雷达(synthetic aperture radar,简称SAR)遥感图像中的内波参数进行自动反演的方法。该方法先对SAR图像进行Canny处理,获取图像中的内波条纹信息,再根据内波传播方向自动选取灰度剖面;然后利用集合经验模态分解(ensemble empirical mode decomposition,简称EEMD)信号特征自适应分解模态函数的特点,再将分解得到的有效模态数作为VMD中参数K的参考值;最后利用VMD分解后的数据进行内波参数反演。试验结果表明:通过对Canny预处理后的条纹信息进行灰度剖面自动选取,解决了人为选取剖面所可能导致的误差;通过对剖面信号进行VMD处理不仅解决了EMD模态混叠的问题,成功地反演出内波的前导波振幅,而且所反演的结果与EEMD反演参数以及实测资料数据吻合得很好。     

Investigating internal waves east of the Hainan Island using optical satellite remote sensing data

Marginal water of east Hainan Island was an area that internal waves occurred frequently, however, few studies was found and mechanism for internal waves formation was unclear. In the paper, China Brazil earth Resources Satellite data (CBERS) was used to detect and calculate distribution, direction, wavelength and amplitude of internal waves in marginal water of east Hainan Island and the mechanism of internal waves formation was also analyzed, results showed that direction of internal wave was off shoreward and wavelength was about 150-200m . The mechanism for internal wave’s formation can be postulated as by upwelling or tide tracing back.     

Downward transfer of momentum by wind-driven waves

A model for the downward transfer of wind momentum is derived for growing waves. It is shown that waves, which grow due to an uneven pressure distribution on the water surface or a wave-coherent surface shear stress have horizontal velocities out of phase with the surface elevation. Further, if the waves grow in the x-direction, while the motion is perhaps time-periodic at any fixed point, the Reynolds stresses associated with the organized motion are positive. This is in agreement with several field and laboratory measurements which were previously unexplained, and the new theory successfully links measured wave growth rates and measured sub-surface Reynolds stresses. Wave coherent air pressure (and/or surface shear stress) is shown to change the speed of wave propagation as well as inducing growth or decay. From air pressure variations that are in phase with the surface elevation, the influence on the waves is simply a phase speed increase. For pressure variations out of phase with surface elevation, both growth (or decay) and phase speed changes occur. The theory is initially developed for long waves, after which the velocity potential and dispersion relation for linear waves in arbitrary depth are given. The model enables a sounder model for the transfer to storm surges or currents of momentum from breaking waves in that it does not rely entirely on ad-hoc turbulent diffusion. Future models of atmosphere-ocean exchanges should also acknowledge that momentum is transferred partly by the organized wave motion, while other species, like heat and gasses, may rely totally on turbulent diffusion. The fact that growing wind waves do in fact not generally obey the dispersion relation for free waves may need to be considered in future wind wave development models.