Whitecap coverage in coastal environment for steady and unsteady wave field conditions

Breaking waves represent a “key” parameter for many applications involved with a large number of environmental phenomena. In particular, it is well recognized that the whitecap cover induced by breaking waves allows substantial enhancement of heat, momentum, gas and particle transfer at the air–sea interface. A large number of studies were conducted during the last decades on the variation of the whitecap fraction, commonly noted W. The results presented in this paper deal with the evolution of the whitecap coverage in coastal zone. In such areas, the wave field is often unsteady with an important variety of sea state developments. The present analysis is based on an extensive series of data obtained during an experimental campaign which took place on the Mediterranean coast in 2001. The results allow observation of the influence of the sea state conditions of the wave field on the whitecap coverage. In addition, this paper confirms the occurrence of a peak in the variations of the whitecap fraction with the wave age for coastal areas as suggested by Lafon et al. [Lafon, C., Piazzola, J., Forget, P., Le Calvé, O. and Despiau, S., 2004. Analysis of the variations of the whitecap fraction as measured in a coastal zone. Boundary-Layer Meteorol., 111: 339-360.]. A wave age dependent model for the whitecap fraction is then proposed, which takes into account both the wind and the wave influence, and hence, is characteristics of the different sea state conditions.     

Characteristics of bubble plumes, bubble-plume bubbles and waves from wind-steepened wave breaking

Observations of breaking waves, associated bubble plumes and bubble-plume size distributions were used to explore the coupled evolution of wave-breaking, wave properties and bubble-plume characteristics. Experiments were made in a large, freshwater, wind-wave channel with mechanical wind-steepened waves and a wind speed of 13 m s^− 1. Bubble plumes exhibited a wide range of bubble distributions, physical extent and dynamics. A classification scheme was developed based on plume extent and “optical density” which is the ability of a plume to optically obscure the image of the background until maximum penetration of the plume. Plumes were classified as either dense (obscure) or diffuse (no-obscure). For each class, the plume bubble population size distribution, Φ(r,t), where r is the bubble radius and t the time, was determined. Dense plumes have a large radius peak in Φ and thus are enhanced in large bubbles. Diffuse plumes are well-described by a weakly size decreasing Φ(r,t) for r < 1000 μm and a more strongly size decreasing Φ(r,t) for r > 1000 μm.The bubble-plume formation rate, P, for each class, wave-breaking rate and wave characteristics were measured with respect to fetch. Wave-breaking rate and intensity are strongly fetch-dependent. In general, the trends in P and wave breaking are similar, reaching a maximum at the fetch of maximum wave breaking. The ratio of P for dense to diffuse plumes is even more sensitive to the occurrence of the most intense wave breaking, where dense plume formation is the greatest.Using P and the bubble size population distributions for each plume class, the global bubble-plume, injection size distribution, Ψ_i(r), was calculated. The volume injection rate for the study area was 640 cm³ s^− 1 divided approximately equally between bubbles smaller and larger than r  1700 μm.     

Amplitude decay and energy dissipation due to the interaction of internal solitary waves with a triangular obstacle in a two-layer fluid system: the blockage parameter

Experiments were carried out in a wave flume to examine the propagation of depression-type internal solitary waves (ISWs) over a submerged triangular-shaped obstacle. We observed the distortion and breaking of the ISW depression in a two-layer stratified fluid system as induced by the obstacle on the bottom. Physical factors, such as the amplitude of the wave, the thickness of the two layers, and the height of the submerged obstacle were utilized in our analysis of the wave–obstacle interaction. Wave breaking was determined in relation to input parameters arranged before the experimental runs. A classification scheme based on the blockage parameter ζ was proposed. The various degrees of ISW-obstacle interaction were visually classified with three schematic forms (ζ < 0.55 for a weak encounter; 0.55 < ζ < 0.7 for a moderate encounter; and 0.7 < ζ for wave breaking). Furthermore, the reflection and transmission coefficients were utilized to explore the resultant influence on changes in amplitude and energy of an ISW. The wave characteristics (e.g., amplitude-based wave reflection, energy-based reflection, amplitude-based transmission, and energy-based transmission) during the wave–obstacle interaction showed an approximately linear relation with the blockage parameter. Influenced by the submarine obstacle, the transmitted waves were found to always consist of a leading pulse (solitary wave) followed by a dispersive wave train. Moreover, due to bottom friction the energy budget of the leading pulse was reduced by a factor of at least 5% which could approach 50% in cases with strong breaking.     

SWAN在台湾海峡台风浪场数值模拟中的应用研究

简要介绍了波浪模式的发展及应用较为广泛的几种第三代能量谱海浪模式的特点。为了研究台湾海峡台风浪场的分布特征,以0903号"莲花"台风为例,选取第三代能量谱海浪模式SWAN,充分考虑底摩擦、风、白浪破碎、波波非线性相互作用、波浪浅化效应等物理过程,模拟了该海域的台风浪场的分布特征。将模拟结果与实测波浪、风资料对比分析,结果表明风速、有效波高计算值与实际值符合性较好,SWAN模式在海域的适应性良好。     

Assessment of wind quality for oceanographic modelling in semi-enclosed basins

The quality of surface winds derived from four meteorological models is assessed in the semi-enclosed Adriatic Sea over a 2-month period: a global hydrostatic model ECMWF T511 (40 km resolution), a hydrostatic limited area model LAMBO (20 km), and two non-hydrostatic limited area models: LAMI (7 km) and COAMPS™ (4 km). These wind models are used to drive a 2 km resolution wave model (SWAN) of the Adriatic, and wind and wave results are compared with observations at the ISMAR oceanographic tower off Venice. Waves are also compared at buoy locations near Ancona and Ortona. Consistently with earlier studies, the ECMWF fields underestimate the wind magnitude and do not reproduce the known spatial structure of strong wind events. The results show that the higher-resolution, limited area models LAMI and COAMPS exhibit better amplitude response than the coarser ECMWF: there is a 3- to 4-fold reduction of the wind underestimation at the platform (from 36% to 8–11%). The wave response is also improved with LAMI and COAMPS: there is a 2-fold reduction in the underestimation of wave heights at the platform. These non-hydrostatic models also produce wind fields with more realistic small-scale, spatial structure during strong wind events. The temporal correlation between observed and modelled wind, however, is highest with the global ECMWF model due to the fact that large-scale features can be predicted deterministically, whereas small-scale features can only be predicted stochastically. Models with less small-scale structure have better correlation because they have less “noise.” This explanation is supported by increased correlation between modelled and observed waves, the waves representing a smoothing of the wind over fetch and duration. Although there is room for improvement, the high-resolution, non-hydrostatic models (LAMI and COAMPS) offer significant advantages for driving oceanographic simulations in semi-enclosed basins such as the Adriatic Sea.     

Stern waves consisting of forward-oriented breaking waves and the remaining following waves

When a ship with a wide, immersed transom stern runs on a deep draft, forward-oriented wave breaking often occurs just behind the transom stern. In such conditions, stern waves can be considered to consist of two main components: the forward-oriented breaking wave and the remaining following waves. In our previous study, which was the first part of the present study, we developed a method to treat the forward-oriented breaking wave, and have clarified that it has a scale effect and its resistance coefficient decreases with an increase in the size of the model ship. On the other hand, the study also indicated that the height of the remaining following waves increases with an increase in the model ship size. The purpose of this paper is a more complete understanding of the two different component characteristics of the stern waves. We have developed a method to estimate the resistance due to the remaining following waves. Using this method, we have reached three main conclusions. The resistance increases considerably if the remaining following waves change to forward-oriented breaking waves. The resistance coefficient of the remaining following waves increases only slightly with an increase in model ship size. This stern wave resistance coefficient is strongly affected by the forward-oriented breaking waves, and therefore decreases with an increase in model ship size. Received: January 5, 2001 / Accepted: May 28, 2001     

Spectral signature of wave breaking in surface wave components of intermediate-length scale

This paper investigates the length scale of ocean surface breaking waves in the spectral range of intermediate wavelength components a few centimeters to a few meters long. The spectral properties of wave breaking are examined first with the dissipation function of the wave action density conservation equation. The analysis reveals a strong breaking signature in wave components between 0.15 and 1.5 m long in the form of a quasi-singular behavior of the dissipation function using the present formulation of the wind-generation and breaking dissipation functions. Independent studies of more-direct breaking observations of radar tracking of sea spikes in the past have shown close correlation between sea spikes and scatterers traveling at the speed of surface waves a few meters long and much shorter than the dominant wavelength. This feature of sea-spike properties is consistent with the breaking signature of the dissipation function in similar wavelengths. The intermediate-scale waves are the primary contributor of the ocean surface mean-square slope. The close correlation between the gas transfer rate and the mean-square slope has been demonstrated repeatedly. A better understanding of the wave dynamics of intermediate-scale waves is important for clarification of various gas transfer mechanisms.     

Asymmetry of Columbia River tidal plume fronts

Columbia River tidal plume dynamics can be explained in terms of two asymmetries related to plume-front depth and internal wave generation. These asymmetries may be an important factor contributing to the observed greater primary productivity and phytoplankton standing crop on the Washington shelf. The tidal plume (the most recent ebb outflow from the estuary) is initially supercritical with respect to the frontal internal Froude number F_R on strong ebbs. It is separated from the rotating plume bulge by a front, whose properties are very different under upwelling vs. downwelling conditions. Under summer upwelling conditions, tidal plume fronts are sharp and narrow (< 20–50 m wide) on their upwind or northern side and mark a transition from supercritical to subcritical flow for up to 12 h after high water. Such sharp fronts are a source of turbulent mixing, despite the strong stratification. Because the tidal plume may overlie newly upwelled waters, these fronts can mix nutrients into the plume. Symmetry would suggest that there should be a sharp front south of the estuary mouth under summer downwelling conditions. Instead, the downwelling tidal plume front is usually diffuse on its upstream side. Mixing is weaker, and the water masses immediately below are low in nutrients. There is also an upwelling–downwelling asymmetry in internal wave generation. During upwelling and weak wind conditions, plume fronts often generate trains of non-linear internal waves as they transition from a supercritical to a subcritical state. Under downwelling conditions, internal wave release is less common and the waves are less energetic. Furthermore, regardless of wind conditions, solition formation almost always begins on the south side of the plume so that the front “unzips” from south to north. This distinction is important, because these internal waves contribute to vertical mixing in the plume bulge and transport low-salinity water across the tidal plume into the plume bulge.F_R and plume depth are key parameters in distinguishing the upwelling and downwelling situations, and these two asymmetries can be explained in terms of potential vorticity conservation. The divergence of the tidal outflow after it leaves the estuary embeds relative vorticity in the emerging tidal plume water mass. This vorticity controls the transition of the tidal plume front to a subcritical state and consequently the timing and location of internal wave generation by plume fronts.     

紧致插值曲线CIP方法及其应用

波浪与建筑物的相互作用过程会涉及到波浪破碎、水气掺混和结构物的动力响应等复杂过程,对数值算法提出了更高要求。文章基于紧致插值曲线CIP（Constrained Interpolation Profile）方法建立了可模拟波浪破碎、翻滚等自由面大变形流动问题的数学模型。模型以CIP方法为流场基本求解器,离散了纳维—斯托克斯（Navier-Stokes：N-S）方程,同时还以CIP方法捕捉了自由面,通过多相流理论描述了流—固—气之间的相互作用。对强非线性自由表面流动问题的典型算例溃坝问题开展了数值模拟,并通过与他人实验结果的比较验证了模型的有效性。最后开展了极端波浪对浮式结构冲击过程的模拟,准确地预测了甲板上浪和结构的动力响应等问题。     

波生近岸流的数学模型研究

在理论上和数值技术上对已有的基于辐射应力理论的波生近岸流数学模型进行了改进,(1)使用考虑非线性作用的多向不规则波联合折射绕射数学模型确定波浪场,以期波场计算更加准确;(2)根据Dally等的研究成果,在波生流运动方程中加入破波切应力作用项,在辐射应力公式中加入了卷破波和波动Stokes漂流(Stokes drift)造成的向岸质量通量项,以期在破碎带内运动方程和辐射应力更为合理;(3)建立了基于两种网格的两套数学模型,即三角形网格有限差分数学模型和矩形网格有限差分数学模型,基于这两种网格的数学模型能满足近岸波生流场的模拟需要。就一模型海区对该文的模型进行了应用。     

Microphytobenthos biomass at Kerguelen's Land (Subantarctic Indian Ocean): repartition and variability during austral summers

Microphytobenthos biomass has been measured at several coastal sites on the SE of the main island of the Kerguelen Archipelago (Indian Ocean), during several austral summers (1985–1992), using a conventional fluorometric method. Heterogeneity tests, conducted on two different intertidal sites (Port-Aux-Français, PAF; and Port-Raymond, PRA), showed low standard deviations, whereas the mean concentrations were highly different. Pigment concentrations showed a high variability related to the characteristics of the sediments: from low biomass in coarse intertidal sand, submitted to intense scouring (0.32±0.31 μg Chl a g⁻¹ dw, 0.29±0.14 μg Phaeo g⁻¹ dw) to high biomass in intertidal muddy sand in sheltered areas, particularly along estuaries (54 μg Chl a, 15 μg Phaeo g⁻¹ dw at Korrigan). The subtidal muddy sediments under a Macrocystis pyrifera (Linné) and Durvillaea antarctica (Chamisso in Choris) belt exhibited high concentrations in phaeopigment (Phaeo) (up to 136±83 μg g⁻¹ dw; PRA), while the concentration of chlorophyll a (Chl a) was relatively low. The dense macroalgal canopy supports an important epiphytic diatom biomass (mainly the genera Cocconeis Ehrenberg and Grammatophora Ehrenberg), which is sedimenting after degradation and is in part responsible of the high levels of Phaeo in all sediments. Macroalgal debris were observed, but diatom frustules were dominant in most surficial subtidal sediments. A circatidal mud, in the Morbihan Bay, made of a sponge spicule mat (50 m deep; 4.96 μg Chl a g⁻¹ dw), showed a very low Chl a/Phaeo ratio (0.1), while it reached up to 6 in intertidal sand. Surprisingly, a penguin rookery beach, at the east side of Courbet Peninsula, was characterized by a very low biomass (0.07±0.04 μg Chl a g⁻¹ dw), while it was nutrient enriched, particularly with nitrates.In comparison with the data at the similar latitude, but in temperate regions from the Northern Hemisphere, the microphytobenthos biomass, recorded at Kerguelen's Land, exhibited relatively high pigment concentrations, particularly the Phaeo, and supported a dense and diversified subtidal macrofauna composed of polychaetes (particularly Thelepus extensus Hutchings and Glasby), sea urchins, mytillids and gammarids. The exuberant macroalgal canopy, coastal indentations and low tidal amplitude must be in part responsible of these large benthic primary and secondary biomasses.     

用一种全非线性Boussinesq方程模拟斜坡上的波浪破碎和爬高

基于一种新的二阶全非线性Boussinesq方程,采用预测-校正格式的有限差分法对该方程进行离散,建立了数值模型.模型中通过“狭槽法“来处理波浪在岸线处的动边界条件,采用涡粘模型来模拟波浪破碎引起的能量耗散.为了验证数值模型的适用性,模拟了斜坡地形上的波浪破碎和爬高.从数值结果和试验结果的比较上看,该模型可以很好地模拟近岸波浪场的实际问题.     

用SWAN模型模拟近岸波破碎

用SWAN波浪模型模拟了波谱在近岸区的演化。在SWAN模型中用“文氏谱”作为输入谱进行数值造波,模拟了不规则波的破碎过程。通过与实验结果和其它波浪模型的计算结果的对比说明,利用“文氏谱”,SWAN模型能够正确地模拟近岸海域不规则波浪的破碎过程。     

Breaking wave at the bow of a fast displacement ship model

We investigated the flow structures under the bow wave generated by a fast displacement ship model (INSEAN model 2340) in the presence of wave breaking. The data acquired were also used for a detailed database for CFD validation. The mean and r.m.s. point-wise values of the wave height were measured by means of a finger probe. The intensity of the breaking wave was taken as the r.m.s value of the wave height. The mean velocity field under the free surface was measured at 0.15 L _PP and 0.2 L _PP downstream of the fore perpendicular by means of a 5-hole Pitot probe. Uncertainty assessment of the wave height and velocity field results was performed following the AIAA Standards S-071-1995. Preliminary CFD results from a RANSE code with a breaking model are shown in comparison with the measured data.     

Numerical simulation of three-dimensional breaking waves

Three-dimensional (3D) wave breaking around bodies of complex geometry has been numerically investigated by use of two types of Navier-Stokes solvers, namely the finite-difference and the finite-volume methods employing rectangular and curvilinear coordinate systems, respectively. Both methods employ the density-function technique to capture the free surface location and can cope with complicated free surface configurations such as breaking waves. The accuracy of the density-function method is examined through the comparison with experimental results, and it is confirmed to be satisfactory when the grid spacing and the time increment are sufficiently small. New computational methods are applied to several problems including 3D breaking waves around ships and wave diffraction around offshore structures. The computed results show good agreement with experimental results indicating that wave breaking phenomena are successfully simulated. The qualitative accuracy, however, could be improved by including the dissipating effect of breaking waves.     

Analysis of velocity fluctuations and their intermittency properties in the surf zone using empirical mode decomposition

We consider here surf zone turbulence measurements, recorded in the Eastern English Channel using a sonic anemometer. In order to characterize the intermittent properties of their fluctuations at many time scales, we analyze the experimental time series using the Empirical Mode Decomposition (EMD) method. The series is decomposed into a sum of modes, each one narrow-banded, and we show that some modes are associated with the energy containing wave breaking scales, and other modes are associated with small-scale intermittent fluctuations. We use the EMD approach in association with a newly developed method based on Hilbert spectral analysis, representing the probability density function in an amplitude–frequency space. We then characterize the fluctuations in a stochastic framework using a cumulant generating function for all scales, and compare the results obtained from direct and classical structure function analysis, to EMD–Hilbert spectral analysis results, showing that the former method saturates at large scales, whereas the latter method is more precise in its scale approach. These results show the strength of the new EMD–Hilbert spectral analysis method for data presenting a strong forcing such as found in shallow water, wave dominated situations.     

波浪在珊瑚礁坪上传播的水槽试验研究

为研究波浪在珊瑚礁上的传播规律,分析波浪传至礁缘后破碎及传播情况,为设计波要素的确定提供参考依据。试验模拟了常年平均波浪和重现期50 a两种波浪条件。试验结果表明:波浪沿传播方向在礁坪边缘附近破碎后继续向坪内传播,并达到波面稳定状态,礁坪上的波浪传播特性表现为礁缘处波浪易破碎和礁坪上波浪衰减较快;波浪破碎表现为行进波破碎,且小于波浪在一般缓坡地形上的破碎指标,破碎波高水深比(Hb/d)约为0.5附近,重现期50 a大浪时礁缘处最大可达0.76。     

Spectral Wave Modeling in Very Shallow Water at Southern Coast of Caspian Sea

This study evaluates the capability of the Simulating WAves Nearshore (SWAN) wave model (version 41.01) in predicting significant wave height and spectral peak energy content for swell waves in very shallow water of surf zone during depth-induced wave breaking and dissipation. The model results were compared with field measurements at five nearshore stations. The results demonstrated that some breaker index formulations were successful for significant wave height prediction in surf zones. However, an incorrect shape of the energy spectrum and overestimated near spectral peak energy content at shallow water stations were obtained using all of the embedded depth-induced wave breaking formulations in SWAN. The dependent breaker index on relative depth (K_pd) formulation, which was successful in predicting near spectral peak energy content, resulted in an average error of 30%. Finally, this formulation was modified to enhance the model performance in reproducing the spectral peak energy content.