Statistical model on the surface elevation of waves with breaking

In the surface wind drift layer with constant momentum flux, two sets of the consistent surface eleva- tion expressions with breaking and occurrence conditions for breaking are deduced from the first in- tegrals of the energy and vortex variations and the kinetic and mathematic breaking criterions, then the expression of the surface elevation with wave breaking is established by using the Heaviside function. On the basis of the form of the sea surface elevation with wave breaking and the understanding of small slope sea waves, a triple composite function of real sea waves is presented including the func- tions for the breaking, weak-nonlinear and basic waves. The expression of the triple composite func- tion and the normal distribution of basic waves are the expected theoretical model for surface elevation statistics.     

层结海洋中小振幅内行进波的演变和破碎

采用高精度的拟谱方法,数值模拟了层结海洋中小振幅内行进波的演变和破碎过程.在演变过程中,导致内波破碎的PSI不稳定机制在共振相互作用中逐渐占据主导地位,能量从初级波向低频、高波数运动缓慢传递并形成一次级波包,随即破碎发生.破碎后产生的层化湍流引起的强烈混合以及湍流间歇性可从总能量和涡度峰度随时间的变化趋势看出.我们分析了层化湍流的一些统计特性,包括动能和有效位能沿垂向波数ky的功率谱.结果表明,动能和有效位能谱都存在一个谱段满足k-3y律,且分别可表示为0.1N4k-3y和0.2N4k-3y(N为Brunt-Visl频率),通常称其为浮力子区.另外,我们分析了Cox数(湍流扩散系数与分子扩散系数之比),在层化湍流维持在一定强度时,计算结果和由海洋内区观测(远离内波强生成源和复杂地形)所推测的结论较为吻合.     

Climate and extrema of ocean waves in the East China Sea

Wave climate plays an important role in the air-sea interaction over marginal seas. Extreme wave height provides fundamental information for various ocean engineering practices, such as hazard mitigation, coastal structure design, and risk assessment. In this paper, we implement a third generation wave model and conduct a high-resolution wave hindcast over the East China Sea to reconstruct a 15-year wave field from 1988 to 2002 for derivation of monthly mean wave parameters and analysis of extreme wave conditions. The numerical results of the wave field are validated through comparison with satellite altimetry measurements, low-resolution reanalysis, and the ocean wave buoy record. The monthly averaged wave height and wave period show seasonal variation and refined spatial patterns of surface waves in the East China Sea. The climatological significant wave height and mean wave period decrease from the open ocean in the southeast toward the continental area in the northwest, with the pattern generally following the bathymetry. Extreme analysis on the significant wave height at the buoy station indicates the hindcast data underestimate the extreme values relative to the observations. The spatial pattern of extreme wave height shows single peak emerges at the southwest of Ryukyu Island although a wind forcing with multi-core structure at the extreme is applied.     

On the small-scale fractal geometrical structure of a living coral reef barrier

The topographical complexity of coral reefs is of primary importance for a number of hydrodynamical and ecological processes. The present study is based on a series of high-resolution seabottom elevation measurements along the Maupiti Barrier Reef, French Polynesia. Several statistical metrics and spectral analysis are used to characterize the spatial evolution of the coral geometrical structure from the reef crest to the backreef. A consistent fractal-like power law exists in the spectral density of bottom elevation for length scales between 0.1 and 7 m, while at larger scale, the reef structure shows a different pattern. Such a fine characterization of the reef geometrical structure provides key elements to reconstruct the reef history, to improve the representation of reef roughness in hydrodynamical models and to monitor the evolution of coral reef systems in the context of global change. © 2020 John Wiley & Sons, Ltd.     

On the interaction between ocean surface waves and seamounts

Of the many topographic features, more specifically seamounts, that are ubiquitous in the ocean floor, we focus our attention on those with relatively shallow summits that can interact with wind-generated surface waves. Among these, especially relatively long waves crossing the oceans (swells) and stormy seas are able to affect the water column up to a considerable depth and therefore interact with these deep-sea features. We quantify this interaction through numerical experiments using a numerical wave model (SWAN), in which a simply shaped seamount is exposed to waves of different length. The results show a strong interaction that leads to significant changes in the wave field, creating wake zones and regions of large wave amplification. This is then exemplified in a practical case where we analyze the interaction of more realistic sea conditions with a very shallow rock in the Yellow Sea. Potentially important for navigation and erosion processes, mutatis mutandis, these results are also indicative of possible interactions with emerged islands and sand banks in shelf seas.     

The energy and energy flux of planetary waves in an ocean of variable depth

Abstract

In a recent paper, Buchwald (1972a) has shown that besides the kinetic energy and gravitational potential energy usually associated with planetary waves in an ocean of uniform depth it is useful to define also a “spin energy”, associated with the rotation.

The present paper is basically an extension of Buchwald's result to a uniformly rotating β-plane ocean of variable depth. As in the previous work, energy conservation equations are derived and the separate energies shown to be independently conserved over the total volume of the ocean. The time-averaged energies are further shown to be propagated in the direction of the group velocity and to satisfy the equipartition rule.

Unlike Buchwald, however, we need not consider the boundary conditions in order to achieve these results. Furthermore, the use of a more realistic ocean configuration admits the possibility of a multiply connected region in the present of mean currents.

Finally, there is a physical explanation for the appearance of a spin energy in a rotating system.     

Suspended-sediment transport in the surf zone: response to breaking waves

A field experiment designed to investigate the influence of wave breaking on suspended-sediment transport was conducted at Duck, NC, from 6 to 9 September 1985. Arrays of optical backscatter sensors, electromagnetic current meters and pressure sensors were deployed at five positions on a shore-normal transect that spanned the surf zone. At each position measurements were made of cross-shore and longshore velocity, sea-surface fluctuations, and suspended sediment at five levels above the bed. Experimental data runs were conducted when incident swell waves ( H_s = 0.5m, T= 10–12s) broke (primarily plunging) within the experimental transect. This paper describes the spatial characteristics of the plunge-to-bore tranformation region and describes (1) the cross-shore variability of sediment resuspension, including the mean concentrations and mean suspended load; (2) the net longshore and cross-shore flux across the surf zone; (3) mean suspended-sediment profiles as a function of wave type, e.g. plunging, spilling and bore, and unbroken at four positions across the surf zone; and (4) discusses the relative contribution of each wave type to the net longshore and cross-shore sediment flux.     

Quasigeostrophic planetary waves in a two-layer ocean with one-dimensional periodic bottom topography

Although the study of topographic effects on the Rossby waves in a stratified ocean has a long history, the wave property over a periodic bottom topography whose lateral scale is comparable to the wavelength is still not clear. The present paper treats this problem in a two-layer ocean with one-dimensional periodic bottom topography by a simple numerical method, in which no restriction on the wavelength and/or the horizontal scale of the topography is required. The dispersion diagram is obtained for a wavenumber range of [?π/L _b , π/L _b ], where L _b is the periodic length of the topography. When the topographic?β?is not negligible compared to the planetary β, the Rossby wave solutions around the wavenumbers which satisfy the resonant condition among the waves and topography disappear and separate into an infinite number of discrete modes. For convenience, each mode is numbered in order of frequency. As topographic height is increased, the high frequency barotropic Rossby wave (mode 1) becomes a topographic mode which can exist even on the f plane, and the highfrequency baroclinic mode (mode 2) becomes a surface intensified mode. Behaviors of low frequency modes are somewhat complicated. When the topographic amplitude is small, the low frequency baroclinic modes tend to be bottom trapped and the low frequency barotropic modes tend to be surface intensified. As topographic amplitude further increases, the relation between the mode number and vertical structure changes. This change can be attributed to the increase of the frequency of the topographic mode with the topographic amplitude.     

Numerical modelling of wind effects on breaking waves in the surf zone

Wind effects on periodic breaking waves in the surf zone have been investigated in this study using a two-phase flow model. The model solves the Reynolds-averaged Navier–Stokes equations with the k ? ?? turbulence model simultaneously for the flows both in the air and water. Both spilling and plunging breakers over a 1:35 sloping beach have been studied under the influence of wind, with a focus during wave breaking. Detailed information of the distribution of wave amplitudes and mean water level, wave-height-to-water-depth ratio, the water surface profiles, velocity, vorticity, and turbulence fields have been presented and discussed. The inclusion of wind alters the air flow structure above water waves, increases the generation of vorticity, and affects the wave shoaling, breaking, overturning, and splash-up processes. Wind increases the water particle velocities and causes water waves to break earlier and seaward, which agrees with the previous experiment.     

海洋中尺度涡与内波的地震图像

海洋反射地震通常用于调查、研究海底地质构造,勘探油气与天然气水合物资源.近期研究表明多道反射地震方法也可以对水柱的热盐细结构成像.中尺度涡与内波是重要的物理海洋现象,但是常规的物理海洋调查是在间隔若干公里的离散测站上进行的,水平分辨率较低,因此对中尺度涡的结构与内波的横向分布了解较差.本文利用在大西洋东部、南海采集的地震数据给出了低频反射地震可以对中尺度涡与内波清晰成像的新的证据.反射地震方法较传统海洋观测手段,具有明显的优势,主要体现在高的水平分辨率和短时间内对整个海水剖面进行成像方面．从地震剖面上,能够清楚地观测到中尺度涡、内波造成的反射特征变化,从而有助于改进对能量在不同尺度的海水运动之间传递过程的认识.     

A preliminary investigation of momentum flux in ocean waves

Summary A pilot investigation was made of the downward flux of downwind momentum through the upper layers of the water, by measuring the covariance between the horizontal and vertical water velocity components. Power spectrum analysis showed the effect to be due largely to the surface waves present.     

Simulation of breaking waves using the high-order spectral method with laboratory experiments: wave-breaking energy dissipation

We examine the implementation of a wave-breaking mechanism into a nonlinear potential flow solver. The success of the mechanism will be studied by implementing it into the numerical model HOS-NWT, which is a computationally efficient, open source code that solves for the free surface in a numerical wave tank using the high-order spectral (HOS) method. Once the breaking mechanism is validated, it can be implemented into other nonlinear potential flow models. To solve for wave-breaking, first a wave-breaking onset parameter is identified, and then a method for computing wave-breaking associated energy loss is determined. Wave-breaking onset is calculated using a breaking criteria introduced by Barthelemy et al. (J Fluid Mech https://arxiv.org/pdf/1508.06002.pdf, submitted) and validated with the experiments of Saket et al. (J Fluid Mech 811:642–658, 2017). Wave-breaking energy dissipation is calculated by adding a viscous diffusion term computed using an eddy viscosity parameter introduced by Tian et al. (Phys Fluids 20(6): 066,604, 2008, Phys Fluids 24(3), 2012), which is estimated based on the pre-breaking wave geometry. A set of two-dimensional experiments is conducted to validate the implemented wave breaking mechanism at a large scale. Breaking waves are generated by using traditional methods of evolution of focused waves and modulational instability, as well as irregular breaking waves with a range of primary frequencies, providing a wide range of breaking conditions to validate the solver. Furthermore, adjustments are made to the method of application and coefficient of the viscous diffusion term with negligible difference, supporting the robustness of the eddy viscosity parameter. The model is able to accurately predict surface elevation and corresponding frequency/amplitude spectrum, as well as energy dissipation when compared with the experimental measurements. This suggests the model is capable of calculating wave-breaking onset and energy dissipation successfully for a wide range of breaking conditions. The model is also able to successfully calculate the transfer of energy between frequencies due to wave focusing and wave breaking. This study is limited to unidirectional waves but provides a valuable basis for future application of the wave-breaking model to a multidirectional wave field. By including parameters for removing energy due to wave-breaking into a nonlinear potential flow solver, the risk of developing numerical instabilities due to an overturning wave is decreased, thereby increasing the application range of the model, including calculating more extreme sea states. A computationally efficient and accurate model for the generation of a nonlinear random wave field is useful for predicting the dynamic response of offshore vessels and marine renewable energy devices, predicting loads on marine structures, and in the study of open ocean wave generation and propagation in a realistic environment.     

A note on the general concept of wave breaking for Rossby and gravity waves

A recently proposed general definition of wave breaking is further discussed, in order to deal with some points on which misunderstanding appears to have arisen. As with surface and internal gravity waves, the classification of Rossby waves into breaking and not breaking is a generic classification based on dynamical considerations, and not a statement about any unique signature or automatically recognizable shape. Nor is it a statement about passive tracers uncorrelated with potential vorticity on isentropic surfaces. A strong motivation for the definition is that proofs of the nonacceleration theorem of wave, mean-flow interaction theory rely, explicitly or implicitly, on a hypothesis that the waves do not break in the sense envisaged.The general definition refers to the qualitative behaviour of a certain set of material contours, namely those, and only those, which would undulate reversibly, with small slopes, under the influence of the waves' restoring mechanism, in those circumstances for which linearized, nondissipative wave theory is a self-consistent approximation to nonlinear reality. The waves' restoring mechanism depends upon the basic-state vertical potential density gradient in the case of gravity waves, and upon the basic-state isentropic gradient of potential vorticity in the case of Rossby waves. In the usual linearized theory of planetary scale Rossby waves on a zonal shear flow, the relevant material contours lie along latitude circles when undisturbed.     

Wave height characteristics in the north Atlantic ocean: a new approach based on statistical and geometrical techniques

The main characteristics of the significant wave height in an area of increased interest, the north Atlantic ocean, are studied based on satellite records and corresponding simulations obtained from the numerical wave prediction model WAM. The two data sets are analyzed by means of a variety of statistical measures mainly focusing on the distributions that they form. Moreover, new techniques for the estimation and minimization of the discrepancies between the observed and modeled values are proposed based on ideas and methodologies from a relatively new branch of mathematics, information geometry. The results obtained prove that the modeled values overestimate the corresponding observations through the whole study period. On the other hand, 2-parameter Weibull distributions fit well the data in the study. However, one cannot use the same probability density function for describing the whole study area since the corresponding scale and shape parameters deviate significantly for points belonging to different regions. This variation should be taken into account in optimization or assimilation procedures, which is possible by means of information geometry techniques.     

The fractal properties of topography: A comparison of methods

In this study the fractal characteristics of fifty-five digital elevation models from seven different United States physiographic provinces are determined using seven methods. The self-similar fractal model tested in this analysis is found to provide a very good fit for some landscapes, but an imperfect fit for others. Thus, outright rejection of this model does not appear to be warranted, but neither does a blind application. The three implementations of the dividers methods considered in this study consistently produce lower dimensions than those produced by the other methods, and those dimensions consistently do not vary much between surfaces. Although the dimensions produced by the cell counting method (applied to the digital elevation model itself) display consistent intersurface variation, the dimensions are generally lower than those produced by the variogram-based methods. Among the variogram-based methods, the dimensions of the quarter-sections of the digital elevation models are generally greater than the dimensions obtained from the other variogram-based methods. The dimensions produced by the variogram method which considered the surfaces on a directional basis are very similar, on average, to the dimensions produced by the entire-surface variogram.     

Trends and variability of ocean waves under RCP8.5 emission scenario in the Mediterranean Sea

Ocean Dynamics - Wind-generated ocean waves are key inputs for several studies and applications, both near the coast (coastal vulnerability assessment, coastal structures design, harbor...     

A spectrum of the acoustic-gravity waves associated with Auroral electro-jet

This model concerns the analysis of Aurora initiated travelling pressure waves in an isothermal atmosphere. Electro-dynamic Lorentz Force associated with auroral electric current density during the periods of geomagnetic activity is invoked as a possible exciting source.The dispersion phenomena in auroral induced acoustic gravity modes in the earth's atmosphere are examined and various cut-off frequencies analysed.Finally, an attempt is made to obtain a far field representation of the forced oscillations by means of Green's Function technique. Therefrom, the spectral amplitudes of the ground-level oscillations are computed. Incorporating various scaling factors, it is deduced that these amplitude components are in reasonable agreement with the results of recent measurements.     

The characteristics of breaking waves, bubble clouds, and near-surface currents observed using side-scan sonar

An inverted 248 kHz two-component side-scan sonar mounted on the sea bed in a mean depth of 34 m has been used to detect the clouds of bubbles produced by breaking surface waves. The sonar has a range of about 150 m. The breaking waves appear on the sonograph records as short-lived intense echoes, and form patterns which can be explained in terms of the behaviour of groups of waves in which the highest are breaking.The bubble clouds are slightly elongated in the wave direction when they are first formed and, in winds of 5.1 m s⁻¹, have lifetimes of up to about 5 min. Soon after a wave breaks, the horizontal motion of the fluid in which the bubbles are formed becomes similar to that of the surroundings, and the bubbles continue to be advected by the near-surface currents. The rate of drift of bubble clouds along the directions of the sonar beams allows the components of the currents to be measured.The sonographs show that large changes in currents can occur over horizontal distances of as little as 5 to 10 m when fronts are passing. The motion of the fronts through the water can be measured. The sonographs have been used to measure surface currents induced by internal waves. Bands of bubbles associated with Langmuir circulation can be detected in strong winds or when moderate winds are accompanied by heavy rain.     

Numerical studies of large-amplitude internal waves shoaling and breaking at shelf slopes

Hydro carbon fields beyond the shelf break are presently being explored and developed, which has increased the scientific focus in this area. Measurements from the slopes reveal large variability in temperature and velocity, and some of the observed events are due to interactions between large-amplitude oscillations of the thermocline and the topography. The present study focuses on the strong currents that are generated near the seabed during shoaling and breaking of internal waves along shelf slopes. The parameter regime used is similar to the one for the Nordic Seas. The results show that, during shoaling of large internal waves along (gentle) slopes, the energy is transferred towards smaller scales and strong velocities (over 1 m s^− 1) can be generated. To resolve all scales involved is still not feasible, and therefore, the model results are sensitive to the grid size and the subgrid scale closure.