Consideration of fine-scale coastal oceanography and 3-D acoustics effects for the ESME sound exposure model

Results and recommendations for evaluating the effects of fine-scale oceanographic scattering and three-dimensional (3-D) acoustic propagation variability on the Effects of Sound on the Marine Environment (ESME) acoustic exposure model are presented. Pertinent acoustic scattering theory is briefly reviewed and ocean sound-speed fluctuation models are discussed. Particular attention is given to the nonlinear and linear components of the ocean internal wave field as a source of sound-speed inhomogeneities. Sound scattering through the mainly isotropic linear internal wave field is presented and new results relating to acoustic scattering by the nonlinear internal wave field in both along and across internal wave wavefront orientations are examined. In many cases, there are noteworthy fine-scale induced intensity biases and fluctuations of order 5-20 dB.     

Tsunami simulation with Green–Naghdi theory

Green–Naghdi (GN) theory is a fully nonlinear wave theory which has been used with success to simulate nonlinear water waves. In previous applications of GN theory to water wave problems the ocean bottom was assumed to be time invariant. In this work no such restriction is made and GN theory is used to simulate tsunami caused by bottom fluctuation. As first test cases we simulate two-dimensional nonlinear surface waves generated by positive bottom movements. The results in the generation region for three different seabed movements compare well against earlier experimental data. The results in the downstream region for impulsive seabed movements show some discrepancies in wave phase and amplitude compared with earlier experimental values. It is suspected that the viscous effects may have played a role. The GN theory is then used to study three-dimensional near-field tsunami amplitudes caused by submarine landslides and slumps spreading in two orthogonal directions. The GN results agree with previous linear solution very well when the ratio of the velocities is v₁/v₂=1.0. But GN theory give more believable results for the case of v_T/v=0.1 and v₁/v₂=0.1.     

Applicability of numerical models to nonlinear dispersive waves

The applicability of three different wave-propagation models in nonlinear dispersive wave fields has been investigated. The numerical models tested here are based on three different wave theories: a fully nonlinear potential theory, a Stokes second-order theory, and a Boussinesq-type theory with an improved dispersion relation. Physical experiments and computations were conducted for wave evolutions during passage over a submerged shelf under various wave conditions. As expected, the fully nonlinear solutions agree better with the measurements than do the other solutions. Although the second-order solution has sufficient accuracy for smaller-amplitude wave cases, the truncation after the third harmonics causes significant discrepancies in wave form for larger waves. In addition, the second-order model markedly overestimates the first- and second-harmonic amplitudes in transmitted waves. The Boussinesq model provides excellent predictions of wave profile over the shelf even in larger wave cases. However, this model also overestimates the magnitudes of several higher harmonics in transmitted waves. These facts may indicate that energy transfer from bound components into free waves in these higher harmonics cannot be accurately evaluated by the Boussinesq-type equations.     

On the possibility of biphase parametrization for wave transformation in the coastal zone

Based on experimental data, we study the possibility of parametrizing the spatial variation in the phase shift (biphase) between the first and second nonlinear harmonics of wave motion during wave transformation over an inclined bottom in the coastal zone. It is revealed that the biphase values vary in the range [–π/2, π/2]. Biphase variations rigorously follow fluctuations in amplitudes of the first and second harmonics and the periodicity of energy exchange between them. Wave breaking influences the biphase value, retaining its variations in the negative domain in the range [–π/2, 0]. The formula applied in modern practice to calculate the biphase, which depends on the Ursell number, is incorrect for calculating the biphase for wave evolution in the coastal zone, because it does not take into account periodic energy exchange between the nonlinear harmonics. We propose a linear approximation of the biphase values from the size of the ratio of the current distance to the coast to the possible spacial duration of the exchange period, which is determined by the dispersion relation. We reveal the dependence of biphase variations on the wave transformation scenario and demonstrate the possibility of constructing a separate parameterization of the biphase for each scenario. Our research and the obtained biphase parameterizations can be used to simulate the sea state in the coastal zone, as well as in problems of predicting the development of coasts under the impact of storm waves.     

Three-dimensional nonlinear random wave groups in intermediate water depth

High waves at ocean occur during a complex space–time evolution of wave groups. In this paper the nonlinear structure of three-dimensional sea wave groups at intermediate water depth is investigated. To this purpose, the Boccotti's Quasi-Determinism theory is firstly applied to describe the linear wave groups when a given exceptionally high crest occurs. Then, the second-order correction to the linear solution is derived for the general condition of three-dimensional wave groups, at a finite water depth. Several numerical applications, finally, have been carried out in order to show how both the spectral bandwidth and the directional spreading modify the nonlinear high waves at different water depth.     

Probability distribution of random wave–current forces

Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave–wave and wave–current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan–Pierson–Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied.     

黄海海浪季节变化的数值模拟研究

利用第三代海浪数值模式SWAN,研究了黄海海浪有效波高的季节变化特征及相关的物理过程。结果表明,在黄海的大部分区域,混合浪有效波高的最大值出现在冬季,而最小值则基本出现在夏季。北黄海北部和山东半岛南岸的近海海域呈现稍微不同的季节变化,有效波高的最大值出现在春季。全年4个季节中混合浪有效波高的空间分布基本一致:均在济州岛西南最大,沿黄海中部区域向北和由中部区域向近岸区域逐渐减小。黄海海浪为风浪占主,涌浪有效波高远小于风浪有效波高。在黄海的大部分区域,白冠耗散和四波非线性相互作用对黄海海浪的季节变化均至关重要;对于外海区域,四波非线性相互作用更为重要,而对于近海区域,白冠耗散则影响更大。本研究旨在研究黄海海浪的季节变化特征及其物理过程,为进一步探讨该海域海浪在其他时间尺度上的变异特征和动力学过程提供研究基础。     

Features of wind waves at the southeastern coast of Sakhalin according to bottom-pressure measurements

The results of wind-wave measurements with bottom-pressure sensors are discussed. These measurements were performed at the southeastern coast of the Island of Sakhalin in 2006–2009. The problems of converting data obtained with these sensors into water-level displacent in the context of the linear theory are noted. Twenty records with a duration of 2 weeks to 3 months were obtained. These records contain from 150000 to 1200000 waves for three different observation points located at the southeastern coast of Sakhalin in the regions of the village of Vzmor’ye, Lake Izmenchivoye, and the Cape of Ostryi. The estimates obtained for wave-height distributions were approximated by the Weibull distribution. They were compared to the theoretical Rayleigh, Forristall, Weibull, and Glukhovskii distributions. As one would expect, in the region of small wave heights, all distributions prove to be close to one another, and, for large wave heights, the Weibull distribution is preferred.     

A Boussinesq Equation-Based Model for Nearshore Wave Breaking

Based on the wave breaking model by Li and Wang (1999), this work is to apply Dally‘ s analytical solution to the wave-height decay instead of the empirical and semi-empirical hypotheses of wave-height distribution within the wave breaking zone. This enhances the applicability of the model. Computational results of shoaling, location of wave breaking, wave-height decay after wave breaking, set-down and set-up for incident regular waves are shown to have good agreement with experimental and field data.     

Nonlinear Dispersion Relation in Wave Transformation

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Tide and surge dynamics along the Iberian Atlantic coast

The eastern Atlantic barotropic dynamics (in a region spanning from 20° N to 48° N and 34° W to 0°) are studied through numerical modelling and in situ measurements. The main source of data is the tidal gauge network REDMAR, managed by Clima Marítimo (Puertos del Estado). The numerical model employed is the HAMSOM, developed both by the Institut für Meereskunde (Hamburg University) and Clima Marítimo.In this paper, tidal and storm surge dynamics are studied for the region, focusing particularly on the nonlinear transfer of energy between the different forcings.The results of tidal simulations show good agreement between semidiurnal harmonic components and the values obtained from the tidal gauges (both coastal and pelagic) and current metres. The nonlinear transfers of energy from semidiurnal to higher order harmonics, such as M4 and M6, were mapped. Those transfers were found to be important in only two areas: The French continental shelf in the Bay of Biscay and the widest part of the African shelf, south of Cabo Bojador. The modelled diurnal constituents show larger relative differences with measurements than semidiurnal harmonics, especially in data concerning the phase.A method to isolate the nonlinear transfers of energy between tidal and atmospheric forcing during a storm surge was developed. These transfers were found to be significant in the same areas where tidal nonlinear activity was present. The effect of short period wind generated waves on sea surface elevation was also investigated. The magnitude of the spatial derivatives of radiation stress was compared with wind-induced stress. As a result of this comparison, we found the inclusion of a forcing term that depends on radiation stress in ocean model simulations at this scale and resolution to be not essential. The effect of computing wind-induced stresses, with a formulation that explicitly depends on sea state, was also explored by means of a coupled run of the HAMSOM and the spectral wave model WAM for a storm surge event in the Spanish coast. This formulation was not found to be an improvement over a classical parameterisation which only depends on wind fields.     

Extraction of ocean wave parameters from HF backscatter received bya four-element array: analysis and application

An algorithm that would extend the capabilities of a four-element square array known as the Coastal Oceans Dynamics Applications Radar (CODAR) to include the yielding of directional wave-height spectra from backscattered radiation is addressed. General expressions for the first- and second-order broadbeam radar cross-sections of the ocean surface are applied to the array. A Fourier-basis-function approach allows the broadbeam cross-sections to be written as a system of integral equations. The second-order radar return involves a double integral whose integrand contains nonlinear combinations of the unknowns, namely, the Fourier coefficients of the ocean wave directional spectrum. The first-order portion of the radar spectrum is used to linearize this integral. The matrix system then formulated is solved using a singular value decomposition (SVD) approach, and the resulting ocean spectral coefficients are used to give the directional spectrum. Test results for the algorithm are reported and discussed     

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.     

Numerical Simulation of Waves Generated by Seafloor Movements

Waves generated by vertical seafloor movements are simulated by use of a fully nonlinear two-dimensional numerical wave tank. In the souree region, the seafloor lifts to a designated height by a generation function. The numerical tests show that the linear theory is only valid for estimating the wave behaviors induced by the seafloor movements with a small amplitude, and the fully nonlinear numerical model should be adopted in the simulation of the wave generation by the large amplitude seafloor movements. Without the background surface waves, many numerical tests on the stable maximum elevations η0^max are carried out by beth the linear theory and the fully nonlinear model. The results of two models are compared and analyzed. For the fully nonlinear model, the influences of the amplitudes and the horizontal lengths on η^max are stronger than that of the characteristic duration times. Furthermore, results reveal that there are significant differences be- tween the linear theory and the fully nonlinear model. When the influences of the background surface waves are considered, the corresponding numerical analyses reveal that with the fully nonlinear model the η0^max near-linearly varies with the wave amplitudes of the surface waves, and the η0^max has significant dependences on the wave lengths and the wave phases of the surface waves. In addition, the differences between the linear theory and the fully nonlinear model are still obvious, and these differences are significantly affected by the wave parameters of the background surface waves, such as the wave amplitude, the wave length and the wave phase.     

三维极限波的产生方法及特性

极限破碎波浪是造成海洋结构物破坏的主要因素之一,对极限波浪的产生方法和特性进行研究具有重要的工程意义.利用长波传播快、短波传播慢的原理,从理论上给出了产生三维极限波的方法,利用基于Boussinesq方程的数值模拟对该方法进行了验证,同时研究了中心频率、频率宽度和频谱形式等对极限波浪特性的影响,为该方法的进一步应用提出了建议.     

Interactions of cnoidal waves with cylinder arrays

The three-dimensional scattering of cnoidal waves by cylinder arrays are studied numerically by using the generalized Boussinesq equations. The boundary-fitted coordinate transformation and a dual-grid technique are used to simplify the finite-difference computation. Also, a set of open boundary conditions and an incident cnoidal wave are incorporated for time-domain simulation. The free-surface elevation and hydrodynamic forces on each cylinder are calculated to illustrate the evolution of nonlinear waves and their interactions with large cylinder arrays. Comparisons are made between the present nonlinear wave loads and those obtained from linear diffraction theory. The sheltering role played by the neighboring cylinders and the feature of wave interference are discussed.     

Predicting Nonlinear Wave Trough Distributions Utilizing A Transformed Linear Simulation Method

This paper first proposes a new approach for predicting the nonlinear wave trough distributions by utilizing a transformed linear simulation method. The linear simulation method is transformed based on a Hermite transformation model where the transformation is chosen to be a monotonic cubic polynomial and calibrated such that the first four moments of the transformed model match the moments of the true process. The proposed new approach is applied for calculating the wave trough distributions of a nonlinear sea state with the surface elevation data measured at the coast of Yura in the Japan Sea, and its accuracy and efficiency are convincingly validated by comparisons with the results from two theoretical distribution models, from a linear simulation model and a second-order nonlinear simulation model. Finally, it is further demonstrated in this paper that the new approach can be applied to all the situations characterized by similar nondimensional spectrum.     

基于三维约束NewWave理论的自升式钻井平台动力响应分析

以某122 m自升式钻井平台为分析对象,建立其有限元模型,包括材料非线性、几何非线性以及桩土非线性相互作用,在风浪流作用下,基于三维约束New Wave理论对自升式钻井平台的动态响应进行分析,研究海洋波浪方向传播特性和随机特性对平台动力响应的影响。在建立模型中实现风暴工况下水面高程和水粒子运动的描述,响应结果按甲板位移进行对比。结果表明,相比其它波浪理论,三维约束New Wave理论在平台动力响应分析中体现了一定的优越性,不仅能较准确地反映波浪的真实特性,而且能确保结构性能评估的安全性和合理性。     

西太平洋暖池形成与维持的动力学机制

建立了一个简单海气耦合模式,其中大气垂直分为两层,为-β平面近似线性模式。在非绝热加热项中包含了对流凝结潜热与大尺度流场之间相互作用的CISK机制以及蒸发、感热与扰动风场之间的反馈机制,并考虑了平均东风区和西风区的不同。由于只研究大气的平均纬向运动,故模式大气中仅含有Kelvin波。海洋模式为一约化重力模式,在一定条件下采用准地转近似,模式海洋中仅保留了Rossby波。对这一海气耦合模式进行特征波动分析,发现海气耦合并不显著改变大气波动的性质。在中东太平洋的平均东风区,大气的Kelvin波仍然增幅和东传。在平均西风区,大气Kelvin波振幅衰减。但耦合作用却使海洋Rossby波的性质发生变化,且波长超过某一临界波长Le的Rossby波的振幅增长。在平均东风区,结论相论。这一理论说明西太平洋暖池的形成与海洋Rossby波有关。在东太平洋,由于是平均东风区,短的Ross-by波振幅增长,不能形成水平尺度很大的“暖池”。而在平均西风的西太平洋区,有可能形成水平尺度很大的“暖池”。