Surface-to-volume wave conversion in shallow water with a corrugated bottom

Acoustic transmission between points onshore or in very shallow water and points in deep water is strongly influenced by the shear rigidity of marine sediments, which control the parameters and the very existence of seismoacoustic surface waves. Previously, it was found that coupling between acoustic modes and the seismoacoustic surface waves is normally weak, although not negligible in the case of a gently sloping seafloor and soft sediments. In this paper, the previous work is extended by accounting for the small-scale roughness of the seafloor. The significant role of roughness in coupling between volume and surface waves is demonstrated. The combined effect of bottom topography, roughness, and wave attenuation in soft marine sediments on the sound propagation between points in shallow and deep water is discussed. Published in Russian in Akusticheskiĭ Zhurnal, 2008, Vol. 54, No. 3, pp. 400–407. The article was translated by the author.     

浅海周期起伏海底环境下的声传播

海底粗糙对水下声传播及水声探测等应用具有重要影响.利用黄海夏季典型海洋环境,分析了同时存在海底周期起伏和强温跃层条件下的声传播特性,结果表明:由于海底周期起伏的存在,对于低频(<1 kHz)、近程(10 km)的声信号,传播损失可增大5—30 d B.总结了声传播损失及脉冲到达结构随声源深度、海底起伏周期及起伏高度等因...     

浅水体系中的多孤立波

形式分离变量法被推广应用于寻求不可积模型的多孤立波解.特别地,应用形式分离变量法于三个描述浅水体系的非线性方程:推广WhithamBroerKaup(WBK)方程、2+1维耦合KortewegdeVries(KdV)方程和1+1维耦合KdV方程,给出了这些体系的明显的解析的多孤立波解 关键词： 浅水体系 多孤立波 形式分离变量法 不可积模型     

Observable parameters from multipath bottom reverberation in shallow water

Multipath ocean reverberation originating from the seabed in shallow isovelocity water, with particular attention to its information content in the cylindrical spreading and mode stripping regions, is considered. The reverberation is evaluated using Weston's flux integral method, both analytically with various simplifying approximations and numerically with all but one of these approximations rescinded. The functional form of the analytical solution is used to infer which physical seabed parameters can be extracted from measurements of reverberation. Coarse- and fine-grained sediments (sand and clay) are both considered. The main purpose of the numerical solutions is to check the accuracy of the analytical approximations; they also serve as a convenient surrogate for measured reverberation.     

Acoustic tomography of shallow water with unknown relief of hard bottom

The possibility of implementing tomography in shallow water with unknown relief of bottom is considered. It is shown that the use of time delays of different modes at different frequencies allows for reconstruction of bottom relief and the sound speed profile in the water layer without any additional activities for separating the effects of reconstructed characteristics of shallow water on the received data.     

Effect of a sloping bottom on sound propagation

Acoustical Physics - The paper presents the results of field measurements of acoustic fields generated in autumn hydrological conditions of the Sea of Japan shelf by a TON-320Hz autonomous signal...     

Second-mode nonlinear internal waves over a sloping bottom

The characteristic features of second-mode internal wave propagation over a sloping bottom are investigated by numerical simulation based on the Korteweg-de Vries equation. A comparison of the transformations that occur for first- and second-mode internal solitons in the course of their propagation over a sloping bottom under the hydrological conditions of the South China Sea is carried out. Convex and concave second-mode waves are considered, and the possibility of their transition from the first to the second state in the course of their propagation from the deep ocean to the shelf is demonstrated. This is an analog of the effect of a change in the internal wave polarity, which earlier was known to occur for only first-mode internal waves.     

浅海海底反射系数幅值参数的反演

理论分析了一种通过混响强度衰减特性获取海底反射系数的幅值参数的方法.将海底反射系数的幅值参数和相位参数引入到全波动混响模型中,为海底反射系数的反演提供理论基础。理论分析和数值仿真表明,在小掠射角条件下,利用混响强度衰减特性反演海底反射系数幅值参数的可行性和准确性。该反演方法只需要输入4个变量:本地混响强度的衰减特性,反射系数的相位参数,海深以及海深处的声速,同时要求混响数据具有一定的混响噪声比(大于6 dB)才能够使反演结果准确可信。根据本地静态混响实验数据成功反演得到海底反射系数的幅值参数.     

ADER schemes for the shallow water equations in channel with irregular bottom elevation

This paper deals with the construction of high-order ADER numerical schemes for solving the one-dimensional shallow water equations with variable bed elevation. The non-linear version of the schemes is based on ENO reconstructions. The governing equations are expressed in terms of total water height, instead of total water depth, and discharge. The ENO polynomial interpolation procedure is also applied to represent the variable bottom elevation. ADER schemes of up to fifth order of accuracy in space and time for the advection and source terms are implemented and systematically assessed, with particular attention to their convergence rates. Non-oscillatory results are obtained for discontinuous solutions both for the steady and unsteady cases. The resulting schemes can be applied to solve realistic problems characterized by non-uniform bottom geometries.     

On the linearized shallow-water waves over a sloping bottom

Summary This paper presents an investigation concerning long waves on sloping beaches. On the other hand, an attempt is made to broaden the class of the realistic forms of bottom topography,h(x), with which an exact solution of the related eigenvalue problem is possible. Under the linearizing assumption, the investigation confirms thath ^−1/2 is a factor associated with the bottom topography which is involved in wave breaking along the shoreline (Green's law). Further, the bottom topography in the neighbourhood of the shoreline is approximated byh(x)=K ₀ x ^j. There-from it is deduced that all positive real values ofj are associated with the possible structure of the bottom profile. Consequently, each can be employed in the construction of possible wave forms. Finally, an attempt is made to obtain a closed form of solution associated with the governing linear differential equation whenh(x) is arbitrary. The comparison of the results with those obtained by using the refraction diagram suggests close agreement over the beach considered.

---

Riassunto In questo lavoro si presenta una ricerca che riguarda onde lunghe su spiagge in pendenza. Inoltre si fa un tentativo di ampliare la classe delle forme realistiche della topografia del fondo,h(x), con cui è possibile una soluzione esatta del problema correlato dell'autovalore. Nell'ipotesi di linearizzazione la ricerca conferma cheh ^−1/2 è un fattore associato con la topografia del fondo che è implicata nella rottura dell'onda lungo la linea di costa (legge di Green). Inoltre, la topografia del fondo in prossimità della linea di costa si approssima conh(x)=K ₀ x ^j. Da questo si deduce che tutti i valori reali positivi dij sono associati con la struttura possibile del profilo del fondo. Di conseguenza, ognuno di questi può essere utilizzato nella costruzione di possibili forme d'onda. Infine, si tenta di ottenere una forma chiusa della soluzione associata con l'equazione principale lineare differenziale quandoh(x) è arbitrario. Il confronto dei risultati con quelli ottenuti usando diagrammi di rifrazione suggerisce un accordo stretto per tutta la spiaggia considerata.

---

Резюме В этой работе исследуются длинные волны на наклонных берегах. С другой стороны делается попытка расширить класс реалистических форм топографии дна,h(x), для которых возможно точное решение проблемы собственных значений. Предполагая линеаризацию, исследование подтверждает, чтоh ^−1/2 представляет фактор, связанный с топографией дна, который входит в разрушение волн вдоль береговой линии. Топографиа дна в окрестности береговой линии аппроксимируется выражениемh(x)=K ₀ x ^j. Отсюда следует, что все положительные значенияj связаны с возможной структурой профиля дна. Следовательно, каждое значение может быть использовано при конструровании возможных волновых форм. В заключение, предпринимается попытка получить замкнутую форму решения, связанного с определяющим дифференциальным уравнением, когдаh(x) является произвольной функцией. Сравнение результатов с результатами, полученными, используя диаграмму рефракции, свидетельствует о согласии вдоль всего рассмотренного берега.

     

基于信道传播理论的多基地远程海底混响研究

针对浅海多基地远程海底混响, 以声传播的线性信道近似理论为基础, 通过确定海底界面的不均匀起伏特性, 对入射声波的远距离异地混响脉冲响应函数进行求解. 对非水平分层介质的浅海波导, 利用绝热简正波求解信道的传输函数, 得出了小角度斜坡海底的远程海底混响强度, 以下坡海底为例, 分析对比了不同海底倾角斜坡海底对远程异地混响强度及其衰减规律的影响. 理论仿真表明, 波导的传输效应对多基地远程海底混响强度的影响不可忽略.     

Matched-field replica model optimization and bottom property inversion in shallow water

Matched-field replica models based on an inaccurate knowledge of geoacoustic parameters such as bottom attenuation, shear, and interfacial sound-speed discontinuities, can predict an incorrect number of propagating modes for a shallow-water channel. The resulting degradation in the matched-field ambiguity surface can be substantially reduced by obtaining optimal replica models via modal-sum-limit optimization or bottom-property inversion. The use of these techniques for multi-tone (70, 95, 145, and 195 Hz) source-tow data recorded near San Diego during the first Shallow-Water Evaluation Cell Experiment (SWellEX-1) significantly increased matched-field correlation levels and improved source localization relative to results obtained with a previous nonoptimized model. The predicted number of propagating modes was also reduced substantially. The inversion for bottom properties (attenuation, interfacial sound-speed discontinuities, no shear) provided sediment attenuation estimates which agree well with Hamilton's models and were an order-of-magnitude greater than that used in the nonoptimized model, which accounts for the reduction in the number of modes. A simulated modal decomposition using the inverted optimal replica model verifies the number of modes predicted by the modal-sum-limit optimization.     

Solitary wave dynamics in shallow water over periodic topography

The problem of long-wave scattering by piecewise-constant periodic topography is studied both for a linear solitary-like wave pulse, and for a weakly nonlinear solitary wave [Korteweg-de Vries (KdV) soliton]. If the characteristic length of the topographic irregularities is larger than the pulse length, the solution of the scattering problem is obtained analytically for a leading wave in the framework of linear shallow-water theory. The wave decrement in the case of the small height of the topographic irregularities is proportional to delta2, where delta is the relative height of the topographic obstacles. An analytical approximate solution is also obtained for the weakly nonlinear problem when the length of the irregularities is larger than the characteristic nonlinear length scale. In this case, the Korteweg-de Vries equation is solved for each piece of constant depth by using the inverse scattering technique; the solutions are matched at each step by using linear shallow-water theory. The weakly nonlinear solitary wave decays more significantly than the linear solitary pulse. Solitary wave dynamics above a random seabed is also discussed, and the results obtained for random topography (including experimental data) are in reasonable agreement with the calculations for piecewise topography.     

Interaction of two sea surface waves over a sloping bottom

A nonlinear model is constructed for the motion of long surface waves over a sloping bottom in the shallow-water approximation. It is shown that if a linear solution is known, the quadratic and cubic nonlinear corrections can be expressed in terms of the derivatives of the functions determining the linear solution. The developed method is applied to the interaction of two periodic waves in the near-shore area.     

深海海底斜坡环境下的声传播

海底地形变化对声传播具有很大影响,在南海深海区域海底斜坡环境下进行了一次声传播实验,实验显示倾斜海底环境下声传播损失出现了一些不同于平坦海底环境下的现象,分析并解释了海底地形变化对产生声传播差异的原因.结果表明,海底斜坡对声波的反射增强作用可使斜坡上方的声传播损失减少约5 d B.当声波第一次入射到达的海底位置有较小幅度的山丘(凸起高度小于1/10海深)时,海底小山丘即可对声波有反射遮挡作用,导致在其反射区特定传播距离和深度上出现倒三角声影区,比平坦海底环境下相同影区位置处的传播损失增大约8 d B,影响深度可达海面以下1500 m.而海底斜坡对声波的反射阻挡作用使得从海面反射及水体向下折射的会聚区结构消失,只剩下从水体向上折射的会聚结构.因此,海底地形对深海声传播影响较大,在水下目标探测和性能评估等应用中应予以重视.     

Photoelasticity effects in superlattices with quantum wells having a sloping bottom near the interband resonances

An analytical expression is obtained for the linear coefficients of photoelasticity in superlattices with quantum wells having a sloping bottom in the vicinity of the interband resonances. It is shown that these coefficients considerably decrease when the slope of the quantum-well bottom is induced by an electric field applied to the superlattice and remain almost unchanged if the slope is produced by the variband method. A new mechanism providing the emergence of linear photoelasticity near the interband resonances is revealed for superlattices based on piezoelectric crystals. This mechanism is associated with the modulation of the band gap of the quantum-well structure by the generated piezoelectric field. Numerical estimates demonstrate that the contribution to the linear photoelasticity in the region of the interband resonances is substantially greater than the corresponding contribution in the exciton region of the spectrum and is comparable in magnitude to the contribution made by the deformation potential.     

由浅海混响反演海底反射和散射系数

对于分层浅海,当海底散射是形成混响的主要散射源时收发合置混响的平均强度可由一简洁的简正波表式计算,它依赖于平面波的海底反射和散射系数。利用随机反演理论(高斯一马尔可夫原理)和多次选代的方法可以由混响强度反演得到对应于各号简正波掠角的海底反射和散射系数。对负跃层浅海作了混响反演的数值模拟,得到较好的结果。文中讨论了提高反演精度和选代收敛性的问题。