Numerical simulation for the two-dimensional nonlinear shallow water waves

This study deals with the general numerical model to simulate the two-dimensional tidal flow, flooding wave (long wave) and shallow water waves (short wave). The foundational model is based on nonlinear Boussinesq equations. Numerical method for modelling the short waves is investigated in detail. The forces, such as Coriolis forces, wind stress, atmosphere and bottom friction, are considered. A two-dimensional implicit difference scheme of Boussinesq equations is proposed. The low-reflection outflow open boundary is suggested. By means of this model,both velocity fields of circulation current in a channel with step expansion and the wave diffraction behind a semi-infinite breakwater are computed, and the results are satisfactory.     

Design of an integrated shallow water wave experiment

The experimental design and instrumentation for an integrated shallow-water surface gravity wave experiment is discussed. The experiment required the measurement of the water surface elevation, meteorological parameters, and directional spectra at a number of locations on a shallow lake. In addition, to acquire data under a wide range of conditions, an experimental period of three years was required. A system of telephone and radio modem links were installed to enable real-time monitoring of instrument performance at eight separate measurement locations on the lake. This system also enabled logging sessions to be optimized to ensure the maximum possible data return from this extended experiment     

Wave-induced motions of an air cushion structure in shallow water

Model tests were conducted on two 1:100 scaled models of a typical concrete gravity substructure at the University of Western Australia. The two models had dimensions 0.5 m length×0.5 m width with the first model being a sealed closed bottom box of height 0.1 m and the second model being an open bottom box with skirt length of 0.1 m. The mass of the air cushion model was changed to accommodate various water plug heights within the skirt chamber. Each model was floated at a constant draft of 0.1 m and tested in water depths ranging between 0.03 m (shallow) and 0.8 m (deep). The environment comprised regular waves with periods ranging between 0.6 and 3.5 s and amplitude of 0.08–0.02 m. To quantify the dynamic response the heave and pitch motions of each model were measured.A simplified theoretical solution based on long wavelength, linear wave assumptions was developed and applied to the geometries in consideration. Improvements to the theory are sought using the forcing function from a boundary element code, as well as utilizing added mass coefficients from free decay experiments. Results show that experimental trends compare reasonably well with analytical solution in particular for periods longer than the natural period. The results show that introducing air cushion support into a CGS increases the pitch response, while having little effect of the heave motion.     

Note on the propagation of a shallow water wave in water of variable depth

In this technical note, the phenomena of non-linear water-wave propagation above a seabed with variable depth is re-examined. The conventional Korteweg-de Vries (KdV) equation is re-derived for the general case of variable water depth. In the new form of KdV equation, the seabed bottom function is included. Two different bottom profiles are considered in this study; case 1: $b^{\prime }\left(x^{\prime }\right)=c\epsilon \sin \lambda x^{\prime }$ and case 2: $b^{\prime }\left(x^{\prime }\right)=c\epsilon {\mathrm{e}}^{-\lambda {\left(x^{\prime }-x_0^{\prime }\right)}^2}$. The effects of three bottom profile parameters, c, λ and ε on the wave profile are examined. Numerical results indicate that both ε and λ affect the wave profile significantly in case 1, while ε significantly affects the wave profile in case 2.     

GEK measurements in a shallow water region

Evidence for the applicability of GEK (Geomagnetic Electrokinetography) measurements to shallow water regions is provided from observations in the shelf region of the East China Sea. The reason for the effectiveness of GEK measurements in this case is investigated theoretically, and it is shown to be attributable to the existence of a thick conductive sedimentary layer. In addition, it is shown that low conductive basement rock can be regarded as a good conductor for GEK measurements if the current width is broad enough and if the ratio of current width to water depth is larger than the resistivity ratio of basement rock to sea water. This implies that barotropic tidal currents can be measured with GEK in any ocean on the earth if they have significant magnitudes.     

二维链间扩展的极化子动力学研究

基于扩展的SSH模型,研究了有序耦合聚合物链系统中的极化子动力学,包括极化子的形成过程及其在外场下的输运.发现,当聚合物链间的耦合较强时,注入到系统中的电子会诱发二维链间扩展的极化子态,分布在多条聚合物链上.另外,动力学模拟表明,与一维链内定域极化子相比,在相同的电场强度下二维极化子具有更大的运动速度,这与实验结果一致.     

浅海水下地形的SAR遥感仿真研究

结合连续性方程和布拉格后向散射模型,在准一维简化浅海水下地形情况下,建立了浅海水下地形SAR海面相对后向散射强度仿真模型,将浅海水下地形区域的SAR海面后向散射强度的相对变化与大尺度背景流场、海面风场和雷达系统参数等联系起来.海上实验和研究结果表明,浅海水下地形的SAR成像主要由通过受水下地形影响的海表层流场对海表面风引起的微尺度波的水动力调制而获取浅海水下地形信息,其中潮流与水下地形的相互作用过程改变海表层流场,变化的海表层流与海表面微尺度波之间的相互作用改变海表面波的空间分布,雷达波与海表面波之间的相互作用决定雷达海面后向散射强度.因此SAR图像中浅海水下地形或水深信息量的多少不仅与海表层流场和海面风速有关,而且与雷达工作波段、雷达波束入射角和极化方式也密切相关.认为由水下地形变化引起的缓慢变化的表层流场中海表面定常微尺度波谱能量密度的变化满足波作用量谱平衡方程;而在波数空间中,海表面微尺度波谱的成长过程也可以用波数谱平衡方程描述,在此基础上,得出了海表面波高频谱(毛细-重力波)形式的解析表达式.众所周知,浅海水下地形信息是由于水下地形影响下SAR海面后向散射强度与背景海面后向散射强度的相对差异而在SAR图像上的呈现,从而在建立浅海水下地形SAR海面相对后向散射强度仿真模型的基础上,仿真计算了浅海水下地形SAR海面相对后向散射强度相对于海表层流场、海面风场等海况参数和SAR工作波段、SAR波束入射角、极化方式等雷达系统参数的数值仿真结果,分析得到了有关浅海水下地形SAR海面相对后向散射强度的特征和SAR浅海水下地形遥感的最佳海况参数与最佳雷达系统参数,为研究和开展SAR浅海水下地形遥感研究提供了有价值的参考.     

Bifurcation structure of a wind-driven shallow water model with layer-outcropping

The steady state bifurcation structure of the double-gyre wind-driven ocean circulation is examined in a shallow water model where the upper layer is allowed to outcrop at the sea surface. In addition to the classical jet-up and jet-down multiple equilibria, we find a new regime in which one of the equilibrium solutions has a large outcropping region in the subpolar gyre. Time dependent simulations show that the outcropping solution equilibrates to a stable periodic orbit with a period of 8 months. Co-existing with the periodic solution is a stable steady state solution without outcropping.A numerical scheme that has the unique advantage of being differentiable while still allowing layers to outcrop at the sea surface is used for the analysis. In contrast, standard schemes for solving layered models with outcropping are non-differentiable and have an ill-defined Jacobian making them unsuitable for solution using Newton’s method. As such, our new scheme expands the applicability of numerical bifurcation techniques to an important class of ocean models whose bifurcation structure had hitherto remained unexplored.     

Geoacoustic inversion of broad-band acoustic data in shallow water on a single hydrophone

The inversion of broad-band low-frequency acoustic signals received on sparse arrays can lead to robust and efficient estimations of sea-bed properties. This paper describes a shallow-water geoacoustic inversion scheme based on the use of a model-based matched-impulse response on a single hydrophone. Results from the INTIMATE'96 experiment on the Portuguese shelf break are reviewed. In order to minimize the effects of strong time variability due to internal tides, only the time-stable waterborne bottom-surface reflected arrivals are exploited. A quasi-linear inversion algorithm is first applied to refine the geometry of the experiment. Then, inversion of bottom parameters is performed with an objective function that only makes use of the bottom-surface reflected arrivals' amplitudes. The experimental results show that broad-band transmissions (300-800 Hz) received on a single hydrophone, combined with the use of a simple eigenray code, are sufficient to correctly resolve geometrical parameters and bottom features. The analysis of the reflection coefficients both on simulated and real data helps to understand the validity of the inverted parameters and to derive the basis of an equivalent medium concept for geoacoustic inversion based on a "through-the-sensor" approach.     

Picard iterations for a finite element shallow water equation model

ADCIRC, a finite element circulation model for shelves, coasts and estuaries, will be used for variational data assimilation. The nonlinear Euler–Lagrange (EL) problem will be solved using the iterated indirect representer algorithm. This algorithm makes such large, nonlinear but functionally smooth optimization problems feasible by iterating on linear approximations of the nonlinear problem (Picard iterations) and by making preconditioned searches in the “data subspace” at each iterate. Before solving the nonlinear EL using such Picard iterations, it essential that the iteration scheme be carefully examined within the framework of the nonassimilative or forward problem.The purpose of this paper is (1) to detail a Picard iteration procedure for ADCIRC, including the problematic bottom friction term; (2) to examine the ability of the iteration scheme to recover the nonlinear forward solution from deficient background fields; and (3) to present a study of different interpolation methods for reducing the memory/disk requirements of the iteration scheme. The iteration scheme is shown to be quite robust in its ability to recover the nonlinear solution from a variety of deficient background fields. A new cubic Hermitian interpolation method is shown to be a more effective alternative to standard linear interpolation for reducing memory/disk requirements, especially for high frequency overtides.     

Seismo-acoustic field statistics in shallow water

The spatial statistics of the acoustic field in shallow water are strongly affected by interfacial roughness and volume fluctuations in the water column or the seabed. These features scatter energy, reducing the coherence of the acoustic field. This paper introduces a consistent, mode-based modeling framework for ocean scattering. First, the rough surface scattering theory of Kuperman and Schmidt is reformulated in terms of normal modes, resulting in computation times which are reduced by several orders of magnitude. Next, a perturbation theory describing scattering from sound speed and density fluctuations in acoustic media is developed. The scattering theories are combined with KRAKEN, creating a unified normal mode code for wave theory modeling of shallow-water spatial statistics. The scattered field statistics are found to be a complicated function of scattering mechanism, scatterer statistics, and acoustic environment. Bottom properties, including elasticity, strongly influence the scattered field     

Wave height distribution in shallow water

Probability distribution of shallow water wave heights, obtained from a pressure type recorder, are examined. It is tested with the theoretical distributions of (a) Rayleigh, (b) Weibull, (c) Gluhovski, (d) Ibrageemov and (e) Goda. The best fit is shown by the Gluhovski probability density function with a correlation coefficient greater than 0.8. The functions of Weibull, Ibrageemov and Goda fit only half of the tested cases. The role of wave steepness in the wave height distribution is found to be negligible.     

Spectral characteristics of high shallow water waves

The spectral characteristics of shallow water waves with significant wave height more than 2 m based on the data collected along the Indian coast is examined. It was found that the value of Joint North Sea Wave Project (JONSWAP) parameters (α and γ) increases with significant wave height and mean wave period and decreases with spectral peak period. The estimated average value (0.0027 and 1.63) of the JONSWAP parameters, α and γ were less than the generally recommended values of 0.0081 and 3.3, respectively. By carrying out a multi-regression analysis, an empirical equation is arrived relating the JONSWAP parameters with significant wave height, peak wave period and mean wave period. It was found that the Scott spectra underestimate the maximum spectral energy of high waves. The study shows that the measured wave spectra can be represented by JONSWAP spectra with the JONSWAP parameters estimated based on the equation proposed in this paper.     

Tomographic mapping of sediments in shallow water

Sediment compressional wave speeds were estimated using broad-band data in range-dependent environments. The environment was assumed as mildly range dependent and was modeled using adiabatic theory. The inversion scheme was based on group speed-dispersion behavior. A genetic algorithm (GA) combined with a neighborhood approach was used for the search. The top layer of sediment was mapped in the shelf region using acoustic data from explosive sources collected on a vertical line array.     

Tomographic reconstruction of shallow water bubble fields

In March of 1997, a shallow water experiment was conducted near the Scripps Pier in La Jolla, CA, USA. The goal was to determine the dynamics, distribution, and acoustic effects of bubbles just offshore from active surf. A major component of the experiment was the “Delta Frame”, an apparatus that supported two acoustic sources and eight receivers. Acoustic intensity was measured at frequencies between 39 and 244 kHz over the resulting 16 horizontal ray paths. Paths ranged in length from 2.5 to 8.6 m. In the present paper, a tomography algorithm is developed and implemented using Delta Frame data. Measurements are combined to produce quantitative cross-sectional images of the attenuation associated with the bubble cloud. Numerical simulations predict that the Frame ran resolve details of the field down to about 2 m. Images constructed at different acoustic frequencies are scaled and compared. A 5-min sequence of images is studied in detail. Swell waves are shown to cause rapid fluctuations in the images     

Analysis of body supercavitation in shallow water

Motion of a cavitating body in shallow waters undergoes a blockage effect. There are influences of the rigid boundary (the sea bottom) and the free boundary (sea surface) in shallow waters. As shown by computation carried out with the ideal fluid theory, the combination of these influences leads to an increase of cavitation number for a cavity of a fixed length and to 3D deformations of the cavity cross-sections, with a swelling of the down cavity part.     

Sensor position estimation and source ranging in a shallow water environment

Underwater acoustic transient signals are generated mechanically at known positions along a wharf. These signals are received by a wide aperture planar array of four underwater acoustic sensors, whose positions relative to the wharf are unknown. A method is described that enables the positions of the sensors to be estimated from accurate differential time-of-arrival measurements (with 0.1 /spl mu/s precision) as the signal wavefronts traverse the array. A comparison of the estimated positions with the nominal positions of the first three sensors, which form a 20-m-wide aperture horizontal line array, reveals a 2-cm displacement of the middle sensor from the line array axis. This slight bowing of the line array results in overranging (bias error of 3%) when the wavefront curvature method is used with the nominal collinear sensor positions to locate a static source of active sonar transmissions at a range of 59.2 m. The use of the spherical intersection method coupled with the estimated sensor positions of the line array provides an order of magnitude improvement in the range estimate (within 0.3% of the actual value). However, systematic ranging errors are observed when the sound propagation medium becomes nonstationary. Next, the differences in the arrival times of the direct path and boundary-reflected path signals at the middle sensor of the wide aperture line array are estimated using the differential phase residue of the analytic signal at the sensor output. These multipath delays are used to estimate the range and depth of the source. Although the average value of the multipath range estimates is within 0.5% of the actual value, the variance of the range estimates is 50 times larger when compared with the results of the spherical intersection and wavefront curvature methods. The multipath delay data are also processed to provide a reliable estimate of the temporal variation in the water depth enabling the tidal variation to be observed.