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.     

Hydrodynamic coefficients of a two-dimensional,truncated rectangular floating structure in shallow water

The paper seeks to examine hydrodynamic coefficients of a rectangular structure in shallow water and to establish analytical formulae for fast computations. A two-dimensional rectangular profile is considered with the under-bottom clearance assumed to be small compared with structure dimensions and the water depth. Following the method of matched asymptotic expansions, the radiation problem is solved under assumptions of the linear wave theory, by matching two ‘outer’ flows with the ‘inner’ flow near the structure edge. Closed asymptotic formulae are obtained for all hydrodynamic coefficients for heave, sway and roll motions. The zero and infinite frequency values of the added mass are examined and formulae are derived intended for quick engineering estimations. Numerical results compare well with those published in literature, and the approach is shown to be consistent with known fundamental relations in the body–wave interaction theory.     

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     

Dispersion and stability analyses of the linearized two-dimensional shallow water equations in Cartesian coordinates

In the present study, a Fourier analysis is used to develop expressions for phase and group speeds for both continuous and discretized, linearized two-dimensional shallow water equations, in Cartesian coordinates. The phase and group speeds of the discrete equations, discretized using a three-point scheme of second order, five-point scheme of fourth order and a three-point compact scheme of fourth order in an Arakawa C grid, are calculated and compared with the corresponding values obtained for the continuous system. The three-point second-order scheme is found to be non-dispersive with grid resolutions greater than 30 grids per wavelength, while both the fourth-order schemes are non-dispersive with grid resolutions greater than six grids per wavelength. A von Neumann stability analysis of the two- and three-time-level temporal schemes showed that both schemes are stable. A wave deformation analysis of the two-time-level Crank–Nicolson scheme for one-dimensional and two-dimensional systems of shallow water equations shows that the scheme is non- dispersive, independent of the Courant number and grid resolution used. The phase error or the dispersion of the scheme decreases with a decrease in the time step or an increase in grid resolution.     

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.     

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.     

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.     

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.     

Modelling shallow water wave generation and transformation in an intertidal estuary

An experiment is described in which wave growth was measured in Manukau Harbour, a New Zealand estuary with relatively large fetches and extensive intertidal flats. Wave spectra were obtained from pressure sensors and current meters placed at six sites across the estuary. The SWAN third-generation spectral model was then used to simulate wave transformation during a part of the study period during which consistent south-westerly winds blew along the instrument transect. The simulations incorporated refraction by currents using output from a circulation model of the estuary. Measured wave variance spectra were compared with the model results, and the contributions of the various processes represented by source terms within the model were compared. It was found that, along with whitecapping, bed friction and exponential growth from wind input, four-wave nonlinear interactions played a dominant role. Some limitations were noted in the discrete interaction approximation which the SWAN model uses to compute the four-wave nonlinear interaction term.     

Antarctic shallow water benthos in an area of recent rapid glacier retreat

The West Antarctic Peninsula is one of the fastest warming regions on Earth. Faster glacier retreat and related calving events lead to more frequent iceberg scouring, fresh water input and higher sediment loads, which in turn affect shallow water benthic marine assemblages in coastal regions. In addition, ice retreat creates new benthic substrates for colonization. We investigated three size classes of benthic biota (microbenthos, meiofauna and macrofauna) at three sites in Potter Cove (King George Island, West Antarctic Peninsula) situated at similar water depths but experiencing different disturbance regimes related to glacier retreat. Our results revealed the presence of a patchy distribution of highly divergent benthic assemblages within a relatively small area (about 1 km²). In areas with frequent ice scouring and higher sediment accumulation rates, an assemblage mainly dominated by macrobenthic scavengers (such as the polychaete Barrukia cristata), vagile organisms and younger individuals of sessile species (such as the bivalve Yoldia eightsi) was found. Macrofauna were low in abundance and very patchily distributed in recently ice‐free areas close to the glacier, whereas the pioneer nematode genus Microlaimus reached a higher relative abundance in these newly exposed sites. The most diverse and abundant macrofaunal assemblage was found in areas most remote from recent glacier influence. By contrast, the meiofauna showed relatively low densities in these areas. The three benthic size classes appeared to respond in different ways to disturbances likely related to ice retreat, suggesting that the capacity to adapt and colonize habitats is dependent on both body size and specific life traits. We predict that, under continued deglaciation, more diverse, but less patchy, benthic assemblages will become established in areas out of reach of glacier‐related disturbance.     

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.     

Three dimensional water quality modeling of a shallow subtropical estuary

Knowledge of estuarine hydrodynamics and water quality comes mostly from studies of large estuarine systems. The processes affecting algae, nutrients, and dissolved oxygen (DO) in small and shallow subtropical estuaries are relatively less studied. This paper documents the development, calibration, and verification of a three dimensional (3D) water quality model for the St. Lucie Estuary (SLE), a small and shallow estuary located on the east coast of south Florida. The water quality model is calibrated and verified using two years of measured data. Statistical analyses indicate that the model is capable of reproducing key water quality characteristics of the estuary within an acceptable range of accuracy. The calibrated model is further applied to study hydrodynamic and eutrophication processes in the estuary. Modeling results reveal that high algae concentrations in the estuary are likely caused by excessive nutrient and algae supplies in freshwater inflows. While algal blooms may lead to reduced DO concentrations near the bottom of the waterbody, this study indicates that stratification and circulation induced by freshwater inflows may also contribute significantly to bottom water hypoxia in the estuary. It is also found that high freshwater inflows from one of the tributaries can change the circulation pattern and nutrient loading, thereby impacting water quality conditions of the entire estuary. Restoration plans for the SLE ecosystem need to consider both a reduction of nutrient loading and regulation of the freshwater discharge pattern.     

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.     

浅水不规则波浪中油轮运动研究

本文对一般油轮在浅水不规则波浪中六自由度运动进行了试验分析,并对其碰底情况做了研究。试验时对有流情况下不同波高、不同装载的条件进行了分析比较。模型的六自由度运动是用非接触式六自由度运动测量与分析方法求得。该方法应用位置测量仪（ＰＳＤ）对安置在模型上的红外线发光源（ＬＥＤ）进行测量,然后所编制的软件计算出模型的六个自由度运动情况。