Propagation of water waves over permeable rippled beds

Unsteady two-dimensional Navier-Stokes equations and Navier-Stokes type model equations for porous flow were solved numerically to simulate the propagation of water waves over a permeable rippled bed. A boundary-fitted coordinate system was adopted to make the computational meshes consistent with the rippled bed. The accuracy of the numerical scheme was confirmed by comparing the numerical results concerning the spatial distribution of wave amplitudes over impermeable and permeable rippled beds with the analytical solutions. For periodic incident waves, the flow field over the wavy wall is discussed in terms of the steady Eulerian streaming velocity. The trajectories of the fluid particles that are initially located close to the ripples were also determined. One of the main results herein is that under the action of periodic water waves, fluid particles on an impermeable rippled bed initially moved back and forth around the ripple crest, with increasing vertical distance from the rippled wall. After one or two wave periods, they are then lifted towards the next ripple crest. All of the marked particles on a permeable rippled bed were shifted onshore with a much larger displacement than those on an impermeable bed. Finally, the flow fields and the particle motions close to impermeable and permeable beds induced by a solitary wave are elucidated.     

A temporally second-order accurate Godunov-type scheme for solving the extended Boussinesq equations

A numerical scheme for solving the class of extended Boussinesq equations is presented. Unlike previous schemes, where the governing equations are integrated through time using a fourth-order method, a second-order Godunov-type scheme is used thus saving storage and computational resources. The spatial derivatives are discretised using a combination of finite-volume and finite-difference methods. A fourth-order MUSCL reconstruction technique is used to compute the values at the cell interfaces for use in the local Riemann problems, whilst the bed source and dispersion terms are discretised using centred finite-differences of up to fourth-order accuracy. Numerical results show that the class of extended Boussinesq equations can be accurately solved without the need for a fourth-order time discretisation, thus improving the computational speed of Boussinesq-type numerical models. The numerical scheme has been applied to model a number of standard test cases for the extended Boussinesq equations and comparisons made to physical wave flume experiments.     

Velocity potential formulations of highly accurate Boussinesq-type models

The highly accurate Boussinesq-type equations of Madsen et al. (Madsen, P.A., Bingham, H.B., Schäffer, H.A., 2003. Boussinesq-type formulations for fully nonlinear and extremely dispersive water waves: Derivation and analysis. Proc. R. Soc. Lond. A 459, 1075–1104; Madsen, P.A., Fuhrman, D.R., Wang, B., 2006. A Boussinesq-type method for fully nonlinear waves interacting with a rapidly varying bathymetry. Coast. Eng. 53, 487–504); Jamois et al. (Jamois, E., Fuhrman, D.R., Bingham, H.B., Molin, B., 2006. Wave-structure interactions and nonlinear wave processes on the weather side of reflective structures. Coast. Eng. 53, 929–945) are re-derived in a more general framework which establishes the correct relationship between the model in a velocity formulation and a velocity potential formulation. Although most work with this model has used the velocity formulation, the potential formulation is of interest because it reduces the computational effort by approximately a factor of two and facilitates a coupling to other potential flow solvers. A new shoaling enhancement operator is introduced to derive new models (in both formulations) with a velocity profile which is always consistent with the kinematic bottom boundary condition. The true behaviour of the velocity potential formulation with respect to linear shoaling is given for the first time, correcting errors made by Jamois et al. (Jamois, E., Fuhrman, D.R., Bingham, H.B., Molin, B., 2006. Wave-structure interactions and nonlinear wave processes on the weather side of reflective structures. Coast. Eng. 53, 929–945). An exact infinite series solution for the potential is obtained via a Taylor expansion about an arbitrary vertical position z = zˆ. For practical implementation however, the solution is expanded based on a slow variation of zˆ and terms are retained to first-order. With shoaling enhancement, the new models obtain a comparable accuracy in linear shoaling to the original velocity formulation. General consistency relations are also derived which are convenient for verifying that the differential operators satisfy a potential flow and/or conserve mass up to the order of truncation of the model. The performance of the new formulation is validated using computations of linear and nonlinear shoaling problems. The behaviour on a rapidly varying bathymetry is also checked using linear wave reflection from a shelf and Bragg scattering from an undulating bottom. Although the new models perform equally well for Bragg scattering they fail earlier than the existing model for reflection/transmission problems in very deep water.     

Tsunami generation,propagation, and run-up with a high-order Boussinesq model

In this work we extend a high-order Boussinesq-type (finite difference) model, capable of simulating waves out to wavenumber times depth kh < 25, to include a moving sea-bed, for the simulation of earthquake- and landslide-induced tsunamis. The extension is straight forward, requiring only an additional term within the kinematic bottom condition. As first test cases we simulate linear and nonlinear surface waves generated from both positive and negative impulsive bottom movements. The computed results compare well against earlier theoretical, numerical, and experimental values. Additionally, we show that the long-time (fully nonlinear) evolution of waves resulting from an upthrusted bottom can eventually result in true solitary waves, consistent with theoretical predictions. It is stressed, however, that the nonlinearity used far exceeds that typical of geophysical tsunamis in the open ocean. The Boussinesq-type model is then used to simulate numerous tsunami-type events generated from submerged landslides, in both one and two horizontal dimensions. The results again compare well against previous experiments and/or numerical simulations. The new extension compliments recently developed run-up capabilities within this approach, and as demonstrated, the model can therefore treat tsunami events from their initial generation, through their later propagation, and final run-up phases. The developed model is shown to maintain reasonable computational efficiency, and is therefore attractive for the simulation of such events, especially in cases where dispersion is important.     

Quantitative analysis for maritime delimitation: Reassessing the Bay of Bengal delimitation between Bangladesh and Myanmar

This article examines technical aspects of the maritime boundary dispute between Bangladesh and Myanmar (the ‘Bay of Bengal case’). This dispute was the first maritime delimitation determined by the International Tribunal for the Law of the Sea (ITLOS). The 2012 decision was also the first time that a maritime boundary for the seabed and subsoil of the Exclusive Economic Zone (EEZ) and the extended continental shelf (ECS) was determined by international adjudication. This was also therefore the first time that detailed technical quantification of seabed areas within the EEZ and ECS was needed for achieving an equitable division of these maritime zones in an international forum. Following review of the principles of maritime delimitation on which the ITLOS reached its determination, this article analyzes the legal status and delimitation effect of St. Martin's Island. Concerning the question of whether the legal regimes of the EEZ and continental shelf should be treated differently in a single delimitation line, although the ITLOS determined that the legal regimes should not be distinguished in the present case, a different approach is proposed for future cases. The article identifies how quantitative modelling can be used to achieve an equitable boundary and proposes a model to adjust provisional equidistance lines in accordance with the complex geophysical rules prescribed for the outer limits of the ECS in Article 76 of the United Nations Law of the Sea Convention (LOSC).     

Molecular identification of ascaridoid nematodes from the deep-sea onion-eye grenadier (Macrourus berglax) from the East Greenland Sea

Macrourus berglax from the East Greenland Sea was studied for the presence of ascaridoid nematodes in 2001, 2002 and 2003. The fishes were collected between 278 and 413 m water depth using a benthopelagic net. Based on the amplification of the internal transcribed spacer ITS-1, 5.8S, ITS-2 and flanking sequences (=ITS+), three ascaridoid nematode species were identified. The prevalence of infestation during the 3 years ranged from 42.9% to 62.9% and 22.9% to 40.0% for the anisakids Anisakis simplex (s.s.) and Pseudoterranova decipiens (s.s.), respectively, and from 28.6% to 60.0% for the raphidascarid Hysterothylacium aduncum. A total of 18 specimens, two of each species and examination year, revealed no sibling species, suggesting a limited distribution of other ascaridoid siblings into the deep sea. The ITS-1, 5.8S and ITS-2 sequences of A. simplex (s.s.) from the East Greenland Sea did not differ from previously published sequence data (GenBank) from other regions in the Atlantic and Pacific oceans. The sequences of P. decipiens (s.s.) corresponded most closely to those of specimens from Richardson Bay, western Pacific, and differed in four positions (0.5%). They corresponded least to those of specimens from Japan (1.5%). The sequence data for H. aduncum differed in two positions in the ITS-1 (0.2%) and three positions in the ITS-2 (0.3%) from sequences from Japan. A high genetic similarity between the regions can be explained by (a) extensive final host migration in the case of A. simplex (s.s.), (b) an overlapping distribution of final host populations along the continental shelves for P. decipiens (s.s.) and (c) a low host specificity and large population size in the intermediate and final hosts for H. aduncum. The occurrence of the identified species in the macrourid fish underlines the potential of cosmopolitan ascaridoid nematodes to distribute not only horizontally but also vertically in the deep sea.     

二阶不稳定型中立型微分方程解的振动准则

改进不稳定型二阶中立型微分方程的最后结果,进一步研究该类方程解的振动条件。     

HUMBOLDT AND THE HABITABILITY OF CANADA'S GREAT NORTHWEST*

ABSTRACT. Alexander von Humboldt's influence in British North America during the nineteenth century was filtered mainly through British imperial applications of “Humboldtian” sciences, including geomagnetism and biogeography. The best‐known examples include Edward Sabine and John Henry Lefroy, Royal Artillery officers who, during the 1830s and 1840s, transformed British North American outposts and territories, including Rupert's Land, into Humboldtian sites and regions in Great Britain's imperial “magnetic crusade.” Important groundwork had already been laid by John Richardson, who applied data accrued during John Franklin's overland Arctic expeditions during the 1820s to systematize Humboldtian inquiries into the habitability of Canada's Great Northwest. Despite both the relative decline of Humboldtian sciences by midcentury and Humboldt's own reservations about the political ramifications of his science, his “cosmic” outlook circulated in Canada to refine territorial expansionists' scientistic arguments justifying annexation of Rupert's Land after the monopoly of the Hudson's Bay Company expired in 1869.     

Boussinesq-type modelling using an unstructured finite element technique

A model for solving the two-dimensional enhanced Boussinesq equations is presented. The model equations are discretised in space using an unstructured finite element technique. The standard Galerkin method with mixed interpolation is applied. The time discretisation is performed using an explicit three-step Taylor–Galerkin method. The model is extended to the surf and swash zone by inclusion of wave breaking and a moving boundary at the shoreline. Breaking is treated by an existing surface roller model, but a new procedure for the detection of the roller thickness is devised. The model is verified using four test cases and the results are compared with experimental data and results from an existing finite difference Boussinesq model.     

基于GPU加速的Boussinesq类波浪传播变形数值模型

Boussinesq波浪模型是一类相位解析模型,在时域内求解需要较高的空间和时间分辨率以保证计算精度。为提高计算效率,有必要针对该类模型开展并行算法的研究。与传统的中央处理器(CPU)相比,图形处理器(GPU)有大量的运算器,可显著提高计算效率。基于统一计算设备架构CUDA C语言和图形处理器,实现了Boussinesq模型的并行运算。将本模型的计算结果同CPU数值模拟结果和解析解相比较,发现得到的结果基本一致。同时也比较了CPU端与GPU端的计算效率,结果表明,GPU数值模型的计算效率有明显提升,并且伴随数值网格的增多,提升效果更为明显。