A new method of describing bottom stress in two-dimensional hydrodynamical models of shallow homogeneous seas, estuaries, and lakes

A new expression for bottom friction is developed for use in two-dimensional hydrodynamical models of shallow homogeneous seas, estuaries, and lakes. Bottom stress is provided by a single relaxation approximation which can be used to replace the conventional parametrization in any existing explicit time-stepping model. The method produces the correct steady state flow for wind-driven circulation in shallow systems. It derives the bottom stress from the vertical eddy viscosity which can have any prescribed variation through the water column. The single relaxation approximation uses a recursive relation for bottom stress involving only values at the previous time step and a pair of precomputed coefficients at each grid point.     

湿度及无机填料对低密度聚乙烯热释电流谱的影响

我们将低密度聚乙烯试样暴露在湿空气中一定的时间,不管在用直流高压极化的前后,甚至在极化后对其经过72h的真空干燥处理,在中温区也存在一个附加的湿致热释电流峰,它可能是由俘获在晶区-非晶区界面的离子热释放所致。 由分析在极化前对含无机填料(经表面处理的高岭土)的低密度聚乙烯试样进行干燥或润湿处理后的热释电流谱表明,聚乙烯中的无机填料与吸收的水分子都可作为电子的受主,前者为电子深陷阱,后者为电子浅陷阱。     

The principle of remote-resonance spectroscopy

To promote the efficiency of the effect of remote-resonance which is induceable in the anomalous dispersion region of the resonator surface in the I.R. region, we have investigated three subjects; One is usage of the multi-piled oscillators made of silica-Si layers. Second is the soft-Zeeman effect (at 0–15 Gauss) which was induced in the system of remote-resonance which consists of the oscillator and the resonator they were situated perpendicularly with some distance in the atomospheric air. Third is usage of the I.R. radiation emitted from the surface of hand and the radiation modulated by some textiles as oscillators. The efficiency of this system was shown as R_i (E_i) (E_i), (E_i). (E_i), (emission efficiency x transferring efficiency x resonance efficiency) and R_i (E_i) was shown as (N_o (E_i)±N_i (E_i))x f{R_o (E_i)±R_i (E_i)} at the spin sensitive region of the resonator surface in the Nf-R relation. Also, we discussed the stress-optical effect, the soft-Zeeman effect and some physiological problems induced in this system based on the statistical spin-quantum mechanics considering the predissociation and dissociation process of the shallow electrons in Si (100) face and CO ₂ ^* excimers and the CO₂ molecules in the air.     

Boundary discretization for high‐order discontinuous Galerkin computations of tidal flows around shallow water islands

In this paper some preliminary results concerning the application of the high‐order discontinuous Galerkin (DG) method for the resolution of realistic problems of tidal flows around shallow water islands are presented. In particular, tidal flows are computed around the Rattray island located in the Great Barrier Reef. This island is a standard benchmark problem well documented in the literature providing useful in situ measurements for validation of the model. Realistic elements of the simulation are a tidal flow forcing, a variable bathymetry and a non‐trivial coastline. The computation of tidal flows in shallow water around an island is very similar to the simulation of the Euler equations around bluff bodies in quasi‐steady flows. The main difference lies in the high irregularity of islands' shapes and in the fact that, in the framework of large‐scale ocean models, the number of elements to represent an island is drastically limited compared with classical engineering computations. We observe that the high‐order DG method applied to shallow water flows around bluff bodies with poor linear boundary representations produces oscillations and spurious eddies. Surprisingly those eddies may have the right size and intensity but may be generated by numerical diffusion and are not always mathematically relevant. Although not interested in solving accurately the boundary layers of an island, we show that a high‐order boundary representation is mandatory to avoid non‐physical eddies and spurious oscillations. It is then possible to parametrize accurately the subgrid‐scale processes to introduce the correct amount of diffusion in the model. The DG results around the Rattray island are eventually compared with current measurements and reveal good agreement. Copyright © 2008 John Wiley & Sons, Ltd.     

Flux and source term discretization in two‐dimensional shallow water models with porosity on unstructured grids

Two‐dimensional shallow water models with porosity appear as an interesting path for the large‐scale modelling of floodplains with urbanized areas. The porosity accounts for the reduction in storage and in the exchange sections due to the presence of buildings and other structures in the floodplain. The introduction of a porosity into the two‐dimensional shallow water equations leads to modified expressions for the fluxes and source terms. An extra source term appears in the momentum equation. This paper presents a discretization of the modified fluxes using a modified HLL Riemann solver on unstructured grids. The source term arising from the gradients in the topography and in the porosity is treated in an upwind fashion so as to enhance the stability of the solution. The Riemann solver is tested against new analytical solutions with variable porosity. A new formulation is proposed for the macroscopic head loss in urban areas. An application example is presented, where the large scale model with porosity is compared to a refined flow model containing obstacles that represent a schematic urban area. The quality of the results illustrates the potential usefulness of porosity‐based shallow water models for large scale floodplain simulations. Copyright © 2005 John Wiley & Sons, Ltd.     

A high‐resolution wetting and drying algorithm for free‐surface hydrodynamics

A new wetting and drying algorithm for numerical modeling free‐surface flows is proposed and analyzed. A well structured, mildly nonlinear system for the discrete water surface elevation is derived from the governing differential equations by requiring a correct mass balance in wet areas as well as in the region of transition from wet to dry and from dry to wet. Existence and uniqueness of the numerical solution, along with a convergence analysis of an iterative scheme for the mildly nonlinear system, is provided. The present algorithm is devised to use high‐resolution bathymetric data at subgrid level. The resulting model is quite efficient, does not require a threshold value for minimal water depth, does not produce un‐physical negative water depths and generates accurate results with relatively coarse mesh and large time step size. These features are illustrated on a severe test‐case with known analytical solution. Copyright © 2008 John Wiley & Sons, Ltd.     

Nonlinear analysis of imperfect squarely-reticulated shallow spherical shells

Nonlinear behavior of single-layer squarely-reticulated shallow spherical shells with geometrical imperfections subjected to a central concentrated (joint) load has been studied in this paper. Using the asymptotic iteration method, an analytical characteristic relationship between the non-dimensional load and central deflection is obtained. The resulting asymptotic solution can be used readily to perform the analysis of parameters and predict the buckling critical load. Meanwhile, numerical examples are presented and effects of imperfection factor and boundary conditions on buckling of the structures are discussed. Comparisons with data based on the finite element method show good exactness of the resulting solution.     

Finite‐volume multi‐stage schemes for shallow‐water flow simulations

A finite‐volume multi‐stage (FMUSTA) scheme is proposed for simulating the free‐surface shallow‐water flows with the hydraulic shocks. On the basis of the multi‐stage (MUSTA) method, the original Riemann problem is transformed to an independent MUSTA mesh. The local Lax–Friedrichs scheme is then adopted for solving the solution of the Riemann problem at the cell interface on the MUSTA mesh. The resulting first‐order monotonic FMUSTA scheme, which does not require the use of the eigenstructure and the special treatment of entropy fixes, has the generality as well as simplicity. In order to achieve the high‐resolution property, the monotonic upstream schemes for conservation laws (MUSCL) method are used. For modeling shallow‐water flows with source terms, the surface gradient method (SGM) is adopted. The proposed schemes are verified using the simulations of six shallow‐water problems, including the 1D idealized dam breaking, the steady transcritical flow over a hump, the 2D oblique hydraulic jump, the circular dam breaking and two dam‐break experiments. The simulated results by the proposed schemes are in satisfactory agreement with the exact solutions and experimental data. It is demonstrated that the proposed FMUSTA schemes have superior overall numerical accuracy among the schemes tested such as the commonly adopted Roe and HLL schemes. Copyright © 2007 John Wiley & Sons, Ltd.     

A numerical model for the transport of salinity in estuaries

In this paper, a numerical model for the simulation of the hydrodynamics and of the evolution of the salinity in shallow water estuaries is presented. This tool is intended to predict the possible effects of Civil Engineering public works and other human actions (dredging, building of docks, spillages, etc.) on the marine habitat, and to evaluate their environmental impact in areas with high productivity of fish and of seafood. The prediction of these effects is essential in the decision making about the different options that could be implemented. The mathematical model consists of two coupled systems of differential equations: the shallow water hydrodynamic equations (that describe the evolution of the depth and of the velocity field) and the shallow water advective–diffusive transport equation (that describes the evolution of the salinity level). Some important issues that must be taken into account are the effects of the tides (including that the seabed could be exposed), the volume of fresh water provided by the rivers and the effects of the winds. Thus, different types of boundary conditions are considered. The numerical model proposed for solving this problem is a second‐order Taylor–Galerkin finite element formulation. The proposed approach is applied to a real case: the analysis of the possible effects of dredging Los Lombos del Ulla, a formation of sandbanks in the Arousa Estuary (Galicia, Spain). A number of simulations have been carried out to compare the actual salinity level with the predicted situation if the different dredging options were executed. Some of the obtained results are presented and discussed. Copyright © 2007 John Wiley & Sons, Ltd.     

A robust high‐resolution finite volume scheme for the simulation of long waves over complex domains

The propagation, runup and rundown of long surface waves are numerically investigated, initially in one dimension, using a well‐balanced high‐resolution finite volume scheme. A conservative form of the nonlinear shallow water equations with source terms is solved numerically using a high‐resolution Godunov‐type explicit scheme coupled with Roe's approximate Riemann solver. The scheme is also extended to handle two‐dimensional complex domains. The numerical difficulties related to the presence of the topography source terms in the model equations along with the appearance of the wet/dry fronts are properly treated and extended. The resulting numerical model accurately describes breaking waves as bores or hydraulic jumps and conserves volume across flow discontinuities. Numerical results show very good agreement with previously presented analytical or asymptotic solutions as well as with experimental benchmark data. Copyright © 2007 John Wiley & Sons, Ltd.