Impact of difference accuracy on computational properties of vertical grids for a nonhydrostatic model

Starting from nonhydrostatic Boussinesq approximation equations, a general method is introduced to deduce the dispersion relationships. A comparative investigation is performed on inertia-gravity wave with horizontal lengths of 100, 10 and 1 km. These are examined using the second-order central difference scheme and the fourth-order compact difference scheme on vertical grids that are currently available from the perspectives of frequency, horizontal and vertical component of group velocity. These findings are compared to analytical solutions. The obtained results suggest that whether for the second-order central difference scheme or for the fourth-order compact difference scheme, Charny-Phillips and Lorenz ( L) grids are suitable for studying waves at the above-mentioned horizontal scales; the Lorenz time-staggered and Charny-Phillips time staggered (CPTS) grids are applicable only to the horizontal scales of less than 10 km, and N grid ( unstaggered grid) is unsuitable for simulating waves at any horizontal scale. Furthermore, by using fourth-order compact difference scheme with higher difference precision, the errors of frequency and group velocity in horizontal and vertical directions produced on all vertical grids in describing the waves with horizontal lengths of 1, 10 and 100 km cannot inevitably be decreased. So in developing a numerical model, the higher-order finite difference scheme, like fourth-order compact difference scheme, should be avoided as much as possible, typically on L and CPTS grids, since it will not only take many efforts to design program but also make the calculated group velocity in horizontal and vertical directions even worse in accuracy.

Impact of spatial resolution and spatial difference accuracy on the performance of Arakawa A-D grids

This paper alms at illustrating the impact of spatial difference scheme and spatial resolution on the performance of Arakawa A-D grids in physical space. Linear shallow water equations are discretized and forecasted on Arakawa A-D grids for 120-minute using the ordinary second-order (M and fourth-order (C4) finite difference schemes with the grid spacing being 100 km, 10 km and I km, respectively. Then the forecasted results are compared with the exact solution, the result indicates that when the grid spacing is I kin, the inertial gravity wave can be simulated on any grid with the same results from C2 scheme or C4 scheme, namely the impact of variable configuration is neglectable; while the inertial gravity wave is simulated with lengthened grid spacing, the effects of different variable configurations are different. However, whether for C2 scheme or for C4 scheme, the RMS is minimal (maximal) on C (D) grid. At the same time it is also shown that when the difference accuracy increases from C2 scheme to C4 scheme, the resulted forecasts do not uniformly decrease, which is validated by the change of the group A velocity relative error from C2 scheme to C4 scheme. Therefore, the impact of the grid spacing is more important than that of the difference accuracy on the performance of Arakawa A-D grid.

Joint statistical distribution of two-point sea surface elevations in finite water depth

Based on the second-order random wave solutions of water wave equations in finite water depth, a joint statistical distribution of two-point sea surface elevations is derived by using the characteristic function expansion method. It is found that the joint distribution depends on five parameters. These five parameters can all be determined by the water depth, the relative position of two points and the wave-number spectrum of ocean waves. As an illustrative example, for fully developed wind-generated sea, the parameters that appeared in the joint distribution are calculated for various wind speeds, water depths and relative positions of two points by using the Donelan and Pierson spectrum and the nonlinear effects of sea waves on the joint distribution are studied. (C) 2003 Elsevier B.V. All rights reserved.

A semi-analytical theory of coastal upwelling and jet

The general forms of the conservation of momentum, temperature and potential vorticity of coastal ocean are obtained in the x-z plane for the nonlinear ocean circulation of Boussinesq fluid, and a elliptic type partial differential equations of second order are derived. Solution of the partial differential equations are obtained under the conditions that the fluid moves along the topography. The numerical results show that there exist both upwelling and downwelling along coastline that mainly depends on the large scale ocean condition. Numerically results of the upwelling (downwelling), coastal jet and temperature front zone are favorable to the observations.

NONLINEAR GRAVITY-WAVES IN DEEP-WATER

In consideration of the problem on the boundary condition of nonlinear free water wave, coordinate transform is used to handle the free boundary. Supposing the solution form be the traveling wave, the ordinary differential equations of the one-order autonomous system with two variables are caused, then expanding the nonlinear terms at the equilibrium point with the Taylor expansion, we obtained the solution to traveling wave. The linear approximate equation near the equilibrium point is the small amplitude wave. A new nonlinear periodic traveling wave and nonlinear dispersion relation are shown when expanding to the second-order terms. A conclusion that the expansion of dispersion relation does not contain any odd-power terms of wave steepness and because of the nonlinear effort an oscillate structure is produced in the vertical direction is drawn.

Highly nonlinear internal solitary waves over the continental shelf of the northwestern South China Sea

Large amplitude internal solitary waves (ISWs) often exhibit highly nonlinear effects and may contribute significantly to mixing and energy transporting in the ocean. We observed highly nonlinear ISWs over the continental shelf of the northwestern South China Sea (19A degrees 35'N, 112A degrees E) in May 2005 during the Wenchang Internal Wave Experiment using in-situ time series data from an array of temperature and salinity sensors, and an acoustic Doppler current profiler (ADCP). We summarized the characteristics of the ISWs and compared them with those of existing internal wave theories. Particular attention has been paid to characterizing solitons in terms of the relationship between shape and amplitude-width. Comparison between theoretical prediction and observation results shows that the high nonlinearity of these waves is better represented by the second-order extended Korteweg-de Vries (KdV) theory than the first-order KdV model. These results indicate that the northwestern South China Sea (SCS) is rich in highly nonlinear ISWs that are an indispensable part of the energy budget of the internal waves in the northern South China Sea.

Probability distribution of random wave-current forces

Based on the second-order solutions obtained for the three-dimensional weakly nonlinear random waves propagating over a steady uniform current in finite water depth, the joint statistical distribution of the velocity and acceleration of the fluid particle in the current direction is derived using the characteristic function expansion method. From the joint distribution and the Morison equation, the theoretical distributions of drag forces, inertia forces and total random forces caused by waves propagating over a steady uniform current are determined. The distribution of inertia forces is Gaussian as that derived using the linear wave model, whereas the distributions of drag forces and total random forces deviate slightly from those derived utilizing the linear wave model. The distributions presented can be determined by the wave number spectrum of ocean waves, current speed and the second order wave-wave and wave-current interactions. As an illustrative example, for fully developed deep ocean waves, the parameters appeared in the distributions near still water level are calculated for various wind speeds and current speeds by using Donelan-Pierson-Banner spectrum and the effects of the current and the nonlinearity of ocean waves on the distribution are studied. (c) 2006 Elsevier Ltd. All rights reserved.

藻体对水环境中N、P及重金属Cu2+、Pb2+、Cd2+、Cr6+的吸附特征研究

随着全球生态环境的恶化，各国日益重视对水体中各种污染物的治理。利用藻类的吸收、富集和降解作用，可以去除污水中的营养物质、重金属离子和有机污染物，与其他物理、化学及工程的方法相比，该技术具有以下优点：成本低、能耗小、治理效果较好，对环境污染小，有利于资源化，有利于整体生态环境的改善，是治理水质污染的新途径。 本文利用几种大型海藻对富营养化海水进行处理，结果发现孔石莼、刚毛藻均有很强的吸收N、P的能力，吸收能力依次为褶曲刚毛藻>束生刚毛藻>孔石莼。水体中褶曲刚毛藻3 g/L含量，在3～5小时之内，可把中等以上富营养化海水中的N、P降低至一类海水水平。利用刚毛藻处理富营养化地下海水和养殖废水，进行海参和大菱鲆养殖试验，探索藻类净化水质和废水循环利用的新模式，使水体保持较低的营养盐状态，减轻养殖废水对环境的影响，实现了海水养殖业与环境的可持续发展。 刚毛藻在我国近海滩涂分布广泛，利用它来处理富营养化水体，并和水产养殖业相结合，既净化水体，使养殖废水能循环利用，满足水产养殖的需求，又改善水产业生态环境。同时，将回收藻体生产优质饲料、食品和药物等，实现藻类资源的高值利用。刚毛藻营养丰富，用其替代鼠尾藻作海参饲料，资源丰富，成本低，效果好，是一种值得加以开发利用的宝贵资源，具有广泛的应用前景。 生物吸附法是一种经济有效的移除废水中有害重金属离子的方法。由于藻类细胞壁中的多聚糖可提供吸附重金属的位点，廉价而蕴藏丰富的海藻对多种重金属表现出很强的吸附能力。所以本文通过分批实验，研究了非活体刚毛藻对水体中重金属Cu2+、Pb2+和Cd2+的吸附影响因子、吸附热力学、吸附动力学及吸附机理，得到了平衡等温线及动力学数据。吸附过程的最佳pH值为5.0，吸附量随温度的升高而增加，水体中常见的Na+、K+、Ca2+、Mg2+阳离子及Cl-、NO3-、SO42-、C2O42-等阴离子的存在对吸附的影响并不显著。EDTA存在时，吸附百分率大大降低。吸附等温线符合Langmuir和Freundlich方程。刚毛藻对重金属Cu2+、Pb2+和Cd2+的吸附容量很高，25℃时，对Cu2+、Pb2+和Cd2+的最大吸附容量分别为1.61 mmol/g、0.96 mmol/g和0.98 mmol/g，且吸附过程为吸热反应。刚毛藻对重金属Cu2+、Pb2+和Cd2+的吸附过程为化学吸附，在吸附过程中藻体表面的官能团可能与金属离子发生了螯合作用。吸附动力学过程符合pseudo-二级动力学模型，在初始的30min内，吸附速率很快，随后速率逐渐降低。解吸试验表明，用EDTA可以对重金属进行回收，刚毛藻可以循环利用。实验结果表明刚毛藻是一种高效、经济实用的生物吸附材料，可用来吸附回收水体中的重金属Cu2+、Pb2+和Cd2+等。 通过非活体刚毛藻对重金属Cr6+的吸附影响因子、吸附动力学、吸附机理的研究发现，刚毛藻对Cr6+具有很强的还原能力，对电镀废水中的Cr6+的还原去除提供了非常好的方法。吸附过程的最佳pH值为2～3，实际电镀废水通常在此pH范围，因此处理实际废水时，首先在原酸性条件下，对Cr6+进行还原去除，然后调废水pH至5.0，继续进行吸附，去除其他二价离子及被还原的三价Cr离子，实现了利用同一材料还原Cr6+为Cr3+，并将Cr3+和其他重金属离子同时去除。通过对机理的讨论，认为刚毛藻对Cr6+的生物吸附过程不是一个简单的“离子交换过程”，而是一个“吸附还原过程”。在海藻量足够的前提下，只要时间足够长，Cr6+可被彻底还原去除。 利用工业废弃物褐藻渣，对水体中重金属离子Cu2+、Pb2+、Cd2+及Cr6+的生物吸附特性分别进行了讨论，结果表明褐藻渣对重金属离子的吸附特性与刚毛藻一致，吸附等温线符合Langmuir和Freundlich方程，在25℃时，pH为5.0时，由Langmuir方程求出褐藻渣对Cu2+、Pb2+和Cd2+的最大吸附容量分别为4.20 mmol/g、3.13 mmol/g和2.97 mmol/g。褐藻渣对低、高浓度的重金属Cr6+都具有很强的吸附能力，且移除效果比较彻底。实际应用结果表明，褐藻渣是一种高效、经济实用的生物吸附材料，可用来吸附回收水体中的重金属离子，具有广泛的应用前景。

Biosorption and desorption of Cd2+ from wastewater by dehydrated shreds of Cladophora fascicularis

The adsorption and desorption of algae Cladophora fascicularis and their relation with initial Cd2+ concentration, initial pH, and co-existing ions were studied. Adsorption equilibrium and biosorption kinetics were established from batch experiments. The adsorption equilibrium was adequately described by the Langmuir isotherm, and biosorption kinetics was in pseudo-second order model. The experiment on co-existing ions showed that the biosorption capacity of biomass decreased with an increasing concentration of competing ions. Desorption experiments indicated that EDTA was efficient desorbent for recovery from Cd2+. With high capacities of metal biosorption and desorption, the biomass of Cladophora fascicularis is promising as a cost-effective biosorbent for the removal of Cd2+ from wastewater.

Sorption and desorption of lead (II) from wastewater by green algae Cladophora fascicularis

Biosorption is an effective method to remove heavy metals from wastewater. In this work, adsorption features of Cladophora fascicularis were investigated as a function of time, initial pH, initial Pb(II) concentrations, temperature and co-existing ions. Kinetics and equilibria were obtained from batch experiments. The biosorption kinetics followed the pseudo-second order model. Adsorption equilibria were well described by the Langmuir and Freundlich isotherm models. The maximum adsorption capacity was 198.5 mg/g at 298 K and pH 5.0. The adsorption processes were endothermic and the biosorption heat was 29.6 kJ/mol. Desorption experiments indicated that 0.01 mol/L Na(2)EDTA was an efficient desorbent for the recovery of Pb(II) from biomass. IR spectrum analysis suggested amido or hydroxy, C=O and C-O could combine intensively with Pb(II). (C) 2006 Elsevier B.V. All rights reserved.

Biosorption of copper (II) and lead (II) from aqueous solutions by nonliving green algae Cladophora fascicularis: Equilibrium, kinetics and environmental effects

Biosorption of Cu2+ and Pb2+ by Cladophora fascicularis was investigated as a function of initial pH, initial heavy metal concentrations, temperature and other co-existing ions. Adsorption equilibriums were well described by Langmuir and Freundlich isotherm models. The maximum adsorption capacities were 1.61 mmol/ g for Cu2+ and 0.96 mmol/ g for Pb2+ at 298K and pH 5.0. The adsorption processes were endothermic and biosorption heats calculated by the Langmuir constant b were 39.0 and 29.6 kJ/ mol for Cu2+ and Pb2+, respectively. The biosorption kinetics followed the pseudo- second order model. No significant effect on the uptake of Cu2+ and Pb2+ by co-existing cations and anions was observed, except EDTA. Desorption experiments indicated that Na(2)EDTA was an efficient desorbent for the recovery of Cu2+ and Pb2+ from biomass. The results showed that Cladophora fascicularis was an effective and economical biosorbent material for the removal and recovery of heavy metal ions from wastewater.

Synthesis and evaluation of a thiourea-modified chitosan derivative applied for adsorption of Hg(II) from synthetic wastewater

In this work, a thiourea-modified chitosan derivative (TMCD) was synthesized through two steps, O-carboxymethylated first and then modified by a polymeric Schiff's base of thiourea/glutaraldehyde. The adsorption behavior of mercury (II) ions onto TMCD was investigated through batch method. The maximum adsorption capacity for Hg(II) was found to be 6.29 mmol/g at pH 5.0 and both kinetic and thermodynamic parameters of the adsorption process were obtained. The results indicated that adsorption process was spontaneous exothermic reaction and kinetically followed pseudo-second-order model. The adsorption experiments also demonstrated TMCD had high adsorption selectivity towards Hg(II) ions when coexisted with Cu(II), Zn(II), Cd(II) and Ca(II) in solution and it could be easily regenerated and efficiently reused. (C) 2010 Elsevier B.V. All rights reserved.

Addition reactions of nitrones on the reconstructed C(100)-2 x 1 surfaces

In this paper, the reactions of nitrone, N-methyl nitrone, N-phenyl nitrone and their hydroxylamine tautomers (vinyl-hydroxylamine, N-methyl-vinyl-hydroxylamine and N-phenyl-vinyl-hydroxylamine) on the reconstructed C(100)-2 x 1 surface have been investigated using hybrid density functional theory (B3LYP), Moller-Plesset second-order perturbation (MP2) and multi-configuration complete-active-space self-consistent-field (CASSCF) methods. The calculations showed that all the nitrones can react with the surface "dimer" via facile 1.3-dipolar cycloaddition with small activation barriers (less than 12.0 kJ/mol at B3LYP/6-31g(d) level). The [2+2] cycloaddition of hydroxylamine tautomers on the C(100) surface follows a diradical mechanism. Hydroxylamine tautomers first form diradical intermediates with the reconstructed C(I 00)-2 x I surface by overcoming a large activation barrier of 50-60 kJ/mol (B3LYP), then generate [2+2] cycloaddition products via diradical transition states with negligible activation barriers. The surface reactions result in hydroxyl or amino-terminated diamond surfaces, which offers new opportunity for further modifications. (C) 2007 Elsevier B.V. All rights reserved.

Addition reaction of nitrones on the reconstructed Si(100)-2 x 1 surface

The reaction of nitrone, N-methyl nitrone, and their hydroxylamine tautomers (vinyl-hydroxylamine and N-methyl vinyl-hydroxylamine) on the reconstructed Si(100)-2 x 1 surface has been investigated by means of hybrid density functional theory (B3LYP) and Moller-Plesset second-order perturbation (MP2) methods. The calculations predicted that both of the nitrones should react with the surface dimer via facile concerted 1,3-dipolar cycloaddition leading to 5-member-ring compounds. The reaction of hydroxylamine tautomers on the Si(100) surface follows pi-complex (intermediate) mechanism. For the reaction of N-methyl vinyl-hydroxylamine, the pi-complex intermediate undergoes [2+2] cycloaddition leading to a 4-member-ring compound. But in the reaction of vinyl-hydroxylamine, the intermediate undergoes H-migration reaction ("ene" reaction) resulting in the oxime-terminated Si surface. All the surface reactions result in the hydroxyl-terminated silicon surfaces, which are very useful for the further modification of the semiconductor.

Theoretical study on adsorption of Na+ and Na+(H2O)(n) (n=1-6) on a clean Si(111) surface

To model the adsorption of Na+ in aqueous solution on the semiconductor surface, the interactions of Na+ and Na+(H2O)(n) (n = 1-6) with a clean Si(111) surface were investigated by using hybrid density functional theory (B3LYP) and Moller-Plesset second-order perturbation (MP2) methods. The Si(111) surface was described with Si8H12, Si16H20, and Si22H21 Cluster models. The effect of the basis set superposition error (BSSE) was taken into account by applying the counterpoise (CP) correction. The calculated results indicated that the interactions between the Na+ cation and the dangling bonds of the Si(111) surface are primarily electrostatic with partial orbital interactions. The magnitude of the binding energies depends weakly on the adsorption sites and the size of the clusters. When water molecules are present, the interaction between the Nal and Si(I 11) surfaces weakens and the binding energy has the tendency to saturate. On a Si22H21 cluster described surface, the optimized Na+-surface distance for Na+(H2O)(5) adsorbed at on-top site is 4.16 angstrom and the CP-corrected binding energy (MP2) is -35.4 kJ/mol, implying a weakly adsorption of hydrated Na+ cation on clean Si(111) surface.