Second-order solutions for random interfacial waves under steady uniform currents

In the present research, the study of Song (2004) for random interfacial waves in two-layer fluid is extended to the case of fluids moving at different steady uniform speeds. The equations describing the random displacements of the density interface and the associated velocity potentials in two-layer fluid are solved to the second order, and the wave-wave interactions of the wave components and the interactions between the waves and currents are described. As expected, the extended solutions include those obtained by Song (2004) as one special case where the steady uniform currents of the two fluids are taken as zero, and the solutions reduce to those derived by Sharma and Dean (1979) for random surface waves if the density of the upper fluid and the current of the lower fluid are both taken as zero.

Second-order solutions for random interfacial waves in N-layer density-stratified fluid with steady uniform currents

In the present paper, the random inter facial waves in N-layer density-stratified fluids moving at different steady uniform speeds are researched by using an expansion technique, and the second-order a symptotic solutions of the random displacements of the density interfaces and the associated velocity potentials in N-layer fluid are presented based on the small amplitude wave theory. The obtained results indicate that the wave-wave second-order nonlinear interactions of the wave components and the second-order nonlinear interactions between the waves and currents are described. As expected, the solutions include those derived by Chen (2006) as a special case where the steady uniform currents of the N-layer fluids are taken as zero, and the solutions also reduce to those obtained by Song (2005) for second-order solutions for random interfacial waves with steady uniform currents if N=2.

Second-order Stokes wave solutions for intefacial waves in three-layer stratified fluid with background current

In this paper, interfacial waves in three-layer stratified fluid with background current are investigated using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes wave solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory, and the Kelvin-Helmholtz instability of interfacial waves is studied. As expected, for three-layer stratified fluid with background current, the first-order asymptotic solutions (linear wave solutions), dispersion relation and the second-order asymptotic solutions derived depend on not only the depths and densities of the three-layer fluid but also the background current of the fluids, and the second-order Stokes wave solutions of the associated elevations of the interfacial waves describe not only the second-order nonlinear wave-wave interactions between the interfacial waves but also the second-order nonlinear interactions between the interfacial waves and currents. It is also noted that the solutions obtained from the present work include the theoretical results derived by Chen et al (2005) as a special case. It also shows that with the given wave number k (real number) the interfacial waves may show Kelvin-Helmholtz instability.

A kind of extended Korteweg-de Vries equation and solitary wave solutions for interfacial waves in a two-fluid system

This paper considers interfacial waves propagating along the interface between a two-dimensional two-fluid with a flat bottom and a rigid upper boundary. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. It just focuses on the weakly non-linear small amplitude waves by introducing two small independent parameters: the nonlinearity ratio epsilon, represented by the ratio of amplitude to depth, and the dispersion ratio mu, represented by the square of the ratio of depth to wave length, which quantify the relative importance of nonlinearity and dispersion. It derives an extended KdV equation of the interfacial waves using the method adopted by Dullin et al in the study of the surface waves when considering the order up to O(mu(2)). As expected, the equation derived from the present work includes, as special cases, those obtained by Dullin et al for surface waves when the surface tension is neglected. The equation derived using an alternative method here is the same as the equation presented by Choi and Camassa. Also it solves the equation by borrowing the method presented by Marchant used for surface waves, and obtains its asymptotic solitary wave solutions when the weakly nonlinear and weakly dispersive terms are balanced in the extended KdV equation.

A bioaugmentation failure caused by phage infection and weak biofilm formation ability

Two biological aerated filters (BAF) were setup for ammonia removal treatment of the circulation water in a marine aquaculture. One of the BAFs was bioaugmented with a heterotrophic nitrifying bacterium, Lutimonas sp. H10, where the ammonia removal was not improved and the massive inoculation was even followed by a nitrification breakdown from day 9 to 18. The nitrification was remained stable in control BAF operated under the same conditions. Fluorescent in situ hybridization (FISH) with rRNA-targeted probes and cultivable method revealed that Lutimonas sp. H10 almost disappeared from the bioaugomented BAF within 3 d, and this was mainly due to the infection of a specific phage as revealed by flask experiment, plaque assay and transmission electron observation. Analyses of 16S rRNA gene libraries showed that bacterial groups from two reactors evolved differently and an overgrowth of protozoa was observed in the bioaugmented BAR Therefore, phage infection and poor biofilm forming ability of the inoculated strain are the main reasons for bioaugmentation failure. In addition, gazing by protozoa of the bacteria might be the reason for the nitrification breakdown in bioaugmented BAF during day 9-18.

Biosorption of Cr(VI) from aqueous solutions by nonliving green algae Cladophora albida

Biosorption of Cr(VI) from aqueous solutions by nonliving green algae Cladophora albida was investigated in batch experiments. The influence of pH, algal dosage, initial Cr(VI) concentration, temperature and coexisting anions on removal efficiencies of C. albida was studied. Cr(VI) removal process was influenced significantly by the variation of pH, and the optimum pH was chosen at a range of 1.0-3.0. The optimum algal dosage 2 g/L was used in the experiment. The removal rate of Cr(VI) was relatively rapid in the first 60 min, but then the rate decreased gradually. Removal mechanism was studied by analyzing Cr(VI) and total Cr in the solution. Biosorption and bioreduction were involved in the Cr(VI) removal. Biosorption of Cr(VI) was the first step. followed by Cr(VI) bioreduction and Cr(III) biosorption on the algal biomass. Actual industrial wastewater was used to evaluate the practicality of the biomass C. albida. From a practical viewpoint, the abundant and economic biomass C. albida could be used for removal of Cr(VI) from wastewater by the reduction of toxic Cr(VI) to less toxic Cr(III). (C) 2008 Elsevier Ltd. All rights reserved.

Biosorption of copper(II) from aqueous solutions by green alga Cladophora fascicularis

Biosorption is an effective means of removal of heavy metals from wastewater. In this work the biosorption behavior of Cladophora fascicularis was investigated as a function of pH, amount of biosorbent, initial Cu2+ concentration, temperature, and co-existing ions. Adsorption equilibria were well described by Langmuir isotherm models. The enthalpy change for the biosorption process was found to be 6.86 kJ mol(-1) by use of the Langmuir constant b. The biosorption process was found to be rapid in the first 30 min. The presence of co-existing cations such as Na+, K+, Mg2+, and Ca2+ and anions such as chloride, nitrate, sulfate, and acetate did not significantly affect uptake of Cu2+ whereas EDTA substantially affected adsorption of the metal. When experiments were performed with different desorbents the results indicated that EDTA was an efficient desorbent for the recovery of Cu2+ from biomass. IR spectral analysis suggested amido or hydroxy, C=O, and C-O could combine strongly with Cu2+.

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.

The inhibition of mild steel corrosion in 1 M hydrochloric acid solutions by triazole derivative

The title compound 1-(4,5-dihydro-3-phenylpyridine-1-yl)-2-(1H-1,2,4-triazole-1-yl)ethyl ketone (DTE) was synthesized and its inhibiting action on the corrosion of mild steel in 1 M hydrochloric acid solutions was investigated by means of weight loss, potentiodynamic polarization, electrochemical impedance spectroscopy (EIS) and scanning electronic microscope (SEM). Results obtained revealed that DIE performed excellently as a corrosion inhibitor for mild steel in 1 M hydrochloric acid media and its efficiency attains more than 90.9% at 1.0 x 10(-3) M at 298 K. Polarization curves indicated that the inhibitor behave mainly as mixed-type inhibitor. EIS showed that the charge transfer controls the corrosion process in the uninhibited and inhibited solutions. Adsorption of the inhibitor on the mild steel surface followed Langmuir adsorption isotherm. And the values of the free energy of adsorption Delta G(ads) indicated that the adsorption of DTE molecule was a spontaneous process and was typical of chemisorption. (c) 2008 Elsevier B.V. All rights reserved.

Suitability of extractants for predicting available sulfur in natural grassland in the Inner Mongolia steppe of China

It was the objective of this study to compare the suitability of different extractants for predicting the availability of sulfur (S) in natural grassland in a sulfur response trial on three different soil types in the Inner Mongolia steppe of China. For soil analysis, seven different extractants have been employed. The inorganic SO4-S concentration was determined by ion chromatography. Additionally, in the Ca(H-2-PO4)(2) extract the total soluble S was determined employing turbidimetry. Weak salt solutions (0.15% CaCl2, Ca(H2PO4)(2), and KH2PO4) extracted similar amounts Of SO4-S. Extraction with 0.025 M KCl provided the lowest SO4-S values. Deionized water dissolved significantly more SO4-S in the control plots than most weak salt extractants. The concentration of soluble organic S decreased in the control plots after 100 days of plant growth, indicating that the organic S pool contributed significantly to the S nutrition of the forage crops. Significant relationships among the SO4-S in the soil determined in different extracts and crop yield, sulfur content in the forage, and total sulfur uptake were only found for the Ca(H2PO4)(2) extract. In general, the correlation coefficients proved to be unsatisfactory for field experimentation.

特大地震激发地球自由振荡的数值模拟研究

Large earthquakes, such as the Chile earthquake in 1960 and the Sumatra-Andaman earthquake on Dec 26, 2004 in Indonesia, have generated the Earth’s free oscillations. The eigenfrequencies of the Earth’s free oscillations are closely related to the Earth’s internal structures. The conventional methods, which mainly focus on calculating the eigenfrequecies by analytical ways, and the analysis on observations can not easily study the whole processes from earthquake occurrence to the Earth’s free oscillation inspired. Therefore, we try to use numerical method incorporated with large-scale parallel computing to study on the Earth’s free oscillations excited by giant earthquakes. We first give a review of researches and developments of the Earth’s free oscillation, and basical theories under spherical coordinate system. We then give a review of the numerical simulation of seismic wave propagation and basical theories of spectral element method to simulate global seismic wave propagation. As a first step to study the Earth’s free oscillations, we use a finite element method to simulate the propagation of elastic waves and the generation of oscillations of the chime bell of Marquis Yi of Zeng, by striking different parts of the bell, which possesses the oval crosssection. The bronze chime bells of Marquis Yi of Zeng are precious cultural relics of China. The bells have a two-tone acoustic characteristic, i.e., striking different parts of the bell generates different tones. By analysis of the vibration in the bell and the spectrum analysis, we further help the understanding of the mechanism of two-tone acoustic characteristics of the chime bell of Marquis Yi of Zeng. The preliminary calculations have clearly shown that two different modes of oscillation can be generated by striking different parts of the bell, and indicate that finite element numerical simulation of the processes of wave propagation and two-tone generation of the chime bell of Marquis Yi of Zeng is feasible. These analyses provide a new quantitative and visual way to explain the mystery of the two-tone acoustic characteristics. The method suggested by this study can be applied to simulate free oscillations excited by great earthquakes with complex Earth structure. Taking into account of such large-scale structure of the Earth, small-scale low-precision numerical simulation can not simply meet the requirement. The increasing capacity in high-performance parallel computing and progress on fully numerical solutions for seismic wave fields in realistic three-dimensional spherical models, Spectral element method and high-performance parallel computing were incorporated to simulate the seismic wave propagation processes in the Earth’s interior, without the effects of the Earth’s gravitational potential. The numerical simulation shows that, the results of the toroidal modes of our calculation agree well with the theoretical values, although the accuracy of our results is much limited, the calculated peaks are little distorted due to three-dimensional effects. There exist much great differences between our calculated values of spheroidal modes and theoretical values, because we don’t consider the effect the Earth’ gravitation in numerical model, which leads our values are smaller than the theoretical values. When , is much smaller, the effect of the Earth’s gravitation make the periods of spheroidal modes become shorter. However, we now can not consider effects of the Earth’s gravitational potential into the numerical model to simulate the spheroidal oscillations, but those results still demonstrate that, the numerical simulation of the Earth’s free oscillation is very feasible. We make the numerical simulation on processes of the Earth’s free oscillations under spherically symmetric Earth model using different special source mechanisms. The results quantitatively show that Earth’s free oscillations excited by different earthquakes are different, and oscillations at different locations are different for free oscillation excited by the same earthquake. We also explore how the Earth’s medium attenuation will take effects on the Earth’s free oscillations, and take comparisons with the observations. The medium attenuation can make influences on the Earth’s free oscillations, though the effects on lower-frequency fundamental oscillations are weak. At last, taking 2008 Wenchuan earthquake for example, we employ spectral element method incorporated with large-scale parallel computing technology to investigate the characteristics of seismic wave propagation excited by Wenchuan earthquake. We calculate synthetic seismograms with one-point source model and three-point source model respectively. Full 3-D visualization of the numerical results displays the profile of the seismic wave propagation with respect to time. The three-point source, which was proposed by the latest investigations through field observation and reverse estimation, can better demonstrate the spatial and temporal characteristics of the source rupture processes than one-point source. Primary results show that those synthetic signals calculated from three-point source agree well with the observations. This can further reveal that the source rupturing process of Wenchuan earthquake is a multi-rupture process, which is composed by at least three or more stages of rupture processes. In conclusion, the numerical simulation can not only solve some problems concluding the Earth’s ellipticity and anisotropy, which can be easily solved by conventional methods, but also finally solve the problems concluding topography model and lateral heterogeneity. We will try to find a way to fully implement self-gravitation in spectral element method in future, and do our best to continue researching the Earth’s free oscillations using the numerical simulations to see how the Earth’ lateral heterogeneous will affect the Earth’s free oscillations. These will make it possible to bring modal spectral data increasingly to bear on furthering our understanding of the Earth’s three-dimensional structure.

各向异性与非线性介质中弹性波场传播特征研究

The topic of this study is about the propagation features of elastic waves in the anisotropic and nonlinear media by numerical methods with high accuracy and stability. The main achievements of this paper are as followings: Firstly, basing on the third order elastic energy formula, principle of energy conservation and circumvolved matrix method, we firstly reported the equations of non-linear elastic waves with two dimensions and three components in VTI media. Secondly, several conclusions about some numerical methods have been obtained in this paper. Namely, the minimum suitable sample stepth in space is about 1/8-1/12 of the main wavelength in order to distinctly reduce the numerical dispersion resulted from the numerical mehtod, at the same time, the higher order conventional finite difference (CFD) schemes will give little contribution to avoid the numerical solutions error accumulating with time. To get the similar accuracy with the fourth order center finite difference method, the half truncation length of SFFT should be no less than 7. The FDFCT method can present with the numerical solutions without obvious dispersion when the paprameters of FCT is suitable (we think they should be in the scope from 0.0001 to 0.07). Fortunately, the NADM method not only can reported us with the higher order accuracy solutions (higher than that of the fourth order finite difference method and lower than that of the sixth order finite difference method), but also can distinctly reduce the numerical dispersion. Thirdly, basing on the numerial and theoretical analysis, we reported such nonlinear response accumulating with time as waveform aberration, harmonic generation and resonant peak shift shown by the propagation of one- and two-dimensional non-linear elasticwaves in this paper. And then, we drew the conclusion that these nonlinear responses are controlled by the product between nonlinear strength (SN) and the amplitude of the source. At last, the modified FDFCT numerical method presented by this paper is used to model the two-dimensional non-linear elastic waves propagating in VTI media. Subsequently, the wavelet analysis and polarization are adopted to investigate and understand the numerical results. And then, we found the following principles (attention: the nonlinear strength presented by this paper is weak, the thickness of the -nonlinear media is thin (200m), the initial energy of the source is weak and the anisotropy of the media is weak too): The non-linear response shown by the elastic waves in VTI media is anisotropic too; The instantaneous main frequency sections of seismic records resulted from the media with a non-linear layer have about 1/4 to 1/2 changes of the initial main frequency of source with that resulted from the media without non-linear layer; The responses shown by the elasic waves about the anisotropy and nonlinearity have obvious mutual reformation, namely, the non-linear response will be stronger in some directions because of the anisotropy and the anisotropic strength shown by the elastic waves will be stronger when the media is nonlinear.