Higher-order Boussinesq-type equations for interfacial waves in a two-fluid system

Interfacial waves propagating along the interface between a three-dimensional two-fluid system with a rigid upper boundary and an uneven bottom are considered. There is a light fluid layer overlying a heavier one in the system, and a small density difference exists between the two layers. A set of higher-order Boussinesq-type equations in terms of the depth-averaged velocities accounting for stronger nonlinearity are derived. When the small parameter measuring frequency dispersion keeping up to lower-order and full nonlinearity are considered, the equations include the Choi and Camassa's results (1999). The enhanced equations in terms of the depth-averaged velocities are obtained by applying the enhancement technique introduced by Madsen et al. (1991) and Schaffer and Madsen (1995a). It is noted that the equations derived from the present study include, as special cases, those obtained by Madsen and Schaffer (1998). By comparison with the dispersion relation of the linear Stokes waves, we found that the dispersion relation is more improved than Choi and Camassa's (1999) results, and the applicable scope of water depth is deeper.

Second-order Stokes solutions for internal waves in three-layer density-stratified fluid

In this paper, internal waves in three-layer stratified fluid are investigated by using a perturbation method, and the second-order asymptotic solutions of the velocity potentials and the second-order Stokes solutions of the associated elevations of the interfacial waves are presented based on the small amplitude wave theory. As expected, the first-order solutions are consistent with ordinary linear theoretical results, and the second-order solutions describe the second-order modification on the linear theory and the interactions between the two interfacial waves. Both the first-order and second-order solutions derived depend on the depths and densities of the three-layer fluid. It is also noted that the solutions obtained from the present work include the theoretical results derived by Umeyama as special cases.

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.

An efficient combination of supercritical fluid extraction and high-speed counter-current chromatography to extract and purify homoisoflavonoids from Ophiopogon japonicus (Thunb.) Ker-Gawler

Supercritical fluid extraction (SFE) was used to extract homoisoflavonoids from Ophiopogon japonicus (Thunb.) Ker-Gawler. The optimization of parameters was carried out using an orthogonal test L-9 (3)(4) including pressure, temperature, dynamic extraction time and the amount of modifier. The process was then scaled up by 100 times with a preparative SFE system under the optimized conditions of 25 MPa, 55 degrees C, 4.0 h and 25% methanol as a modifier. Then crude extracts were separated and purified by high-speed counter-current chromatography (HSCCC) with a two-phase solvent system composed of n-hexane/ethyl acetate/methanol/ACN/water (1.8:1.0:1.0:1.2:1.0 v/v). There three homoisoflavonoidal compounds including methylophiopogonanone A 6-aldehydo-isoophiopogonone A, and 6-formyl-isoophiopogonanone A, were successfully isolated and purified in one step. The collected fractions were analyzed by HPLC. In each operation, 140 mg crude extracts was separated and yielded 15.3 mg of methylophiopogonanone A (96.9% purity), 4.1 mg of 6-aldehydo-isoophiopogonone A (98.3% purity) and 13.5 mg of 6-formyl-isoophiopogonanone A (97.3% purity) respectively. The chemical structure of the three homoisoflavonoids are identified by means of ESI-MS and NMR analysis.

卡林型金矿不可见金与超压流体（Overpressured fluid）关系探讨——以贵州贞丰水银洞金矿为例

贵州水银洞(岩上)微细浸染型金矿产于贵州省贞丰县境内，是目前我国第一个成功地从原生硫化物矿石中商业性生产出金的微细浸染型金矿矿山。该矿床的矿体产于灰家堡背斜东段核部的上二叠统龙潭组地层中及其与中二叠统茅口组灰岩的接触带，呈几层基本平行排布的似层状和透镜状产出。金矿化主要赋存于硅化白云石化生物碎屑灰岩和泥灰岩(85％)和强硅化角砾状粘土岩(14％)中。