若干流体力学问题的数学性质研究

该文利用高智的扩散抛物化方程组理论及流体力学基本方程组的特征次特征理论,流体大小尺度（LSS）方程组理论以及摄动有限差分（PFD）方法,研究若干流体力学问题的数学性质.该文得到的主要结论有：1.利用湍流大小尺度（LSS）方程组推导出湍流大小尺度涡量（LSSV）方程组,并证明两个关于湍流大小尺度涡量的命题,从而得到湍流封闭大小尺度涡量（CLSSV）方程组,并对已有的近程相互作用命题进行推广.2.根据扩散抛物化方程组理论和流体力学层次结构方程组的特征和次特征方法,研究了抛物化稳定性方程组（PSE）的特征和次特征以及消除PSE的剩余椭圆特性的问题.3.利用摄动有限差分（PFD）方法得到对流扩散反应方程的变步长摄动有限差分格式,是等步长摄动有限差分格式的推广.

湍流大小尺度涡量方程组及其封闭

利用流体大小尺度（LSS）方程组推导出湍流大小尺度涡量（LSSV）方程组，给出两个关于湍流大小尺度涡量的命题，从而得到湍流封闭大小尺度涡量（CLSSV）方程组。同时，对近程相互作用命题进行了推广。

Multiscale Method for Turbulent-Flow Computations

A main method of predicting turbulent flows is to solve LES equations, which was called traditional LES method. The traditional LES method solves the motions of large eddies of size larger than filtering scale An while modeling unresolved scales less than Delta_n. Hughes et al argued that many shortcomings of the traditional LES approaches were associated with their inabilities to successfully differentiate between large and small scales. One may guess that a priori scale-separation would be better, because it can predict scale-interaction well compared with posteriori scale-separation. To this end, a multi-scale method was suggested to perform scale-separation computation. The primary contents of the multiscale method are l) A space average is used to differentiate scale. 2) The basic equations include the large scale equations and fluctuation equations. 3) The large-scale equations and fluctuation equations are coupled through turbulent stress terms. We use the multiscale equations of n=2, i.e., the large and small scale (LSS) equations, to simulate 3-D evolutions of a channel flow and a planar mixing layer flow Some interesting results are given.

Small-scale species richness and its spatial variation in an alpine meadow on the Qinghai-Tibet Plateau

We investigated how the high small-scale species richness of an alpine meadow on the Qinghai-Tibet Plateau, China, is maintained. This area is characterized by strong wind and severe cold during long winters. In winter, most livestock is grazed on dead leaves in small pastures near farmers' residences, whereas in the short summer, livestock is grazed in mountainous areas far from farmers' residences. The number of plant species and the aboveground biomass were surveyed for three adjacent pastures differing in grazing management: a late-winter grazing pasture grazed moderately from 1 February to 30 April, an early-winter grazing pasture grazed lightly from 20 September to late October, and a whole-year grazing pasture grazed intensively throughout the entire year. In each pasture, we harvested the aboveground biomass from 80 or 100 quadrats of 0.01 m(2) along a transect and classified the contents by species. We observed 15.5-19.7 species per 0.01 m(2), which is high richness per 0.01 m(2) on a worldwide scale. The species richness in the two winter grazing pastures was higher than that in the whole-year grazing pasture. The spatial variation in species richness and species composition in the two winter grazing pastures in which species richness was high was greater than that in the whole-year grazing pasture in which species richness was lower. Most of the leaves that are preserved on the winter grazing pastures during summer are blown away by strong winds during winter, and the remaining leaves are completely exhausted in winter by livestock grazing. A pasture with a high richess is accompanied by a high spatial variation in species richness and species composition. There is a high possibility that the characteristic of spatial variation is also caused by traditional grazing practices in this area.

A kinematic subgrid scale model for large-eddy simulation of turbulence generated sound

In the hybrid approach of large-eddy simulation (LES) and Lighthill’s acoustic analogy for turbulence-generated sound, the turbulence source fields are obtained using an LES and the turbulence-generated sound at far fields is calculated from Lighthill’s acoustic analogy. As only the velocity fields at resolved scales are available from the LES, the Lighthill stress tensor, serving as a source term in Lighthill’s acoustic equation, has to be evaluated from the resolved velocity fields. As a result, the contribution from the unresolved velocity fields is missing in the conventional LES. The sound of missing scales is shown to be important and hence needs to be modeled. The present study proposes a kinematic subgrid-scale (SGS) model which recasts the unresolved velocity fields into Lighthill’s stress tensors. A kinematic simulation is used to construct the unresolved velocity fields with the imposed temporal statistics, which is consistent with the random sweeping hypothesis. The kinematic SGS model is used to calculate sound power spectra from isotropic turbulence and yields an improved result: the missing portion of the sound power spectra is approximately recovered in the LES.

Computation of turbulence-generated noise by large-eddy simulation

The hybrid method of large eddy simulation (LES) and the Lighthill analogy is being developed to compute the sound radiated from turbulent flows. The results obtained from the hybrid method are often contaminated by the absence of small scales in LES, since the energy level of sound is much smaller than that of turbulent flows. Previous researches investigate the effects of subgrid sacle (SGS) eddies on the frequency spectra of sound radiated by isotropic turbulence and suggest a SGS noise model to represent the SGS contributions to the frequency spectra. Their investigations are conducted in physical space and are unavoidably influenced by boundary conditions. In this paper, we propose to perform such calculations in Fourier space so that the effects of boundary conditions can be correctly treated. Posteriori tests are carried out to investigate the SGS contribution to the sound. The results obtained recover the -7/2 law within certain wave-number ranges, but under-estimate the amplitudes of the frequency spectra. The reason for the underestimation is also discussed.

A Lagrangian for von Karman Equations of Large Deflection Problem of Thin Circular Plate

By the semi-inverse method proposed by He, a Lagrangian is established for the large deflection problem of thin circular plate. Ritz method is used to obtain an approximate analytical solution of the problem. First order approximate solution is obtained, which is similar to those in open literature. By Mathematica a more accurate solution can be deduced.

Small scale, grain size and substrate effects in nano-indentation experiment of film-substrate systems

The mechanical properties of film-substrate systems have been investigated through nano-indentation experiments in our former paper (Chen, S.H., Liu, L., Wang, T.C., 2005. Investigation of the mechanical properties of thin films by nano-indentation, considering the effects of thickness and different coating-substrate combinations. Surf. Coat. Technol., 191, 25-32), in which Al-Glass with three different film thicknesses are adopted and it is found that the relation between the hardness H and normalized indentation depth h/t, where t denotes the film thickness, exhibits three different regimes: (i) the hardness decreases obviously with increasing indentation depth; (ii) then, the hardness keeps an almost constant value in the range of 0.1-0.7 of the normalized indentation depth h/t; (iii) after that, the hardness increases with increasing indentation depth. In this paper, the indentation image is further investigated and finite element method is used to analyze the nano-indentation phenomena with both classical plasticity and strain gradient plasticity theories. Not only the case with an ideal sharp indenter tip but also that with a round one is considered in both theories. Finally, we find that the classical plasticity theory can not predict the experimental results, even considering the indenter tip curvature. However, the strain gradient plasticity theory can describe the experimental data very well not only at a shallow indentation depth but also at a deep depth. Strain gradient and substrate effects are proved to coexist in film-substrate nano-indentation experiments. (c) 2006 Elsevier Ltd. All rights reserved.

Statistics of Turbulence in Benthal Boundary Layers

This paper deals with turbulence behavior inbenthalboundarylayers by means of large eddy simulation (LES). The flow is modeled by moving an infinite plate in an otherwise quiescent water with an oscillatory and a steady velocity components. The oscillatory one aims to simulate wave effect on the flow. A number of large-scale turbulence databases have been established, based on which we have obtained turbulencestatisticsof the boundarylayers, such as Reynolds stress, turbulence intensity, skewness and flatness ofturbulence, and temporal and spatial scales of turbulent bursts, etc. Particular attention is paid to the dependences of those statistics on two nondimensional parameters, namely the Reynolds number and the current-wave velocity ratio defined as the steady current velocity over the oscillatory velocity amplitude. It is found that the Reynolds stress and turbulence intensity profile differently from phase to phase, and exhibit two types of distributions in an oscillatory cycle. One is monotonic occurring during the time when current and wave-induced components are in the same direction, and the other inflectional occurring during the time when current and wave-induced components are in opposite directions. Current component makes an asymmetrical time series of Reynolds stress, as well as turbulence intensity, although the mean velocity series is symmetrical as a sine/cosine function. The skewness and flatness variations suggest that the turbulence distribution is not a normal function but approaches to a normal one with the increasing of Reynolds number and the current-wave velocity ratio as well. As for turbulent bursting, the dimensionless period and the mean area of all bursts per unit bed area tend to increase with Reynolds number and current-wave velocity ratio, rather than being constant as in steady channel flows.

PHYSICAL MODEL FOR SMALL SCALE SANDWAVES MIGRATION IN NORTH GULF OF SOUTH CHINA SEA

The aim of this paper is to investigate the mechanism of small scale sand-wave migration. According to the environmental characteristic of the north gulf of South China Sea, a quasi-3D mechanics model has been built for simulating the small scale sand wave migration. The calculation results are shown to be consistent with the observed data in the trough of sand ridge. Considering the effect of environmental actions and sand wave features, we develop an effective formula to predict sand-wave migration. It is indicated that the physical models should be used to predict the migration of the small scale sand-wave, which is rarely dominated by wave activity.

Column chromatographic purification free synthesis of long-chain monodisperse oligo(1,4-phenyleneethynylene)s: towards large-scale automatic synthesis of molecular wires

A facile, mild and rapid solid phase synthetic route free of column chromatographic purification to the synthesis of soluble monodisperse long-chain oligo(1,4-phenyleneethynylene)s is presented.

Wintertime meso-scale horizontal distribution of large tintinnids in the southern Yellow Sea

Spatial distribution of some large tintinnid species (nominally > 76 mu m) is investigated on samples vertically towed in the southern Yellow Sea in winters of 2001 to 2004. Nine tintinnid species are recorded: Codonellopsis morchella, Stenosemella pacifica, S. steini, Tintinnopsis schotti, T. radix, T. karajacensis, Eutintinnus tenuis, Parafavella sp., Leprotintinnus neriticus, of which C. morchella and T. radix dominated in the warm tongue-shaped zone of the Yellow Sea Warm Current (YSWC), and S. pacifica is the next in abundance. Our study shows that these tintinnids occur repeatedly in certain special distribution patterns.