On the RH relations across weak and strong shocks in van der Waals gases

The Rankine–Hugoniot (RH) jump relations for normal shock waves in van der Waals fluids have been studied in order to improve a theoretical understanding of those shock related phenomena as observed in a real atmosphere which cannot be accounted for by the ideal gas model. The RH jump relations for the pressure, density, particle velocity, temperature, speed of sound, adiabatic compressibility and change-in-entropy across the shock front have been analysed in terms of the non-idealness parameter of the gas, downstream Mach number and adiabatic index of the gas. Further, as the strength of shock waves may range from weak to strong, the convenient forms of RH jump relations for weak and strong shock waves have been discussed, simultaneously. Finally, the effects on the flow-field behind the shock front have been explored due to the non-idealness parameter of the gas, downstream Mach number and adiabatic index of the gas.     

Solute transport scales in an unsaturated stony soil

Solute transport parameters are known to be scale-dependent due mainly to the increasing scale of heterogeneities with transport distance and with the lateral extent of the transport field examined. Based on a transect solute transport experiment, in this paper we studied this scale dependence by distinguishing three different scales with different homogeneity degrees of the porous medium: the observation scale, transport scale and transect scale. The main objective was to extend the approach proposed by van Wesenbeeck and Kachanoski to evaluating the role of textural heterogeneities on the transition from the observation scale to the transport scale. The approach is based on the scale dependence of transport moments estimated from solute concentrations distributions. In our study, these moments were calculated starting from time normalized resident concentrations measured by time domain reflectometry (TDR) probes at three depths in 37 soil sites 1 m apart along a transect during a steady state transport experiment. The Generalized Transfer Function (GTF) was used to describe the evolution of apparent solute spreading along the soil profile at each observation site by analyzing the propagation of the moments of the concentration distributions. Spectral analysis was used to quantify the relationship between the solid phase heterogeneities (namely, texture and stones) and the scale dependence of the solute transport parameters. Coupling the two approaches allowed us to identify two different transport scales (around 4-5 m and 20 m, respectively) mainly induced by the spatial pattern of soil textural properties. The analysis showed that the larger transport scale is mainly determined by the skeleton pattern of variability. Our analysis showed that the organization in hierarchical levels of soil variability may have major effects on the differences between solute transport behavior at transport scale and transect scale, as the transect scale parameters will include information from different scales of heterogeneities.     

On some early attempts to determine the variation of the magnetic force with distance

We describe two experiments made by the 18th-century physicists Francis Hauksbee and Pieter van Musschenbroek, designed to find the dependence of the magnetic force on distance. From the experimental results, given in the form of tables, the authors did not infer any simple law. We calculated the values obtained by assuming that the force varies as the inverse square of the distance and found a good agreement with their results. It therefore appears that these remarkable experiments could have provided an experimental proof of the law.     

Influence of heterogeneity on unsaturated hydraulic properties (2) – percentage and shape of heterogeneity

In subsurface porous media, the soil water retention curve (WRC) and unsaturated hydraulic conductivity curve (UHC) are two important soil hydraulic property curves. Spatial heterogeneity is ubiquitous in nature, which may significantly affect soil hydraulic property curves. The main theme of this paper is to investigate how spatial heterogeneities, including their arrangements and amounts in soil flumes, affect soil hydraulic property curves. This paper uses a two‐dimensional variably saturated flow and solute transport finite element model to simulate variations of pressure and moisture content in soil flumes under a constant head boundary condition. To investigate the behavior of soil hydraulic property curves owing to variations of heterogeneities and their arrangements as well, cases with different proportions of heterogeneities are carried out. A quantitative evaluation of parameter variations in the van Genuchten model (VG model) resulting from heterogeneity is presented. Results show that the soil hydraulic properties are strongly affected by variations of heterogeneities and their arrangements. If the pressure head remains at a specific value, the soil moisture increases when heterogeneities increase in the soil flumes. On the other hand, the unsaturated hydraulic conductivity decreases when heterogeneities increase in the soil flumes under a constant pressure head. Moreover, results reveal that parameters estimated from both WRC and UHC also are affected by shapes of heterogeneity; this indicates that the parameters obtained from the WRC are not suitable for predicting the UHC of different shapes in heterogeneous media. Copyright © 2011 John Wiley & Sons, Ltd.     

Cracking risk of partially saturated porous media—Part II: Application to drying shrinkage

Drying of deformable porous media results in their shrinkage, and it may cause cracking provided that shrinkage deformations are hindered by kinematic constraints. Herein, we focus on slow drying of an initially water‐saturated sample of a microheterogeneous poroelastic material damaged by parallel mesocracks. The cracking risk is analyzed by means of the thermodynamics‐based microporoelasticity model described in the companion paper (Part I), which is extended toward consideration of the hierarchical organization of cracked argillite. Drying of a material sample is studied in a framework where macrodisplacements in direction of the crack normal are blocked, while elsewise macrostress‐free boundary conditions prevail. The model implies that the opening/closure behavior of the cracks is governed by an effective pressure, in which the average crack (under)pressure, making the crack opening smaller, competes with the average micropore (under)pressure that makes the crack opening larger. The driving force for crack propagation is a quadratic function of this effective pressure. The model proposes that if drying shrinkage deformations are hindered by kinematic constraints, onset of cracking becomes possible once air entry into the cracks is observed. Copyright © 2009 John Wiley & Sons, Ltd.     

利用Van Genuchten模型拟合土壤水分特征曲线

利用Van Genuchten模型对用砂性漏斗测量中砂的吸湿过程和脱湿过程土壤水分特征曲线进行拟合,结果表明实测曲线和拟合曲线吻合很好,并得出Van Genuchten模型中的残余含水量、特性参数α和n,模拟计算表明,中砂有αw=1.69αd的关系,为研究水分和污染物在非饱和土壤中运移问题提供土壤水分运动键参数.     

A Linking Test to reduce the number of hydraulic parameters necessary to simulate groundwater recharge in unsaturated soils

In environmental studies, numerical simulation models are valuable tools for testing hypothesis about systems functioning and to perform sensitivity studies under scenarios of land use or climate changes. The simulations depend upon parameters which are not always measurable quantities and must be calibrated against observations, using for instance inverse modelling. Due to the scarcity of these observations, it has been found that parameter sets allowing a good matching between simulated and measured quantities are often non-unique, leading to the problem of equifinality. This can lead to non-physical values, erroneous fluxes and misleading sensitivity analysis. Therefore, a simple but robust inverse method coined the Linking Test is presented to determine if the parameters are linked. Linked parameters are then sub-divided into classes according to their impact on water fluxes. The Linking Test establishes the causes of non-uniqueness of parameter sets and the feasibility of the inverse modelling.