Solid–liquid–air coupling in multiphase porous media

This paper addresses various issues concerning the modelling of solid–liquid–air coupling in multiphase porous media with an application to unsaturated soils. General considerations based on thermodynamics permit the derivation and discussion of the general form of field equations; two cases are considered: a three phase porous material with solid, liquid and gas, and a two phase porous material with solid, liquid and empty space. Emphasis is placed on the presentation of differences in the formulation and on the role of the gas phase. The finite element method is used for the discrete approximation of the partial differential equations governing the problem. The two formulations are then analysed with respect to a documented drainage experiment carried out by the authors. The merits and shortcomings of the two approaches are shown. Copyright © 2003 John Wiley & Sons, Ltd.     

IMPROVEMENT OF A GLOBAL SPECTRAL MODEL BY INTRODUCING THE SECONDLAW OF THERMODYNAMICS*

The second law of thermodynamics has never been taken into account in the traditional hydrodynamics and numerical weather prediction models,which is a serious oversight in the history of mechanics.Introducing the thermodynamic irreversibility into the hydrodynamic systems,the theory and method proposed in this study would not only lead the outputs of a numerical weather prediction model to noticeable improvement,but lead the structure of hydrodynamics to deepgoing transformation.     

长石溶解过程的热力学计算及其在碎屑岩储层研究中的意义

基于对反应过程吉布斯自由能增量的计算,探讨了长石的3种端元组成（钾长石、钠长石和钙长石）溶解生成高岭石、伊利石的热力学性质。结果表明：钾长石、钠长石和钙长石在成岩过程中均可以自发地向高岭石、伊利石转化。在长石的这3种类型中,钙长石溶解反应的吉布斯自由能增量最低,并明显具有正的温度效应,说明钙长石最不稳定且在低温条件下更易溶解;钾长石溶解反应的吉布斯自由能增量最高,并具有较大的负的温度效应,说明钾长石稳定性较高且在埋藏成岩条件下更易溶解;钠长石溶解反应的吉布斯自由能增量中等,受温度影响不大,但温度升高时其稳定性仍有所下降。与温度相比,压力对反应的吉布斯自由能增量几乎没有影响。因此,砂岩中的次生孔隙,尤其是埋藏成岩过程中形成的次生孔隙应与钾长石的关系最为密切,其次是钠长石,但其可能受到蒙皂石向伊利石转化反应的缓冲,在埋藏成岩条件下溶解较为困难,并可能造成斜长石的钠长石化或自生钠长石的沉淀。     

Variations of thermodynamical parameters in the atmospheric boundary layer over the Deccan plateau region,India

The thermodynamical structure of the atmospheric boundary layer over the Deccan plateau region has been studied with aerological data for 1980 and 1981.The temperatures in the sub-cloud layer were lower on active monsoon days than dose on weak monsoon days. An opposite trend was noticed in the layer above the 900 mbar level. The moisture content on active monsoon days was higher than that on weak monsoon days. The profile of relative humidity above the 850 mbar level showed large deviations between the active and weak monsoon conditions. On active monsoon days the values of dry static stability were higher than those on weak monsoon days. An opposite trend was noticed in the case of moist static stability. On active monsoon days the magnitudes of thev components of wind were small compared with those of theu components, and the latter showed a gradual decrease with height.     

Foreword

Protons of energy 10⁹ GeV and 10⁴ GeV accelerating by the magnetic field of very strongly magnetized neutron stars and of extreme Kerr-Newmann black holes (respectively) may undergo instantaneous decay.     

How well known are the thermodynamics of Fe–Mg–Ca garnet? Evidence from experimentally determined exchange equilibria

ABSTRACT Many thermodynamic calculations relating to metamorphic rocks hinge on the thermodynamic parameters of garnet. Though some models are widely used, it is not clear whether their underlying premise is correct: that a single set of equations can be written for the activities of the end-members of garnet covering the whole compositional range. A voluminous body of data can be used to constrain the thermodynamics of garnet, namely Fe–Mg exchange experimental data involving garnet and another mineral, particularly clinopyroxene, orthopyroxene and olivine. However, examination of these data reveals inconsistencies, apparently stemming from differences between the thermodynamics of low-Ca and high-Ca garnets, with a boundary of about X^g_Ca= 0.15. In the two regions, for the high P–T of the experimental data, the thermodynamics follow the regular model, with values for the interaction parameters in the low Ca region of about w^g_FeMg= 50R and w_aFe–w^g_MgCa=– 1300R, in which R is the gas constant, and in the high Ca region of about w^g_FeMg= 1100R and w^g_CaFe–w^g_MgCa=– 2200R. Using the subregular, rather than the regular, model does not remove the discrepancy. The cause of the discrepancy needs to be identified if reliable calculations on rocks are to be made.     

Application of thermodynamics to the global modelling of shallow foundations on frictional material

Soil–shallow foundation interaction has been theoretically analysed within the framework of thermomechanics. The design of a global interaction model has been achieved with an original treatment of the Clausius–Duhem inequality. The role of the gravity volume forces is emphasized. The paper is focused on a strip footing based on dense sand and subjected to time‐independent plastic processes. The theoretical approach has confirmed that an associated global flow rule cannot be expected to hold true. The analysis of the sources of dissipation has led to the development of a soil–footing interface model and a complete interaction model accounting for the interface constraints and the intrinsic frictional properties of the soil. Finally, the abilities of the complete model are checked by comparisons with experimental results found in the literature. Copyright © 2001 John Wiley & Sons, Ltd.     

Comparison of different numerical approaches to the 1D sea-ice thermodynamics problem

The vertical one-dimensional sea-ice thermodynamic problem using the principle of conservation of enthalpy is revisited here using (1) the Bitz and Lipscomb (1999) finite-difference approach (FD), (2) a reformulation of the sigma-level transformation of Huwald et al. (2005b) (FV) and (3) a Finite Element approach also in sigma coordinates (FE). These three formulations are compared in terms of physics, numerics, and performance, in order to identify the best choice for large-scale climate models. The BL99 formulation sequentially treats the diffusion of heat and the changes in the vertical position of the ice-snow layers. In contrast, the FV sigma-level transformation elegantly treats both simultaneously. The original FV formulation suffers however from slow convergence. The convergence can nonetheless be improved significantly with a few simple modifications to the original code. The three formulations are compared following the experimental protocol of the Sea Ice Model Intercomparison Project for ice thermodynamics (SIMIP2). It is found that all formulations converge to the same solution. The FD approach, however, suffers from the added cost of the remapping step at large number of ice layers (we include in the appendix an optimized version of the FD code–written by one of the reviewer–that resolves this issue). Finally the FE formulation results in a sub-surface temperature over-estimation at low resolution, a problem which disappears at high resolution. Hence, only FD and FV are found suitable for climate models.     

海冰热力模式及北极海冰季节变化的数值模拟

本文给出了一个改进的海冰热力模式,主要通过海面和冰面的温度变化及热量收支,用来计算海冰面积和厚度的时空分布。