On the energy flux of Hide waves

Summary There are two ways to define the energy flux for Hide waves, one from its equations of motion and the other by multiplying its mean energy density by group velocity and these lead to different results FollowingLonguet-Higgins we point out that this is due to certain arbitrariness in the definition of the energy flux and that their difference is just a solenoidal vector.Dedicated to the memory of Dr.V. A. Wynne, 1945–1972.     

Propagator matrix formulation for earth currents of deep internal origin

Summary The problem of the distribution of the poloidal electric field in the mantle, originating from the core-mantle boundary, is formulated in terms of propagator matrices suitable for calculations for a wide variety of piece-wise continuous models of the mantle. The elements of the propagator matrix for some interesting variations of the electric conductivity are presented.     

Propagator matrices for some geothermal problems

Summary In problems of linear flow of heat in inhomogeneous media, the governing equation is a second order ordinary differential equation with variable coefficients. When transformed into a set of first order ordinary differential equations with variable coefficients, the problem becomes amenable to an elegant method of propagator matrices. In this paper the propagator matrices for some steady and unsteady heat conduction problems (including a case of heat generation by an irreversible first order reaction) having conductivity and heat generation functions as piecewise continuous, have been described.     

Swell-compressibility characteristics of lime-blended and cement-blended expansive clays – A comparative study

Chemical stabilisation of expansive soils has been quite efficacious in reducing swelling characteristics, namely, swell potential (S%) and swelling pressure (p_s). When chemicals such as lime and cement are added to an expansive clay, flocculation and cementation take place. Flocculation, which is an immediate reaction, is instrumental in reducing plasticity and swell potential significantly. It also reduces the time required for equilibrium heave. This paper presents experimental data on lime-blended and cement-blended expansive clay specimens. Free swell index (FSI), heave, rate of heave and swelling pressure were studied. FSI, heave and rate of heave decreased with increasing lime content and cement content in the blends. But, during a 3-day inundation (a period, generally allowed for the sample to attain to equilibrium heave), cementitious products developed and resisted the applied compressive loads stiffly, resulting in high swelling pressures in the case of lime-blended specimens. Swelling pressure could not be determined in the case of cement-blended specimens. Hence, short inundation tests (inundating the specimens only for 15 minutes) were performed. But, even from these tests, swelling pressure could not be determined for cement-blended specimens. This indicated the development of strong cementitious products in them. It was interesting to find that, in both long and short duration, the lime- and cement-blended specimens attained to equilibrium heave in the same time period. FSI decreased from 185% to 63.63% when lime content was increased from 0% to 4%, and from 185% to 110% when cement content was increased from 0% to 20%. Swell potential reduced by 42.5% at 4% lime and by 46.4% at 20% cement. Swelling pressure increased from 210 kPa to 320 kPa when lime content was increased from 0% to 4%. Linear shrinkage of the specimens also decreased with increasing additive content.     

Physical Habitat Assessment of River Denwa Using GIS Techniques

Physical habitat of any aquatic ecosystem is an integral part upon which the biological structures of resident communities are built. Degradation of the physical habitat has serious consequences on aquatic communities and is among the leading causes of stream impairment worldwide. Therefore, a sound habitat assessment approach is necessary to assess the condition of running water and to determine if habitat degradation is responsible for any degradation in biological condition. The present study was focused on Physical Habitat Assessment of Denwa River, a sub tributary of river Narmada in central India, for generating a Habitat Suitability map. The Denwa River originates from Satpura ranges in central India and flows through entire Pachmarhi plateau supporting a diversity of habitats for aquatic flora and fauna. A survey was carried out to assess the physical characteristic of Denwa river (84 kms) from its origin to the confluence point of Tawa Denwa river. Six reaches have been identified in study area on the basis of their physiographic conditions. For Habitat Assessment measurement, Rapid Bioassessment Protocols for Stream and Wadeable rivers by United States Environmental Protection Agency (USEPA, 841-B-99-002) have been used. Seven parameters from this protocol have been chosen for physical characterization. GIS techniques have been used to develop a Habitat Suitability Map of the study area based on scores to illustrate its suitability to support aquatic life. The present paper discusses in detail the suitability of the different reaches of the River Denwa for supporting the aquatic biodiversity.     

A Method to Represent a Well in a Three-Dimensional Discrete Fracture Network Model

In discrete fracture network (DFN) modeling, fractures are randomly generated and placed in the model domain. The rock matrix is considered impermeable. Small fractures and isolated fractures are often ignored to reduce computational expense. As a result, the rock matrix between fractures could be large and intersections may not be found between a well introduced in the model and the hydraulically connected fracture networks (fracture backbones). To overcome this issue, this study developed a method to conceptualize a well in a three-dimensional (3D) DFN using two orthogonal rectangular fractures oriented along the well's axis. Six parameters were introduced to parameterize the well screen and skin zone, and to control the connectivity between the well and the fracture backbones. The two orthogonal fractures were discretized using a high-resolution mesh to improve the quality of flow and transport simulations around and along the well. The method was successfully implemented within dfnWorks 2.0 (Hyman et al. 2015) to incorporate a well in a 3D DFN and to track particles leaving an injection well and migrating to a pumping well. Verification of the method against MODFLOW/MODPATH found a perfect match in simulated hydraulic head and particle tracking. Using three examples, the study showed that the method ensured the connectivity between wells and fracture backbones, and honored the physical processes of flow and transport along and around wells in DFNs. Recommendations are given for estimating the values of the six introduced well parameters in a real-world case study.     

Robertson-Walker cosmological models with perfect fluid in general relativity

Einstein's field equations with variable gravitational and cosmological constants are considered in the presence of perfect fluid for a Robertson-Walker universe by assuming the cosmological term to be proportional to R-m(R is a scale factor and m is a constant).A variety of solutions is presented.The physical significance of the cosmological models has also been discussed.     

Weak MHD discontinuities in a radiation-induced flow field

The growth of weak MHD discontinuities have been studied in a radiation induced flow field at very high temperature. Growth and decay properties of weak MHD discontinuities have been discussed under the influences of time-dependent gasdynamic field, the radiation field and the magnetic field with finite electrical conductivity. The effects of thermal radiation and conduction of the global behaviour of weak MHD discontinuities have been studied under a quasi-equilibrium and quasi-isotropic hypothesis of the differential approximation to the radiative heat transfer equation. It is shown that the existence of the time-dependent radiation field gives rise to a radiation induced wave which has a negligibly small effect on the non-relativistic flow properties of the gasdynamic field. It is also shown that the radiation stresses resist the steepening tendency of a compressive weak wave and help in stabilizing it whereas the thermal conduction effects counteracts to destabilize it. It is found that under radiation effects the shock formation is either disallowed or delayed. The two cases of diverging waves and converging waves have been studied separately to answer a particular question as to when a shock discontinuity or a coustic will be formed or disallowed under curvature effects.