Asymptotic behaviour of solutions to the problem of wetting fronts in one-dimensional,horizontal and infinite porous media

The asymptotic behavior of solutions to the problem of wetting fronts is studied in one-dimensional, horizontal and infinite porous media with the soil-water diffusivity proportional to some power of the water content. The uniqueness of the similarity solution for the problem is studied and the properties of this solution are presented. It is shown that the similarity solution is an asymptotic solution of a wide class of initial value problems of wetting fronts in the media. The use of the similarity solution is discussed for the experimental determination of the soil-water diffusivity.     

A soil water and heat transfer model including changes in soil frost and thaw fronts

Freeze-thaw processes in soils,including changes in frost and thaw fronts(FTFs),are important physical processes.The movement of FTFs affects soil hydrothermal characteristics,as well as energy and water exchanges between the land surface and the atmosphere and hydrothermal processes in the land surface.This paper reduces the issue of soil freezing and thawing to a multiple moving-boundary problem and develops a soil water and heat transfer model which considers the effects of FTF on soil hydrothermal processes.A local adaptive variable-grid method is used to discretize the model.Sensitivity tests based on the hierarchical structure of the Community Land Model(CLM)show that multiple FTFs can be continuously tracked,which overcomes the difficulties of isotherms that cannot simultaneously simulate multiple FTFs in the same soil layer.The local adaptive variable-grid method is stable and offers computational efficiency several times greater than the high-resolution case.The simulated FTF depths,soil temperatures,and soil moisture values fit well with the observed data,which further demonstrates the potential application of this simulation to the land-surface process model.     

Dynamic response of partially sealed circular tunnel in viscoelastic saturated soil

Based on Biot's wave equation, dynamic response of a circular tunnel with partially sealed liner in viscoelastic saturated soil is investigated. By introducing two scalar potential functions, the analytical solutions of stresses, displacements and pore pressure induced by axisymmetric gradually applied step load are derived in Laplace transform domain. Numerical results are obtained by inverting Laplace transform presented by Durbin and used to analyze the influences of partial permeable property of boundary and viscoelastic damping coefficient of soil on dynamic response of the tunnel. It is shown that the attenuation of radial displacement appeared with the increase of viscoelastic damping coefficient of soil, and relative rigidity of liner and soil, and the influence of partial sealing property of boundary on stresses, displacements and pore pressure is remarkable. The available solutions of permeable and impermeable boundary conditions are only two extreme cases of this paper.     

Transient dynamic response of fluid-saturated soil under a moving cyclic loading

Based on the Theory of Porous Media (TPM), a mathematical model of a two-dimensional incompressible fluid-saturated elastic soil is established, and the periodic boundary conditions are presented to analyze the transient dynamic response of this soil under a moving cyclic loading. The differential quadrature method (DQM) and the second-order backward difference scheme are applied to discretize the governing equations on the spatial and temporal domains, respectively. As application, a typical two-dimensional wave-induced transient problem with a seabed of finite thickness is analyzed, and the numerical results are compared with the analytical results presented in the present work. In addition, a transient dynamic response of fluid-saturated soil under limit moving vehicle loadings is studied. The effects of the velocity of vehicle and the volume fraction on the settlement and the pore water pressure are studied.     

Focused infiltration of snowmelt water in partially frozen soil under small depressions

Ephemeral puddles in small closed depressions can play an important role in the hydrology and ecology of many landscapes, by storing runoff water, recharging soil moisture and shallow groundwater, and by providing food and habitat for many organisms. Infiltration of snowmelt water under small depressions (<1000 m²) has been studied in the St. Denis National Wildlife Area in Saskatchewan, Canada, located within the northern glaciated prairie of North America where numerous depressions of varying sizes exist. The depressions stored most of the snowmelt runoff generated within their respective watersheds. The water level in a typical depression declined at 0.6 mm/h while the underlying frozen soil was thawing. This rate was likely limited by the rate of downward movement of the thawing front, which was functioning as a moving impermeable boundary. The rate of thawing was controlled by the external energy input from the ground surface. Standing water in depressions efficiently trapped incoming radiation and conducted it to the thawing front. The recession rate increased to 1.1 mm/h when the soil under the depression thawed completely. The recession rate at this later stage appears to be limited by the hydraulic conductivity of the subsoil (0.04–4 mm/h), which is much smaller than the topsoil conductivity (10–20 mm/h).     

Mechanisms of conversion of kinetic into magnetic energy in partially ionized plasmas

The processes involved in the transformation of kinetic into magnetic energy in partially ionized compressible plasmas are not limited to the well-known mechanism of transport and diffusion of single-fluid magnetohydrodynamics. The induction equation, in this new case, may be written for any mean of the ion and electron velocities, and it possesses a natural scaling parameter equal to the ratio of the electron and ion masses. This produces a hierarchy of sources able to generate a magnetic field. The first of these sources corresponds to the classical stretching of magnetic field lines by the flow and ohmic diffusion, and a compressional effect due to the flow of electromagnetic energy into the regions of higher density. A potentially important effect is caused by dragging of electrons by neutral particles through collisions; this term could dissipate as well as enhance the magnetic field depending on the geometry of the neutral flow. Finally, there exists a term analogous to the stretching one, this time involving the current density and with the opposite effect. Its presence implies that not only the magnetic field but also the current density grows at most exponentially with a growth rate bounded by the maximum of the strain matrix. While the effect of these nonclassical sources, acting alone, is in all probability extremely small, they could be relevant in the creation of seed magnetic fields for subsequent dynamo action.     

移动荷载作用下双层Euler梁模型土动力响应分析

本文以弹性波动理论为基础,利用分层法计算了双层连续支撑Euler梁下地基土的位移,同时考虑了不同的车辆荷载模型,并将计算的结果和单层Euler梁下地基土的位移进行了比较,比较表明：轨道结构本身和车辆悬挂体系具有一定的减振功能。因此,该研究对由交通荷载引起的环境振动分析和评价具有一定的应用价值。     

Seismic bearing capacity of strip footing on partially saturated soil using modal response analysis

The present study proposes a novel and simplified methodology to assess the seismic bearing capacity(SBC) of a shallow strip footing by incorporating strength non-linearity arising due to partial saturation of a soil matrix. Furthermore, developed methodology incorporates the modal response analysis of soil layers to assess SBC. A constant matric suction distribution profile has been considered throughout the depth of the soil. The Van Genuchten equation and corresponding fitting parameters have...     

Non-linear laminar flow into well partially penetrating a porous aquifer of finite thickness

In steady state condition, non-linear laminar flow of fluid into a well partially penetrating a porous aquifer of finite thickness is considered. The influence of such a flow on discharge and its dependence on related physical quantities are investigated. It is observed that the discharge into the well decreases as the depth of the well is decreased and the region of non-linear laminar flow is widened, which is quite obvious from physical considerations. As a particular case, result for a fully penetrating well has been deduced.     

Motion of foundation on a layered soil medium - II. Response analysis

The objective of the present approach is to determine the structural response to external force excitations and earthquake excitations with consideration of soil-structure interaction. The physical model concerned is a flexible structure resting on a rigid or flexible foundation embedded in a layered soil medium. The vibration of the structure is first analyzed using the wave propagation approach without reference to the interaction. The interaction effect is recovered by the impedance relationship developed in the companion paper. In an attempt to use the free field ground motion as the input to the system, the Maxwell's reciprocal theorem is applied to remedy the difference between the free field and real ground motion in the presence of the structure. As a result, the structural response at any location is written as a linear function of external excitations and the seismic source. Such a solution form is convenient for statistical analysis.     

Stability and stable modes of coastal fronts

Abstract

The stability of a single layer, geostrophic front of zero potential vorticity bounded by a vertical coast (wall) is investigated by means of a Rayleigh integral. It is proved that the flow of the density-driven current is stable at all wavenumbers provided the mean velocity of basic flow exceeds fL (where f is the Coriolis parameter and L is the distance between the wall and the free streamline). The frequency of the stable long waves is either zero or super-inertial.     

Motion of foundation on a layered soil medium — I. Impedance characteristics

An impedance matrix is derived for the relationship between displacements and external excitations of a rigid or flexible foundation embedded in a layered soil medium. The unknown contact distributed force between the foundation and soil is expanded in the frequency domain as a twofold series of azimuthal and radial components; each term represents a basic or fundamental distribution. As a result, the total response of the soil, either of displacements or stresses, has the same type of series expression except for the fundamental distributions replaced by influence functions. The coefficients of the series expansion, appearing in both equilibrium conditions of the foundation and compatibility conditions on the contact surface, relate the foundation displacements and excitations, and, therefore, result in the impedance matrix. Avoidance of integral equations in the soil-structure interaction analysis is the merit of the present approach.     

Patterns of soil water repellency change with wetting and drying: the influence of cracks,roots and drainage conditions

Laboratory experiments were used to investigate the influence of simulated cracks and roots on soil water repellency (SWR) dynamics with and without basal drainage impedance in wetting–drying cycles. Observations and measurements were taken following water application equivalent to 9.2‐mm rainfall and then periodically during 80 h of drying. In total, 180 experiments were carried out using 60 samples of three homogeneous, reconstituted soils with different organic matter contents and textures, but of similar initial severity of SWR [18% molarity of an ethanol droplet (MED)]. Water flowing down the cracks and roots left the soil matrix largely dry and water repellent except for vertical zones adjacent to them and a shallow surface layer. A hydrophilic shallow basal layer was produced in experiments where basal drainage was impeded. During drying, changes in SWR were largely confined to the zones that had been wetted. Soil that had remained dry retained the initial severity of SWR, while wetted soil re‐established either the same or slightly lower severity of SWR. In organic‐rich soil, the scale of recovery to pre‐wetting MED levels was much higher, perhaps associated with temporarily raised levels (up to 36% MED) of SWR recorded during drying of these soils. With all three soils, the re‐establishment of the original SWR level was less widespread for surface than subsurface soil and with impeded than unimpeded basal drainage. Key findings are that as follows: (1) with unimpeded basal drainage, the soils remained at pre‐wetting repellency levels except for a wettable thin surface layer and zones close to roots and cracks, (2) basal drainage impedance produced hydrophilic basal and surface layers, (3) thorough wetting delayed a return to water‐repellent conditions on drying, and (4) temporarily enhanced SWR occurred in organic‐rich soils at intermediate moisture levels during drying. Hydrological implications are discussed, and the roles of cracks and roots are placed into context with other influences on preferential flow and SWR under field conditions. Copyright © 2014 John Wiley & Sons, Ltd.     

Neurofuzzy mapping of CPT values into soil dynamic properties

Ever since the early days of soil mechanics there has been a strong tendency to develop correlations between easy-to-obtain parameters and mechanical properties of geotechnical materials. This interest has not decreased as more elaborated methods have been proposed. On the contrary, once a method under development reaches certain degree of sophistication, researchers usually devote a great deal of time to establish simplified procedures. The study presented in this paper follows a similar path in the sense that a data-based knowledge procedure instead of mathematically based methods is used to develop a manner to estimate soil dynamic properties directly from cone-tip penetration resistances. This method is based on a hybrid system integrated by merging artificial neural networks and fuzzy logic. The procedure is evaluated comparing its results with actual measurements of cone-tip penetration resistances and shear wave velocities done in twin borings.     

Linear stability and stable modes of geostrophic fronts

Abstract

A Rayleigh integral is used to prove that an unbounded geostrophic front of uniform potential vorticity is stable with respect to small perturbations of arbitrary wavelength. The ageostrophic theory developed in this study yields a stable, near-inertial, long trapped mode. Recent oceanic observations of the increase in the energy of the inertial peak in the vicinity of fronts support the existence of this inertial trapped mode. In addition the theory yields a geostrophic mode which is expected to become unstable when the potential vorticity is not uniform.     

Tomographic measurements of pore filling at infiltration fronts

For certain porous media and initial conditions, constant flux infiltrations show a saturation profile which exhibits overshoot. This overshoot is the cause of gravity driven fingering, cannot be described by standard models of unsaturated flow, and is likely controlled by the exact nature of the pore filling at the initial front. Here we report synchrotron X-ray micro-tomography measurements of the porous medium and measure which pores are filled by water and air at the initial wetting front as a function of flux. We find that at high fluxes all the pores are filled with water; for intermediate fluxes, the pores along the edge of the column remain unsaturated; and for low fluxes the pores in the bulk of the experimental column remain unsaturated. This suggests that the unsaturated overshoot conditions observed at higher fluxes are primarily an edge effect of the column. The results can help delineate the correct continuum models that can capture overshoot and gravity driven fingering.     

Taking magnetic deviation into account when it is measured at a moving object

The works devoted to taking magnetic deviation into account on vehicles are reviewed. Different methods for taking deviation into account are presented. These methods can be conditionally divided into three groups: the usage of parameters of magnetic deviation measured at sites, compensation for vehicle deviation using different methods, and removal of magnetic sensors to a certain distance from a vehicle. A substantial disadvantage of all methods consists in that it is impossible to determine deviation in an on-line mode. The on-line technique for determining deviation of magnetized bodies developed by us is briefly described.     

The motion of magnetic fronts in spiral galaxies

Abstract

We study the nonlinear asymptotic thin disc approximation to the mean field dynamo equations, as applicable to spiral galaxies. The circumstances in which sharp magnetic field structures (fronts) can propagate radially are investigated, and an expression for the speed of propagation derived. We find that the speed of an interior front is proportional to η//R _? (where η is the diffusivity and R_t the galactic radius), whereas an exterior front moves with speed of order , where γ is the local growth rate of the dynamo. Numerical simulations are presented, that agree well with our asymptotic results. Further, we perform numerical experiments using the 'no-z' approximation for thin disc dynamos, and show that the propagation of magnetic fronts in this approximation can also be understood in terms of our asymptotic results.