Experimental observations of watertable waves in an unconfined aquifer with a sloping boundary

Observations of horizontal and vertical variations in piezometric head in a homogeneous, laboratory aquifer are presented and discussed. The observed fluctuations are induced by a simple harmonic oscillation in the clear water reservoir acting across a sloping boundary. The data qualitatively supports existing theories in that higher harmonics are generated in the active forcing zone and that a significant increase in the inland, asymptotic watertable over height (relative to that found for the vertical boundary case) is observed. The observed overheight is shown to be accurately reproduced by existing small-amplitude perturbation theory. Detailed measurements in the vicinity of the sloping boundary reveal that the signal of generated higher harmonics is strongest near the sand surface and that vertical flows are significant in this region. The aquifer is of finite-depth and is influenced by capillary effects, the experimental data therefore exposes limitations of theories which are based on the assumption of a shallow aquifer free of capillary effects. The dispersive properties of the measured pressure wave in the aquifer are comparable to those found from field observations and likewise do not agree with those predicted by the capillary free, shallow aquifer theory. Although some improvement is obtained, discrepancies between the data and theory persist even when a finite-depth aquifer and capillary effects are considered in the theoretical model. Further sand column experiments eliminate a truncated capillary fringe as a possible contributor to these discrepancies. However, the neglect of horizontal flows in the fringe may have caused the discrepancies. (C) 2004 Elsevier Ltd. All rights reserved.

Application of a coupled ground-surface water flow model to simulate periodic groundwater flow influenced by a sloping boundary, capillarity and vertical flows

Theoretical developments as well as field and laboratory data have shown the influence of the capillary fringe on water table fluctuations to increase with the fluctuation frequency. The numerical solution of a full, partially saturated flow equation can be computationally expensive. In this paper, the influence of the capillary fringe on water table fluctuations is simplified through its parameterisation into the storage coefficient of a fully-saturated groundwater flow model using the complex effective porosity concept [Nielsen, P., Perrochet, P., 2000. Water table dynamics under capillary fringes: experiments and modelling. Advances in Water Resources 23 (1), 503-515; Nielsen, P., Perrochet, P., 2000. ERRATA: water table dynamics under capillary fringes: experiments and modelling (Advances in Water Resources 23 (2000) 503-515). Advances in Water Resources 23, 907-908]. The model is applied to sand flume observations of periodic water table fluctuations induced by simple harmonic forcing across a sloping boundary, analogous to many beach groundwater systems. While not providing information on the moisture distribution within the aquifer, this approach can reasonably predict the water table fluctuations in response to periodic forcing across a sloping boundary. Furthermore, he coupled ground-surface water model accurately predicts the extent of the seepage face formed at the sloping boundary. (C) 2005 Elsevier Ltd. All rights reserved.

A semi-experimental approach to plane problems in elasticity

A semi-experimental approach to solve two-dimensional problems in elasticity is given. The method has been applied to two problems, (i) a square deep beam, and (ii) a bridge pier with a sloping boundary. For the first problem sufficient analytical results are available and hence the accuracy of the method can be verified. Then the method has been extended to the second problem for which sufficient results are not available.

An improved boundary layer scaling with ramp heating on a sloping plate

A scaling analysis for the natural convection boundary layer adjacent to an inclined semi-infinite plate subject to a non-instantaneous heating in the form of an imposed wall temperature which increases linearly up to a prescribed steady value over a prescribed time is reported. The development of the boundary layer flow from start-up to a steady-state has been described based on scaling analyses and verified by numerical simulations. The analysis reveals that, if the period of temperature growth on the wall is sufficiently long, the boundary layer reaches a quasi-steady mode before the growth of the temperature is completed. In this mode the thermal boundary layer at first grows in thickness and then contracts with increasing time. However, if the imposed wall temperature growth period is sufficiently short, the boundary layer develops differently, but after the wall temperature growth is completed, the boundary layer develops as though the startup had been instantaneous. The steady state values of the boundary layer for both cases are ultimately the same.

Natural convection in attic-shaped spaces subject to sudden and ramp heating boundary conditions

In this study, a discussion of the fluid dynamics in the attic space is reported, focusing on its transient response to sudden and linear changes of temperature along the two inclined walls. The transient behaviour of an attic space is relevant to our daily life. The instantaneous and non-instantaneous (ramp) heating boundary condition is applied on the sloping walls of the attic space. A theoretical understanding of the transient behaviour of the flow in the enclosure is performed through scaling analysis. A proper identification of the timescales, the velocity and the thickness relevant to the flow that develops inside the cavity makes it possible to predict theoretically the basic flow features that will survive once the thermal flow in the enclosure reaches a steady state. A time scale for the heating-up of the whole cavity together with the heat transfer scales through the inclined walls has also been obtained through scaling analysis. All scales are verified by the numerical simulations.

A new analytical solution for water table fluctuations in coastal aquifers with sloping beaches

The Boussinesq equation appears as the zeroth-order term in the shallow water flow expansion of the non-linear equation describing the flow of fluid in an unconfined aquifer. One-dimensional models based on the Boussinesq equation have been used to analyse tide-induced water table fluctuations in coastal aquifers. Previous analytical solutions for a sloping beach are based on the perturbation parameter, epsilon(N) = alphaepsilon cot beta (in which beta is the beach slope, alpha is the amplitude parameter and epsilon is the shallow water parameter) and are limited to tan(-1) (alphaepsilon) much less than beta less than or equal to pi/2. In this paper, a new higher-order solution to the non-linear boundary value problem is derived. The results demonstrate the significant influence of the higher-order components and beach slope on the water table fluctuations. The relative difference between the linear solution and the present solution increases as 6 and a increase, and reaches 7% of the linear solution. (C) 2003 Elsevier Ltd. All rights reserved.

Numerical approximation of a fractional-in-space diffusion equation (II) - with nonhomogeneous boundary conditions

In this paper, a space fractional di®usion equation (SFDE) with non- homogeneous boundary conditions on a bounded domain is considered. A new matrix transfer technique (MTT) for solving the SFDE is proposed. The method is based on a matrix representation of the fractional-in-space operator and the novelty of this approach is that a standard discretisation of the operator leads to a system of linear ODEs with the matrix raised to the same fractional power. Analytic solutions of the SFDE are derived. Finally, some numerical results are given to demonstrate that the MTT is a computationally e±cient and accurate method for solving SFDE.

Biotribological assessment for artificial synovial joints : the role of boundary lubrication

Biotribology, the study of lubrication, wear and friction within the body, has become a topic of high importance in recent times as we continue to encounter debilitating diseases and trauma that destroy function of the joints. A highly successful surgical procedure to replace the joint with an artificial equivalent alleviates dysfunction and pain. However, the wear of the bearing surfaces in prosthetic joints is a significant clinical problem and more patients are surviving longer than the life expectancy of the joint replacement. Revision surgery is associated with increased morbidity and mortality and has a far less successful outcome than primary joint replacement. As such, it is essential to ensure that everything possible is done to limit the rate of revision surgery. Past experience indicates that the survival rate of the implant will be influenced by many parameters, of primary importance, the material properties of the implant, the composition of the synovial fluid and the method of lubrication. In prosthetic joints, effective boundary lubrication is known to take place. The interaction of the boundary lubricant and the bearing material is of utmost importance. The identity of the vital active ingredient within synovial fluid (SF) to which we owe the near frictionless performance of our articulating joints has been the quest of researchers for many years. Once identified, tribo tests can determine what materials and more importantly what surfaces this fraction of SF can function most optimally with. Surface-Active Phospholipids (SAPL) have been implicated as the body’s natural load bearing lubricant. Studies in this thesis are the first to fully characterise the adsorbed SAPL detected on the surface of retrieved prostheses and the first to verify the presence of SAPL on knee prostheses. Rinsings from the bearing surfaces of both hip and knee prostheses removed from revision operations were analysed using High Performance Liquid Chromatography (HPLC) to determine the presence and profile of SAPL. Several common prosthetic materials along with a novel biomaterial were investigated to determine their tribological interaction with various SAPLs. A pin-on-flat tribometer was used to make comparative friction measurements between the various tribo-pairs. A novel material, Pyrolytic Carbon (PyC) was screened as a potential candidate as a load bearing prosthetic material. Friction measurements were also performed on explanted prostheses. SAPL was detected on all retrieved implant bearing surfaces. As a result of the study eight different species of phosphatidylcholines were identified. The relative concentrations of each species were also determined indicating that the unsaturated species are dominant. Initial tribo tests employed a saturated phosphatidylcholine (SPC) and the subsequent tests adopted the addition of the newly identified major constituents of SAPL, unsaturated phosphatidylcholine (USPC), as the test lubricant. All tribo tests showed a dramatic reduction in friction when synthetic SAPL was used as the lubricant under boundary lubrication conditions. Some tribopairs showed more of an affinity to SAPL than others. PyC performed superior to the other prosthetic materials. Friction measurements with explanted prostheses verified the presence and performance of SAPL. SAPL, in particular phosphatidylcholine, plays an essential role in the lubrication of prosthetic joints. Of particular interest was the ability of SAPLs to reduce friction and ultimately wear of the bearing materials. The identification and knowledge of the lubricating constituents of SF is invaluable for not only the future development of artificial joints but also in developing effective cures for several disease processes where lubrication may play a role. The tribological interaction of the various tribo-pairs and SAPL is extremely favourable in the context of reducing friction at the bearing interface. PyC is highly recommended as a future candidate material for use in load bearing prosthetic joints considering its impressive tribological performance.

Nanoparticle melting as a Stefan moving boundary problem

The melting of spherical nanoparticles is considered from the perspective of heat flow in a pure material and as a moving boundary (Stefan) problem. The dependence of the melting temperature on both the size of the particle and the interfacial tension is described by the Gibbs-Thomson effect, and the resulting two-phase model is solved numerically using a front-fixing method. Results show that interfacial tension increases the speed of the melting process, and furthermore, the temperature distribution within the solid core of the particle exhibits behaviour that is qualitatively different to that predicted by the classical models without interfacial tension.

The moderating role of self-efficacy on the relationship between emotional exhaustion and job strain for boundary-spanning service employees

Appropriate behaviours toward customers often requires employees to suppress some genuine emotions and/or express other emotions; genuine or contrived. Managing one's emotions in this way gives rise to emotional exhaustion. This can have consequences for psychological ill health, in the form of work place strain, and ultimately employee's desire to leave. This student examines the relationships between emotional management, emotional exhaustion and turnover intentions amongst diversional therapy professionals. We find that some forms of emotional management have a significant impact on emotional exhaustion and that this predicts workplace strain. Furthermore, the deleterious effects of emotional exhaustion are mitigated somewhat for employees who have strong beliefs in their ability to provide good service, compared to employees with lower self efficacy beliefs.