An efficient shock capturing algorithm for compressible flows in a duct of variable cross-section

A numerical scheme is presented for the solution of the Euler equations of compressible flow of a gas in a single spatial co-ordinate. This includes flow in a duct of variable cross-section as well as flow with slab, cylindrical or spherical symmetry and can prove useful when testing codes for the two-dimensional equations governing compressible flow of a gas. The resulting scheme requires an average of the flow variables across the interface between cells and for computational efficiency this average is chosen to be the arithmetic mean, which is in contrast to the usual ‘square root’ averages found in this type of scheme. The scheme is applied with success to five problems with either slab or cylindrical symmetry and a comparison is made in the cylindrical case with results from a two-dimensional problem with no sources.

The appraisal of data centres: deconstructing the cash flow

This paper analyses the appraisal of a specialized form of real estate - data centres - that has a unique blend of locational, physical and technological characteristics that differentiate it from conventional real estate assets. Market immaturity, limited trading and a lack of pricing signals enhance levels of appraisal uncertainty and disagreement relative to conventional real estate assets. Given the problems of applying standard discounted cash flow, an approach to appraisal is proposed that uses pricing signals from traded cash flows that are similar to the cash flows generated from data centres. Based upon ‘the law of one price’, it is assumed that two assets that are expected to generate identical cash flows in the future must have the same value now. It is suggested that the expected cash flow of assets should be analysed over the life cycle of the building. Corporate bond yields are used to provide a proxy for the appropriate discount rates for lease income. Since liabilities are quite diverse, a number of proxies are suggested as discount and capitalisation rates including indexed-linked, fixed interest and zero-coupon bonds.

On the existence of two-dimensional Euler flows satisfying energy-Casimir stability criteria

The energy-Casimir stability method, also known as the Arnold stability method, has been widely used in fluid dynamical applications to derive sufficient conditions for nonlinear stability. The most commonly studied system is two-dimensional Euler flow. It is shown that the set of two-dimensional Euler flows satisfying the energy-Casimir stability criteria is empty for two important cases: (i) domains having the topology of the sphere, and (ii) simply-connected bounded domains with zero net vorticity. The results apply to both the first and the second of Arnold’s stability theorems. In the spirit of Andrews’ theorem, this puts a further limitation on the applicability of the method. © 2000 American Institute of Physics.

Flow-induced morphological instability of a mushy layer

A morphological instability of a mushy layer due to a forced flow in the melt is analysed. The instability is caused by flow induced in the mushy layer by Bernoulli suction at the crests of a sinusoidally perturbed mush–melt interface. The flow in the mushy layer advects heat away from crests which promotes solidification. Two linear stability analyses are presented: the fundamental mechanism for instability is elucidated by considering the case of uniform flow of an inviscid melt; a more complete analysis is then presented for the case of a parallel shear flow of a viscous melt. The novel instability mechanism we analyse here is contrasted with that investigated by Gilpin et al. (1980) and is found to be more potent for the case of newly forming sea ice.

Stability of an ice sheet on an elastic bed

The stability of stationary flow of a two-dimensional ice sheet is studied when the ice obeys a power flow law (Glen's flow law). The mass accumulation rate at the top is assumed to depend on elevation and span and the bed supporting the ice sheet consists of an elastic layer lying on a rigid surface. The normal perturbation of the free surface of the ice sheet is a singular eigenvalue problem. The singularity of the perturbation at the front of the ice sheet is considered using matched asymptotic expansions, and the eigenvalue problem is seen to reduce to that with fixed ice front. Numerical solution of the perturbation eigenvalue problem shows that the dependence of accumulation rate on elevation permits the existence of unstable solutions when the equilibrium line is higher than the bed at the ice divide. Alternatively, when the equilibrium line is lower than the bed, there are only stable solutions. Softening of the bed, expressed through a decrease of its elastic modulus, has a stabilising effect on the ice sheet.

The influence of ocean flow on newly forming sea ice

The heat and mass balance of the Arctic Ocean is very sensitive to the growth and decay of sea ice and the interaction between the heat and salt fields in the oceanic boundary layer. The hydraulic roughness of sea ice controls the detailed nature of turbulent fluxes in the boundary layer and hence is an important ingredient in model parameterizations. We describe a novel mechanism for the generation of corrugations of the sea ice–ocean interface, present a mathematical analysis elucidating the mechanism, and present numerical calculations for geophysically relevant conditions. The mechanism relies on brine flows developing in the sea ice due to Bernoulli suction by flow of ocean past the interface. For oceanic shears at the ice interface of 0.2 s−1, we expect the corrugations to form with a wavelength dependent upon the permeability structure of the sea ice which is described herein. The mechanism should be particularly important during sea ice formation in wind-maintained coastal polynyas and in leads. This paper applies our earlier analyses of the fundamental instability to field conditions and extends it to take account of the anisotropic and heterogeneous permeability of sea ice.

The counterpropagating Rossby wave perspective on Kelvin Helmholtz instability as a limiting case of a Rayleigh shear layer with zero width

The Kelvin Helmholtz (KH) problem, with zero stratification, is examined as a limiting case of the Rayleigh model of a single shear layer whose width tends to zero. The transition of the Rayleigh modal dispersion relation to the KH one, as well as the disappearance of the supermodal transient growth in the KH limit, are both rationalized from the counterpropagating Rossby wave perspective.

Potential predictability of rapid changes in the Atlantic meridional overturning circulation

We explore the potential predictability of rapid changes in the Atlantic meridional overturning circulation (MOC) using a coupled global climate model (HadCM3). Rapid changes in the temperature and salinity of surface water in the Nordic Seas, and the flow of dense water through Denmark Strait, are found to be precursors to rapid changes in the model's MOC, with a lead time of around 10 years. The mechanism proposed to explain this potential predictability relies on the development of density anomalies in the Nordic Seas which propagate through Denmark Strait and along the deep western boundary current, affecting the overturning. These rapid changes in the MOC have significant, and widespread, climate impacts which are potentially predictable a few years ahead. Whilst the flow through Denmark Strait is too strong in HadCM3, the presence of such potential predictability motivates the monitoring of water properties in the Nordic Seas and Denmark Strait.

Enhanced Templating in the Crystallisation of Poly(E-caprolactone) Using 1,3:2,4-di(4-Chlorobenzylidene) Sorbitol

We show that small quantities of 1,3:2,4-di(4-chlorobenzylidene) sorbitol dispersed in poly(epsilon-caprolactone) provide a very effective self-assembling nanoscale framework which, with a flow field, yields extremely high levels of polymer crystal orientation. During modest shear flow of the polymer melt, the additive forms highly extended nano-particles which adopt a preferred alignment with respect to the flow field. On cooling, polymer crystallisation is directed by these particles. This chloro substituted dibenzylidene sorbitol is considerably more effective at directing the crystal growth of poly(epsilon-caprolactone) than the unsubstituted compound.

Transport and distribution of lindane and simazine in a riverine environment: measurements in bed sediments and modelling

Aquatic sediments often remove hydrophobic contaminants from fresh waters. The subsequent distribution and concentration of contaminants in bed sediments determines their effect on benthic organisms and the risk of re-entry into the water and/or leaching to groundwater. This study examines the transport of simazine and lindane in aquatic bed sediments with the aim of understanding the processes that determine their depth distribution. Experiments in flume channels (water flow of 10 cm s(-1)) determined the persistence of the compounds in the absence of sediment with (a) de-ionised water and (b) a solution that had been in contact with river sediment. In further experiments with river bed sediments in light and dark conditions, measurements were made of the concentration of the compounds in the overlying water and the development of bacterial/algal biofilms and bioturbation activity. At the end of the experiments, concentrations in sediments and associated pore waters were determined in sections of the sediment at 1 mm resolution down to 5 mm and then at 10 mm resolution to 50 mm depth and these distributions analysed using a sorption-diffusion-degradation model. The fine resolution in the depth profile permitted the detection of a maximum in the concentration of the compounds in the pore water near the surface, whereas concentrations in the sediment increased to a maximum at the surface itself. Experimental distribution coefficients determined from the pore water and sediment concentrations indicated a gradient with depth that was partly explained by an increase in organic matter content and specific surface area of the solids near the interface. The modelling showed that degradation of lindane within the sediment was necessary to explain the concentration profiles, with the optimum agreement between the measured and theoretical profiles obtained with differential degradation in the oxic and anoxic zones. The compounds penetrated to a depth of 40-50 rum over a period of 42 days. (C) 2004 Society of Chemical Industry.

The analysis of ranked observations of soil structure using indicator geostatistics

Structure is an important physical feature of the soil that is associated with water movement, the soil atmosphere, microorganism activity and nutrient uptake. A soil without any obvious organisation of its components is known as apedal and this state can have marked effects on several soil processes. Accurate maps of topsoil and subsoil structure are desirable for a wide range of models that aim to predict erosion, solute transport, or flow of water through the soil. Also such maps would be useful to precision farmers when deciding how to apply nutrients and pesticides in a site-specific way, and to target subsoiling and soil structure stabilization procedures. Typically, soil structure is inferred from bulk density or penetrometer resistance measurements and more recently from soil resistivity and conductivity surveys. To measure the former is both time-consuming and costly, whereas observations made by the latter methods can be made automatically and swiftly using a vehicle-mounted penetrometer or resistivity and conductivity sensors. The results of each of these methods, however, are affected by other soil properties, in particular moisture content at the time of sampling, texture, and the presence of stones. Traditional methods of observing soil structure identify the type of ped and its degree of development. Methods of ranking such observations from good to poor for different soil textures have been developed. Indicator variograms can be computed for each category or rank of structure and these can be summed to give the sum of indicator variograms (SIV). Observations of the topsoil and subsoil structure were made at four field sites where the soil had developed on different parent materials. The observations were ranked by four methods and indicator and the sum of indicator variograms were computed and modelled for each method of ranking. The individual indicators were then kriged with the parameters of the appropriate indicator variogram model to map the probability of encountering soil with the structure represented by that indicator. The model parameters of the SIVs for each ranking system were used with the data to krige the soil structure classes, and the results are compared with those for the individual indicators. The relations between maps of soil structure and selected wavebands from aerial photographs are examined as basis for planning surveys of soil structure. (C) 2007 Elsevier B.V. All rights reserved.

Acoustic and petrophysical relationships in low-shale sandstone reservoir rocks

This paper describes the measurements of the acoustic and petrophysical properties of two suites of low-shale sandstone samples from North Sea hydrocarbon reservoirs, under simulated reservoir conditions. The acoustic velocities and quality factors of the samples, saturated with different pore fluids (brine, dead oil and kerosene), were measured at a frequency of about 0.8 MHz and over a range of pressures from 5 MPa to 40 MPa. The compressional-wave velocity is strongly correlated with the shear-wave velocity in this suite of rocks. The ratio V-P/V-S varies significantly with change of both pore-fluid type and differential pressure, confirming the usefulness of this parameter for seismic monitoring of producing reservoirs. The results of quality factor measurements were compared with predictions from Biot-flow and squirt-flow loss mechanisms. The results suggested that the dominating loss in these samples is due to squirt-flow of fluid between the pores of various geometries. The contribution of the Biot-flow loss mechanism to the total loss is negligible. The compressional-wave quality factor was shown to be inversely correlated with rock permeability, suggesting the possibility of using attenuation as a permeability indicator tool in low-shale, high-porosity sandstone reservoirs.

Earthworms produce granules of intricately zoned calcite

Earthworms of the family Lumbricidae, which includes many common species, produce and secrete up to millimeter-sized calcite granules, and the intricate fine-scale zoning of their constituent crystals is unique for a biomineral. Granule calcite is produced by crystallization of amorphous calcium carbonate (ACC) that initially precipitates within the earthworm calciferous glands, then forms protogranules by accretion on quartz grain cores. Crystallization of ACC is mediated by migrating fluid films and is largely complete within 24 11 of ACC production and before granules leave the earthworm. Variations in the density of defects formed as a byproduct of trace element incorporation during calcite crystall growth have generated zoning that can be resolved by cathodoluminescence imaging at ultraviolet to blue wavelengths and using the novel technique of scanning electron microscope charge contrast imaging. Mapping of calcite crystal orientations by electron backscatter diffraction reveals an approximate radial fabric to the granules that reflects crystal growth from internal nucleation sites toward their margins. The survival within granules of ACC inclusions for months after they enter soils indicates that they crystallize only within the earthworm and in the presence of fluids containing biochemical catalysts. The earthworm probably promotes crystallization of ACC in order to prevent remobilization of the calcium carbonate by dissolution. Calcite granules vividly illustrate the role of transient precursors in biomineralization, but the underlying question of why earth-worms produce granules in volumes sufficient to have a measurable impact on soil carbon cycling remains to be answered.

Quantification of ruminal Clostridium proteoclasticum by real-time PCR using a molecular beacon approach

Aims: All members of the ruminal Butyrivibrio group convert linoleic acid (cis-9,cis-12-18 : 2) via conjugated 18 : 2 metabolites (mainly cis-9,trans-11-18 : 2, conjugated linoleic acid) to vaccenic acid (trans-11-18 : 1), but only members of a small branch, which includes Clostridium proteoclasticum, of this heterogeneous group further reduce vaccenic acid to stearic acid (18 : 0, SA). The aims of this study were to develop a real-time polymerase chain reaction (PCR) assay that would detect and quantify these key SA producers and to use this method to detect diet-associated changes in their populations in ruminal digesta of lactating cows. Materials and Results: The use of primers targeting the 16S rRNA gene of Cl. proteoclasticum was not sufficiently specific when only binding dyes were used for detection in real-time PCR. Their sequences were too similar to some nonproducing strains. A molecular beacon probe was designed specifically to detect and quantify the 16S rRNA genes of the Cl. proteoclasticum subgroup. The probe was characterized by its melting curve and validated using five SA-producing and ten nonproducing Butyrivibrio-like strains and 13 other common ruminal bacteria. Analysis of ruminal digesta collected from dairy cows fed different proportions of starch and fibre indicated a Cl. proteoclasticum population of 2-9% of the eubacterial community. The influence of diet on numbers of these bacteria was less than variations between individual cows. Conclusion: A molecular beacon approach in qPCR enables the detection of Cl. proteoclasticum in ruminal digesta. Their numbers are highly variable between individual animals. Signifance and Impact of the Study: SA producers are fundamental to the flow of polyunsaturated fatty acid and vaccenic acid from the rumen. The method described here enabled preliminary information to be obtained about the size of this population. Further application of the method to digesta samples from cows fed diets of more variable composition should enable us to understand how to control these bacteria in order to enhance the nutritional characteristics of ruminant-derived foods, including milk and beef.

An HMV mapping study of a pulsating jet system

A new system for the generation of hydrodynamic modulated voltammetry (HMV) is presented. This system consists of an oscillating jet produced through the mechanical vibration of a large diaphragm. The structure of the cell is such that a relatively small vibration is transferred to a large fluid flow at the jet outlet. Positioning of an electrode (Pt, 0.5 mm or 25 mu m diameter) over the exit of this jet enables the detection of the modulated flow of liquid. While this flow creates modest mass transfer rates (time averaged similar to 0.015 cm s(-1)) it can also be used to create a HMV system where a 'lock-in' approach is adopted to investigate the redox chemistry in question. This is demonstrated for the Fe(CN)(6)(3-/4-) redox system. Here 'lock-in' to the modulated hydrodynamic signal is achieved through the deployment of bespoke software. The apparatus and procedure is shown to produce a simple and efficient way to obtain the desired signal. In addition the spatial variation of the HMV signal, phase correction and time averaged current with respect to the jet orifice is presented. (C) 2008 Elsevier B.V. All rights reserved.