Interaction of viscous free-surface flows with topography

The interaction of gravitationally driven, free-surface flows of viscous fluid with topographic features is investigated theoretically. The motion is studied in the regime where the depth of the flow is much smaller than the streamwise extent of the topography. A lubrication model of the motion is developed, integrated numerically and analysed asymptotically. For small mounds, it is shown that the flow surmounts the obstacles, but for larger mounds the flow is deflected around it and can form dry zones in its wake into which fluid does not flow, as well as forming deeper ponded regions upstream. Which of these phenomena prevails is shown to depend upon the amplitude of the mound height and the thickness of the oncoming flow relative to the streamwise length scale over which the topography varies. By using numerical and asymptotic results, we demonstrate that relatively wide mounds lead to the development of deep ponds of material upstream, which may lead to flow overtopping if the mound is not sufficiently high. These insights can be used to inform the design of barriers that defend built infrastructures from lava flows, and it is shown how this model can also provide an upper bound on the force exerted by the flow on them.</jats:p

Shallow free-surface Stokes flow around a corner.

The steady lateral spreading of a free-surface viscous flow down an inclined plane around a vertex from which the channel width increases linearly with downstream distance is investigated analytically, numerically and experimentally. From the vertex the channel wall opens by an angle α to the downslope direction and the viscous fluid spreads laterally along it before detaching. The motion is modelled using lubrication theory and the distance at which the flow detaches is computed as a function of α using analytical and numerical methods. Far downslope after detachment, it is shown that the motion is accurately modelled in terms of a similarity solution. Moreover, the detachment point is well approximated by a simple expression for a broad range of opening angles. The results are corroborated through a series of laboratory experiments and the implication for the design of barriers to divert lava flows are discussed. This article is part of the theme issue 'Stokes at 200 (Part 1)'

Shear dispersion in a porous medium. Part 1. Fixed-extent immiscible intrusion.

The dispersion of tracer through a liquid injected into a confined aquifer with vertically varying permeability is studied theoretically. The injected fluid is buoyant and of high viscosity relative to the original fluid in the aquifer, which causes the nose region of the flow, where the thickness of the injected fluid is less than the thickness of the aquifer, to advance with constant velocity and fixed shape. Behind the nose, tracer is sheared at early times owing to the vertically varying permeability. At later times, cross-aquifer diffusion homogenises the tracer distribution, which becomes independent of depth but spreads longitudinally in this shear dispersion regime, which leads to much faster spreading than by diffusion alone. As tracer diffuses symmetrically in the longitudinal direction, it eventually reaches the nose. Subsequently, the nose acts as a no-flux boundary and the concentration profile transitions to a half-Gaussian, with the maximum concentration at the front. The centre of mass of the tracer spreads backwards relative to the fixed nose at a rate proportional to [D(T −T 0 )] 1/2 where D is the dispersion coefficient and T 0 is a time offset owing to the adjustment to shear dispersion and the interaction with the nose. The initial release of tracer may not be vertically uniform owing to the heterogeneity and we show that this can lead to the centre of mass of tracer initially advancing faster than the mean flow. We consider the implications of our results on tracer migration in sedimentary layers

The effect of vertically varying permeability on tracer dispersion

We study the migration of a tracer within an injection-driven flow in a horizontal aquifer in which the permeability varies with depth. The permeability gradient produces a shear and this leads to lateral dispersion of the tracer. In the high permeability regions, the tracer moves substantially faster than the mean flow and eventually enters the nose region of the flow where the depth of the current is less than the depth of the aquifer. Depending on the influence of (i) the viscosity contrast between the injected fluid and the original fluid, and (ii) the vertical permeability gradient, the nose of the current may be of fixed shape or may gradually lengthen with time. This leads to a variety of patterns of dispersal of the tracer, which may either remain in the nose or cycle through the nose and be left behind. Our results illustrate the complexity of the migration of a tracer in a heterogeneous aquifer which has important implications for interpreting the results of tracer tests as may be proposed for monitoring$\text{CO}_{2}$or gas injected into subsurface reservoirs.</jats:p

Shear dispersion in a porous medium. Part 2. Growing immiscible intrusion.

The dispersion of a pulse of tracer through a liquid injected into a confined aquifer with vertically varying permeability is studied theoretically. The injected fluid is buoyant and of low viscosity relative to the original fluid in the aquifer. The nose region of the flow, where the thickness of the injected fluid is less than the thickness of the aquifer, grows in proportion to time T and as a result the tracer continually migrates further into the nose where it has a progressively smaller vertical extent. The spreading of the nose stretches a pulse of initial length, L 0 , longitudinally to have a length proportional to L 0 (T /T E ) 1/2 in the absence of diffusion, where T E is the nose entry time. Diffusion acts at the same rate and the combination of the two processes results in the tracer spreading longitudinally with a length proportional to (DT log T ) 1/2 at long times after entering the nose. The results are generalised to consider the case in which the permeability in the aquifer varies with depth. The shearing of the tracer associated with the permeability variation is eventually balanced by vertical homogenisation. As the tracer migrates into continually thinner regions of the growing nose, the permeability contrast sampled by the tracer rapidly decays. The role of the shear becomes dominated by the stretching of the nose and ultimately the late-time behaviour is as in a uniform aquifer. However, the effective pulse length of the tracer upon asymptoting to the stretching regime is now given by L 0 = ∆U T E , where ∆U is the magnitude of the shear. The spreading in the stretching regime then has a lengthscale of ∆U (T E T ) 1/2 , which may be much faster than in the case of a uniform aquifer. If the diffusion is sufficiently fast, there may be an intermediate regime in which Taylor dispersion is important prior to the stretching dominating. The results have significant implications for tracer tests that are used in CO 2 sequestration because the influence of the early shear associated with any heterogeneity can be observed long after the tracer is in a thin region of the nose

Discovery of a z = 0.65 post-starburst BAL quasar in the DES supernova fields

We present the discovery of a z = 0.65 low-ionization broad absorption line (LoBAL) quasar in a post-starburst galaxy in data from the Dark Energy Survey (DES) and spectroscopy from the Australian Dark Energy Survey (OzDES). LoBAL quasars are a minority of all BALs, and rarer still is that this object also exhibits broad Fe II (an FeLoBAL) and Balmer absorption. This is the first BAL quasar that has signatures of recently truncated star formation, which we estimate ended about 40 Myr ago. The characteristic signatures of an FeLoBAL require high column densities, which could be explained by the emergence of a young quasar from an early, dust-enshrouded phase, or by clouds compressed by a blast wave. The age of the starburst component is comparable to estimates of the lifetime of quasars, so if we assume the quasar activity is related to the truncation of the star formation, this object is better explained by the blast wave scenario

Protocol for the development of a core outcome set for stillbirth care research (iCHOOSE Study)

IntroductionStillbirth is associated with significant physical, psychosocial and economic consequences for parents, families, wider society and the healthcare system. There is emerging momentum to design and evaluate interventions for care after stillbirth and in subsequent pregnancies. However, there is insufficient evidence to inform clinical practice compounded by inconsistent outcome reporting in research studies. To address this paucity of evidence, we plan to develop a core outcome set for stillbirth care research, through an international consensus process with key stakeholders including parents, healthcare professionals and researchers.Methods and analysisThe development of this core outcome set will be divided into five distinct phases: (1) Identifying potential outcomes from a mixed-methods systematic review and analysis of interviews with parents who have experienced stillbirth; (2) Creating a comprehensive outcome long-list and piloting of a Delphi questionnaire using think-aloud interviews; (3) Choosing the most important outcomes by conducting an international two-round Delphi survey including high-income, middle-income and low-income countries; (4) Deciding the core outcome set by consensus meetings with key stakeholders and (5) Dissemination and promotion of the core outcome set. A parent and public involvement panel and international steering committee has been convened to coproduce every stage of the development of this core outcome set.Ethics and disseminationEthical approval for the qualitative interviews has been approved by Berkshire Ethics Committee REC Reference 12/SC/0495. Ethical approval for the think-aloud interviews, Delphi survey and consensus meetings has been awarded from the University of Bristol Faculty of Health Sciences Research Ethics Committee (Reference number: 116535). The dissemination strategy is being developed with the parent and public involvement panel and steering committee. Results will be published in peer-reviewed specialty journals, shared at national and international conferences and promoted through parent organisations and charities.PROSPERO registration numberCRD42018087748.</jats:sec

The seeds of divergence: the economy of French North America, 1688 to 1760

Generally, Canada has been ignored in the literature on the colonial origins of divergence with most of the attention going to the United States. Late nineteenth century estimates of income per capita show that Canada was relatively poorer than the United States and that within Canada, the French and Catholic population of Quebec was considerably poorer. Was this gap long standing? Some evidence has been advanced for earlier periods, but it is quite limited and not well-suited for comparison with other societies. This thesis aims to contribute both to Canadian economic history and to comparative work on inequality across nations during the early modern period. With the use of novel prices and wages from Quebec—which was then the largest settlement in Canada and under French rule—a price index, a series of real wages and a measurement of Gross Domestic Product (GDP) are constructed. They are used to shed light both on the course of economic development until the French were defeated by the British in 1760 and on standards of living in that colony relative to the mother country, France, as well as the American colonies. The work is divided into three components. The first component relates to the construction of a price index. The absence of such an index has been a thorn in the side of Canadian historians as it has limited the ability of historians to obtain real values of wages, output and living standards. This index shows that prices did not follow any trend and remained at a stable level. However, there were episodes of wide swings—mostly due to wars and the monetary experiment of playing card money. The creation of this index lays the foundation of the next component. The second component constructs a standardized real wage series in the form of welfare ratios (a consumption basket divided by nominal wage rate multiplied by length of work year) to compare Canada with France, England and Colonial America. Two measures are derived. The first relies on a “bare bones” definition of consumption with a large share of land-intensive goods. This measure indicates that Canada was poorer than England and Colonial America and not appreciably richer than France. However, this measure overestimates the relative position of Canada to the Old World because of the strong presence of land-intensive goods. A second measure is created using a “respectable” definition of consumption in which the basket includes a larger share of manufactured goods and capital-intensive goods. This second basket better reflects differences in living standards since the abundance of land in Canada (and Colonial America) made it easy to achieve bare subsistence, but the scarcity of capital and skilled labor made the consumption of luxuries and manufactured goods (clothing, lighting, imported goods) highly expensive. With this measure, the advantage of New France over France evaporates and turns slightly negative. In comparison with Britain and Colonial America, the gap widens appreciably. This element is the most important for future research. By showing a reversal because of a shift to a different type of basket, it shows that Old World and New World comparisons are very sensitive to how we measure the cost of living. Furthermore, there are no sustained improvements in living standards over the period regardless of the measure used. Gaps in living standards observed later in the nineteenth century existed as far back as the seventeenth century. In a wider American perspective that includes the Spanish colonies, Canada fares better. The third component computes a new series for Gross Domestic Product (GDP). This is to avoid problems associated with using real wages in the form of welfare ratios which assume a constant labor supply. This assumption is hard to defend in the case of Colonial Canada as there were many signs of increasing industriousness during the eighteenth and nineteenth centuries. The GDP series suggest no long-run trend in living standards (from 1688 to circa 1765). The long peace era of 1713 to 1740 was marked by modest economic growth which offset a steady decline that had started in 1688, but by 1760 (as a result of constant warfare) living standards had sunk below their 1688 levels. These developments are accompanied by observations that suggest that other indicators of living standard declined. The flat-lining of incomes is accompanied by substantial increases in the amount of time worked, rising mortality and rising infant mortality. In addition, comparisons of incomes with the American colonies confirm the results obtained with wages— Canada was considerably poorer. At the end, a long conclusion is provides an exploratory discussion of why Canada would have diverged early on. In structural terms, it is argued that the French colony was plagued by the problem of a small population which prohibited the existence of scale effects. In combination with the fact that it was dispersed throughout the territory, the small population of New France limited the scope for specialization and economies of scale. However, this problem was in part created, and in part aggravated, by institutional factors like seigneurial tenure. The colonial origins of French America’s divergence from the rest of North America are thus partly institutional