Bow and stern flows with constant vorticity

Free surface flows of a rotational fluid past a two-dimensional semi-infinite body are considered. The fluid is assumed to be inviscid, incompressible, and of finite depth. A boundary integral method is used to solve the problem for the case where the free surface meets the body at a stagnation point. Supercritical solutions which satisfy the radiation condition are found for various values of the Froude number and the dimensionless vorticity. Subcritical solutions are also found; however these solutions violate the radiation condition and are characterized by a train of waves upstream. It is shown numerically that the amplitude of these waves increases as each of the Froude number, vorticity and height of the body above the bottom increases.

Linear stern waves in finite depth channels

This paper formulates an analytically tractable problem for the wake generated by a long flat bottom ship by considering the steady free surface flow of an inviscid, incompressible fluid emerging from beneath a semi-infinite rigid plate. The flow is considered to be irrotational and two-dimensional so that classical potential flow methods can be exploited. In addition, it is assumed that the draft of the plate is small compared to the depth of the channel. The linearised problem is solved exactly using a Fourier transform and the Wiener-Hopf technique, and it is shown that there is a family of subcritical solutions characterised by a train of sinusoidal waves on the downstream free surface. The amplitude of these waves decreases as the Froude number increases. Supercritical solutions are also obtained, but, in general, these have infinite vertical velocities at the trailing edge of the plate. Consideration of further terms in the expansions suggests a way of canceling the singularity for certain values of the Froude number.

New stress and velocity fields for highly frictional granular materials

The idealised theory for the quasi-static flow of granular materials which satisfy the Coulomb-Mohr hypothesis is considered. This theory arises in the limit that the angle of internal friction approaches $\pi/2$, and accordingly these materials may be referred to as being `highly frictional'. In this limit, the stress field for both two-dimensional and axially symmetric flows may be formulated in terms of a single nonlinear second order partial differential equation for the stress angle. To obtain an accompanying velocity field, a flow rule must be employed. Assuming the non-dilatant double-shearing flow rule, a further partial differential equation may be derived in each case, this time for the streamfunction. Using Lie symmetry methods, a complete set of group-invariant solutions is derived for both systems, and through this process new exact solutions are constructed. Only a limited number of exact solutions for gravity driven granular flows are known, so these results are potentially important in many practical applications. The problem of mass flow through a two-dimensional wedge hopper is examined as an illustration.

Lie group symmetry analysis for granular media stress equations

The Airy stress function, although frequently employed in classical linear elasticity, does not receive similar usage for granular media problems. For plane strain quasi-static deformations of a cohesionless Coulomb–Mohr granular solid, a single nonlinear partial differential equation is formulated for the Airy stress function by combining the equilibrium equations with the yield condition. This has certain advantages from the usual approach, in which two stress invariants and a stress angle are introduced, and a system of two partial differential equations is needed to describe the flow. In the present study, the symmetry analysis of differential equations is utilised for our single partial differential equation, and by computing an optimal system of one-dimensional Lie algebras, a complete set of group-invariant solutions is derived. By this it is meant that any group-invariant solution of the governing partial differential equation (provided it can be derived via the classical symmetries method) may be obtained as a member of this set by a suitable group transformation. For general values of the parameters (angle of internal friction and gravity g) it is found there are three distinct classes of solutions which correspond to granular flows considered previously in the literature. For the two limiting cases of high angle of internal friction and zero gravity, the governing partial differential equation admit larger families of Lie point symmetries, and from these symmetries, further solutions are derived, many of which are new. Furthermore, the majority of these solutions are exact, which is rare for granular flow, especially in the case of gravity driven flows.

Free surface problems for static Coulomb-Mohr granular solids

This paper is concerned with some plane strain and axially symmetric free surface problems which arise in the study of static granular solids that satisfy the Coulomb-Mohr yield condition. Such problems are inherently nonlinear, and hence difficult to attack analytically. Given a Coulomb friction condition holds on a solid boundary, it is shown that the angle a free surface is allowed to attach to the boundary is dependent only on the angle of wall friction, assuming the stresses are all continuous at the attachment point, and assuming also that the coefficient of cohesion is nonzero. As a model problem, the formation of stable cohesive arches in hoppers is considered. This undesirable phenomena is an obstacle to flow, and occurs when the hopper outlet is too small. Typically, engineers are concerned with predicting the critical outlet size for a given hopper and granular solid, so that for hoppers with outlets larger than this critical value, arching cannot occur. This is a topic of considerable practical interest, with most accepted engineering methods being conservative in nature. Here, the governing equations in two limiting cases (small cohesion and high angle of internal friction) are considered directly. No information on the critical outlet size is found; however solutions for the shape of the free boundary (the arch) are presented, for both plane and axially symmetric geometries.

Perturbation solutions for flow through symmetrical hoppers with inserts and asymmetrical wedge hoppers

Under certain circumstances, an industrial hopper which operates under the "funnel-flow" regime can be converted to the "mass-flow" regime with the addition of a flow-corrective insert. This paper is concerned with calculating granular flow patterns near the outlet of hoppers that incorporate a particular type of insert, the cone-in-cone insert. The flow is considered to be quasi-static, and governed by the Coulomb-Mohr yield condition together with the non-dilatant double-shearing theory. In two dimensions, the hoppers are wedge-shaped, and as such the formulation for the wedge-in-wedge hopper also includes the case of asymmetrical hoppers. A perturbation approach, valid for high angles of internal friction, is used for both two-dimensional and axially symmetric flows, with analytic results possible for both leading order and correction terms. This perturbation scheme is compared with numerical solutions to the governing equations, and is shown to work very well for angles of internal friction in excess of 45 degree.

Using routinely collected hospital data for child maltreatment surveillance : issues, methods and patterns

Background: International data on child maltreatment are largely derived from child protection agencies, and predominantly report only substantiated cases of child maltreatment. This approach underestimates the incidence of maltreatment and makes inter-jurisdictional comparisons difficult. There has been a growing recognition of the importance of health professionals in identifying, documenting and reporting suspected child maltreatment. This study aimed to describe the issues around case identification using coded morbidity data, outline methods for selecting and grouping relevant codes, and illustrate patterns of maltreatment identified. Methods: A comprehensive review of the ICD-10-AM classification system was undertaken, including review of index terms, a free text search of tabular volumes, and a review of coding standards pertaining to child maltreatment coding. Identified codes were further categorised into maltreatment types including physical abuse, sexual abuse, emotional or psychological abuse, and neglect. Using these code groupings, one year of Australian hospitalisation data for children under 18 years of age was examined to quantify the proportion of patients identified and to explore the characteristics of cases assigned maltreatment-related codes. Results: Less than 0.5% of children hospitalised in Australia between 2005 and 2006 had a maltreatment code assigned, almost 4% of children with a principal diagnosis of a mental and behavioural disorder and over 1% of children with an injury or poisoning as the principal diagnosis had a maltreatment code assigned. The patterns of children assigned with definitive T74 codes varied by sex and age group. For males selected as having a maltreatment-related presentation, physical abuse was most commonly coded (62.6% of maltreatment cases) while for females selected as having a maltreatment-related presentation, sexual abuse was the most commonly assigned form of maltreatment (52.9% of maltreatment cases). Conclusion: This study has demonstrated that hospital data could provide valuable information for routine monitoring and surveillance of child maltreatment, even in the absence of population-based linked data sources. With national and international calls for a public health response to child maltreatment, better understanding of, investment in and utilisation of our core national routinely collected data sources will enhance the evidence-base needed to support an appropriate response to children at risk.

Reliability of routinely collected hospital data for child maltreatment surveillance

Background: Internationally, research on child maltreatment-related injuries has been hampered by a lack of available routinely collected health data to identify cases, examine causes, identify risk factors and explore health outcomes. Routinely collected hospital separation data coded using the International Classification of Diseases and Related Health Problems (ICD) system provide an internationally standardised data source for classifying and aggregating diseases, injuries, causes of injuries and related health conditions for statistical purposes. However, there has been limited research to examine the reliability of these data for child maltreatment surveillance purposes. This study examined the reliability of coding of child maltreatment in Queensland, Australia. Methods: A retrospective medical record review and recoding methodology was used to assess the reliability of coding of child maltreatment. A stratified sample of hospitals across Queensland was selected for this study, and a stratified random sample of cases was selected from within those hospitals. Results: In 3.6% of cases the coders disagreed on whether any maltreatment code could be assigned (definite or possible) versus no maltreatment being assigned (unintentional injury), giving a sensitivity of 0.982 and specificity of 0.948. The review of these cases where discrepancies existed revealed that all cases had some indications of risk documented in the records. 15.5% of cases originally assigned a definite or possible maltreatment code, were recoded to a more or less definite strata. In terms of the number and type of maltreatment codes assigned, the auditor assigned a greater number of maltreatment types based on the medical documentation than the original coder assigned (22% of the auditor coded cases had more than one maltreatment type assigned compared to only 6% of the original coded data). The maltreatment types which were the most ‘under-coded’ by the original coder were psychological abuse and neglect. Cases coded with a sexual abuse code showed the highest level of reliability. Conclusion: Given the increasing international attention being given to improving the uniformity of reporting of child-maltreatment related injuries and the emphasis on the better utilisation of routinely collected health data, this study provides an estimate of the reliability of maltreatment-specific ICD-10-AM codes assigned in an inpatient setting.

Hydrodynamic and thruster model validation for autonomous underwater vehicles

From Pontryagin’s Maximum Principle to the Duke Kahanamoku Aquatic Complex; we develop the theory and generate implementable time efficient trajectories for a test-bed autonomous underwater vehicle (AUV). This paper is the beginning of the journey from theory to implementation. We begin by considering pure motion trajectories and move into a rectangular trajectory which is a concatenation of pure surge and pure sway. These trajectories are tested using our numerical model and demonstrated by our AUV in the pool. In this paper we demonstrate that the above motions are realizable through our method, and we gain confidence in our numerical model. We conclude that using our current techniques, implementation of time efficient trajectories is likely to succeed.

Optimal fluid injection strategies for in situ mineral leaching in two-dimensions

This paper examines the ground-water flow problem associated with the injection and recovery of certain corrosive fluids into mineral bearing rock. The aim is to dissolve the minerals in situ, and then recover them in solution. In general, it is not possible to recover all the injected fluid, which is of concern economically and environmentally. However, a new strategy is proposed here, that allows all the leaching fluid to be recovered. A mathematical model of the situation is solved approximately using an asymptotic solution, and exactly using a boundary integral approach. Solutions are shown for two-dimensional flow, which is of some practical interest as it is achievable in old mine tunnels, for example.

Free surface flow into a horizontal slot with zero gravity

The two-dimensional free surface flow of a finite-depth fluid into a horizontal slot is considered. For this study, the effects of viscosity and gravity are ignored. A generalised Schwarz-Christoffel mapping is used to formulate the problem in terms of a linear integral equation, which is solved exactly with the use of a Fourier transform. The resulting free surface profile is given explicitly in closed-form.

Smoothly attaching bow flows with constant vorticity

The free surface flow of a finite depth fluid past a semi-infinite body is considered. The fluid is assumed to have constant vorticity throughout and the free surface is assumed to attach smoothly to the front face of the body. Numerical solutions are found using a boundary integral method in the physical plane and it is shown that solutions exist for all supercritical Froude numbers. The related problem of the cusp-like flow due to a submerged sink in a corner is also considered. Vorticity is included in the flow and it is shown that the behaviour of the solutions is qualitatively the same as that found in the problem described above.

The largest volcanic eruptions on Earth

Large igneous provinces (LIPs) are sites of the most frequently recurring, largest volume basaltic and silicic eruptions in Earth history. These large-volume (N1000 km3 dense rock equivalent) and large-magnitude (NM8) eruptions produce areally extensive (104–105 km2) basaltic lava flow fields and silicic ignimbrites that are the main building blocks of LIPs. Available information on the largest eruptive units are primarily from the Columbia River and Deccan provinces for the dimensions of flood basalt eruptions, and the Paraná–Etendeka and Afro-Arabian provinces for the silicic ignimbrite eruptions. In addition, three large-volume (675– 2000 km3) silicic lava flows have also been mapped out in the Proterozoic Gawler Range province (Australia), an interpreted LIP remnant. Magma volumes of N1000 km3 have also been emplaced as high-level basaltic and rhyolitic sills in LIPs. The data sets indicate comparable eruption magnitudes between the basaltic and silicic eruptions, but due to considerable volumes residing as co-ignimbrite ash deposits, the current volume constraints for the silicic ignimbrite eruptions may be considerably underestimated. Magma composition thus appears to be no barrier to the volume of magma emitted during an individual eruption. Despite this general similarity in magnitude, flood basaltic and silicic eruptions are very different in terms of eruption style, duration, intensity, vent configuration, and emplacement style. Flood basaltic eruptions are dominantly effusive and Hawaiian–Strombolian in style, with magma discharge rates of ~106–108 kg s−1 and eruption durations estimated at years to tens of years that emplace dominantly compound pahoehoe lava flow fields. Effusive and fissural eruptions have also emplaced some large-volume silicic lavas, but discharge rates are unknown, and may be up to an order of magnitude greater than those of flood basalt lava eruptions for emplacement to be on realistic time scales (b10 years). Most silicic eruptions, however, are moderately to highly explosive, producing co-current pyroclastic fountains (rarely Plinian) with discharge rates of 109– 1011 kg s−1 that emplace welded to rheomorphic ignimbrites. At present, durations for the large-magnitude silicic eruptions are unconstrained; at discharge rates of 109 kg s−1, equivalent to the peak of the 1991 Mt Pinatubo eruption, the largest silicic eruptions would take many months to evacuate N5000 km3 of magma. The generally simple deposit structure is more suggestive of short-duration (hours to days) and high intensity (~1011 kg s−1) eruptions, perhaps with hiatuses in some cases. These extreme discharge rates would be facilitated by multiple point, fissure and/or ring fracture venting of magma. Eruption frequencies are much elevated for large-magnitude eruptions of both magma types during LIP-forming episodes. However, in basaltdominated provinces (continental and ocean basin flood basalt provinces, oceanic plateaus, volcanic rifted margins), large magnitude (NM8) basaltic eruptions have much shorter recurrence intervals of 103–104 years, whereas similar magnitude silicic eruptions may have recurrence intervals of up to 105 years. The Paraná– Etendeka province was the site of at least nine NM8 silicic eruptions over an ~1 Myr period at ~132 Ma; a similar eruption frequency, although with a fewer number of silicic eruptions is also observed for the Afro- Arabian Province. The huge volumes of basaltic and silicic magma erupted in quick succession during LIP events raises several unresolved issues in terms of locus of magma generation and storage (if any) in the crust prior to eruption, and paths and rates of ascent from magma reservoirs to the surface.

Pre-eruptive uplift in the Emeishan? [Correspondence]

In their correspondence, He and colleagues question our conclusion of little or no uplift preceding Emeishan volcanism that we reported in our letter1. Debate concerns the nature of the contact between the Maokou limestone and Emeishan volcanics, the depositional environment and volumetric significance of mafic hydromagmatic deposits (MHDs), and evidence for symmetrical domal thinning. MHDs in the Daqiao section are separated from the Maokou limestone by 100 m of subaerial basaltic lavas, but elsewhere MHDs — previously interpreted as basal conglomerates2, 3 — directly overlie the Maokou2, 3. MHDs thus feature strongly in basal sections of the Emeishan lava succession, as also recently shown4 elsewhere in the Emeishan. An irregular surface at the top of the Maokou limestone has been interpreted as an erosional unconformity2, 3, but clastic deposits presented as evidence of this erosion2, 3 are MHDs produced by explosive magma–water interaction1. A clear demonstration that this irregular top surface is an erosional truncation of limestone reef facies (slope/rim, flat, lagoonal) is currently lacking, but is critical because reefs and carbonate platforms show considerable natural relief of tens of metres. The persistent hot, wet climate since the Oligocene has produced well-developed weathering profiles on exposed Palaeozoic marine sedimentary sequences5, but weathering and karst relief of the uppermost Maokou limestone underlying the flood basalts have not been properly documented, nor shown to be of middle Permian age and immediately preceding emplacement of the large igneous province.