Flow structure and variability in the subtropical Indian Ocean: Instability of the South Indian Ocean Countercurrent

The origin of the eddy variability around the 25°S band in the Indian Ocean is investigated. We have found that the surface circulation east of Madagascar shows an anticyclonic subgyre bounded to the south by eastward flow from southwest Madagascar, and to the north by the westward flowing South Equatorial Current (SEC) between 15° and 20°S. The shallow, eastward flowing South Indian Ocean Countercurrent (SICC) extends above the deep reaching, westward flowing SEC to 95°E around the latitude of the high variability band. Applying a two-layer model reveals that regions of large vertical shear along the SICC-SEC system are baroclinically unstable. Estimates of the frequencies (3.5–6 times/year) and wavelengths (290–470 km) of the unstable modes are close to observations of the mesoscale variability derived from altimetry data. It is likely then that Rossby wave variability locally generated in the subtropical South Indian Ocean by baroclinic instability is the origin of the eddy variability around 25°S as seen, for example, in satellite altimetry.

Approximate Riemann solutions of the two-dimensional shallow-water equations

A finite-difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow-water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gasdynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearised problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second-order scheme which avoids non-physical, spurious oscillations. An extension to the two-dimensional equations with source terms, is included. The scheme is applied to a dam-break problem with cylindrical symmetry.

An efficient numerical scheme for the two-dimensional shallow water equations using arithmetic averaging

A finite difference scheme based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations of ideal fluid flow. A linearised problem, analogous to that of Riemann for gas dynamics is defined, and a scheme, based on numerical characteristic decomposition is presented for obtaining approximate solutions to the linearised problem, and incorporates the technique of operator splitting. An average of the flow variables across the interface between cells is required, and this average is chosen to be the arithmetic mean for computational efficiency leading to arithmetic averaging. This is in contrast to usual ‘square root’ averages found in this type of Riemann solver, where the computational expense can be prohibitive. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids nonphysical, spurious oscillations. An extension to the two-dimensional equations with source terms is included. The scheme is applied to the one-dimensional problems of a breaking dam and reflection of a bore, and in each case the approximate solution is compared to the exact solution of ideal fluid flow. The scheme is also applied to a problem of stationary bore generation in a channel of variable cross-section. Finally, the scheme is applied to two other dam-break problems, this time in two dimensions with one having cylindrical symmetry. Each approximate solution compares well with those given by other authors.

A shock capturing scheme for steady, supercritical, free-surface flow

Abstract A finite difference scheme is presented for the solution of the two-dimensional shallow water equations in steady, supercritical flow. The scheme incorporates numerical characteristic decomposition, is shock capturing by design and incorporates space-marching as a result of the assumption that the flow is wholly supercritical in at least one space dimension. Results are shown for problems involving oblique hydraulic jumps and reflection from a wall.

An algorithm for the shallow water equations with body fitted meshes

An efficient algorithm based on flux difference splitting is presented for the solution of the two-dimensional shallow water equations in a generalised coordinate system. The scheme is based on solving linearised Riemann problems approximately and in more than one dimension incorporates operator splitting. The scheme has good jump capturing properties and the advantage of using body-fitted meshes. Numerical results are shown for flow past a circular obstruction.

An isentropic flow algorithm with body fitted meshes

An efficient algorithm based on flux difference splitting is presented for the solution of the three-dimensional equations of isentropic flow in a generalised coordinate system, and with a general convex gas law. The scheme is based on solving linearised Riemann problems approximately and in more than one dimension incorporates operator splitting. The algorithm requires only one function evaluation of the gas law in each computational cell. The scheme has good shock capturing properties and the advantage of using body-fitted meshes. Numerical results are shown for Mach 3 flow of air past a circular cylinder. Furthermore, the algorithm also applies to shallow water flows by employing the familiar gas dynamics analogy.

Prediction of supercritical flow in open channels

A finite difference scheme based on flux difference splitting is presented for the solution of the one-dimensional shallow water equations in open channels. A linearised problem, analogous to that of Riemann for gas dynamics, is defined and a scheme, based on numerical characteristic decomposition, is presented for obtaining approximate solutions to the linearised problem. The method of upwind differencing is used for the resulting scalar problems, together with a flux limiter for obtaining a second order scheme which avoids non-physical, spurious oscillations. The scheme is applied to a problem of flow in a river whose geometry induces a region of supercritical flow.

A policy critique of Stansted Airport's expansion to 25 million passengers per annum (MPPA)

In this paper we undertake a preliminary assessment of the regional planning and development implications of BAA Stansted Airport’s planning permission to grow to 25 million passengers per annum (mppa) by 2010. Our concern is not simply to consider the overall growth of the airport on the airport site itself but the nature and type of growth both on- and off-site. In this document we focus on the submitted planning permission documents and test them. The methodology we employed was to draw on published and unpublished numerical estimates of the airport’s growth – particularly including estimates produced by the airport owner, BAA, and their economic and planning consultants DTZ Pieda - and critically, and systematically analyse their figures. We adopted this approach because unless the figures which were employed in the initial calculations were correct then all of the subsequent projections which flow from them - and the polices which could then be based on them – could be flawed. The analysis is divided into two parts – firstly, are the growth forecasts correct?; and secondly, what do these forecasts actually mean in developmental terms? In effect, what we have done is to produce a critique of the existing body of evidence by questioning underpinning assumptions and then draw some preliminary conclusions for the region based on this analysis. A major focus of this report has been analyse the figures involved in the planning application to expand Stansted to 25mppa. Ironically, one of our key findings, that the local impact of Stansted’s proposed expansion in employment terms might well be less than was originally thought, might make it easier to gain the acceptance of the relevant local authorities involved to allow the development to take place. Our main overall findings are that the BAA projections over-estimate the local employment impact of the airport’s proposed growth and under-estimate its potential regional ‘transportation’ employment effect. These two findings are, of course, related to each other in important ways, and we also feel that they have potentially significant medium and long-term economic, competitiveness and planning policy implications for the East of England region

Direct Computation of Stochastic Flow in Reservoirs with Uncertain Parameters

A direct method is presented for determining the uncertainty in reservoir pressure, flow, and net present value (NPV) using the time-dependent, one phase, two- or three-dimensional equations of flow through a porous medium. The uncertainty in the solution is modelled as a probability distribution function and is computed from given statistical data for input parameters such as permeability. The method generates an expansion for the mean of the pressure about a deterministic solution to the system equations using a perturbation to the mean of the input parameters. Hierarchical equations that define approximations to the mean solution at each point and to the field covariance of the pressure are developed and solved numerically. The procedure is then used to find the statistics of the flow and the risked value of the field, defined by the NPV, for a given development scenario. This method involves only one (albeit complicated) solution of the equations and contrasts with the more usual Monte-Carlo approach where many such solutions are required. The procedure is applied easily to other physical systems modelled by linear or nonlinear partial differential equations with uncertain data.

Stirring and mixing in two-dimensional divergent flow

While stirring and mixing properties in the stratosphere are reasonably well understood in the context of balanced (slow) dynamics, as is evidenced in numerous studies of chaotic advection, the strongly enhanced presence of high-frequency gravity waves in the mesosphere gives rise to a significant unbalanced (fast) component to the flow. The present investigation analyses result from two idealized shallow-water numerical simulations representative of stratospheric and mesospheric dynamics on a quasi-horizontal isentropic surface. A generalization of the Hua–Klein Eulerian diagnostic to divergent flow reveals that velocity gradients are strongly influenced by the unbalanced component of the flow. The Lagrangian diagnostic of patchiness nevertheless demonstrates the persistence of coherent features in the zonal component of the flow, in contrast to the destruction of coherent features in the meridional component. Single-particle statistics demonstrate t2 scaling for both the stratospheric and mesospheric regimes in the case of zonal dispersion, and distinctive scaling laws for the two regimes in the case of meridional dispersion. This is in contrast to two-particle statistics, which in the mesospheric (unbalanced) regime demonstrate a more rapid approach to Richardson’s t3 law in the case of zonal dispersion and is evidence of enhanced meridional dispersion.

Desert dust deposition on Mt. Elbrus, Caucasus Mountains, Russia in 2009-2012 as recorded in snow and shallow ice core: high-resolution "provenancing", transport patterns, physical properties and soluble ionic composition

A record of dust deposition events between 2009 and 2012 on Mt. Elbrus, Caucasus Mountains derived from a snow pit and a shallow ice core is presented for the first time for this region. A combination of isotopic analysis, SEVIRI red-green-blue composite imagery, MODIS atmospheric optical depth fields derived using the Deep Blue algorithm, air mass trajectories derived using the HYSPLIT model and analysis of meteorological data enabled identification of dust source regions with high temporal (hours) and spatial (cf. 20–100 km) resolution. Seventeen dust deposition events were detected; fourteen occurred in March–June, one in February and two in October. Four events originated in the Sahara, predominantly in north-eastern Libya and eastern Algeria. Thirteen events originated in the Middle East, in the Syrian Desert and northern Mesopotamia, from a mixture of natural and anthropogenic sources. Dust transportation from Sahara was associated with vigorous Saharan depressions, strong surface winds in the source region and mid-tropospheric south-westerly flow with daily winds speeds of 20–30 m s−1 at 700 hPa level and, although these events were less frequent, they resulted in higher dust concentrations in snow. Dust transportation from the Middle East was associated with weaker depressions forming over the source region, high pressure centered over or extending towards the Caspian Sea and a weaker southerly or south-easterly flow towards the Caucasus Mountains with daily wind speeds of 12–18 m s−1 at 700 hPa level. Higher concentrations of nitrates and ammonium characterise dust from the Middle East deposited on Mt. Elbrus in 2009 indicating contribution of anthropogenic sources. The modal values of particle size distributions ranged between 1.98 μm and 4.16 μm. Most samples were characterised by modal values of 2.0–2.8 μm with an average of 2.6 μm and there was no significant difference between dust from the Sahara and the Middle East.

A numerical model of the ionospheric signatures of time-varying magnetic reconnection: II. Measuring expansions in the ionospheric flow response

A numerical model embodying the concepts of the Cowley-Lockwood (Cowley and Lockwood, 1992, 1997) paradigm has been used to produce a simple Cowley– Lockwood type expanding flow pattern and to calculate the resulting change in ion temperature. Cross-correlation, fixed threshold analysis and threshold relative to peak are used to determine the phase speed of the change in convection pattern, in response to a change in applied reconnection. Each of these methods fails to fully recover the expansion of the onset of the convection response that is inherent in the simulations. The results of this study indicate that any expansion of the convection pattern will be best observed in time-series data using a threshold which is a fixed fraction of the peak response. We show that these methods used to determine the expansion velocity can be used to discriminate between the two main models for the convection response to a change in reconnection.

A moving point approach to model shallow ice sheets: a study case with radially-symmetrical ice sheets

Predicting the evolution of ice sheets requires numerical models able to accurately track the migration of ice sheet continental margins or grounding lines. We introduce a physically based moving point approach for the flow of ice sheets based on the conservation of local masses. This allows the ice sheet margins to be tracked explicitly and the waiting time behaviours to be modelled efficiently. A finite difference moving point scheme is derived and applied in a simplified context (continental radially-symmetrical shallow ice approximation). The scheme, which is inexpensive, is validated by comparing the results with moving-margin exact solutions and steady states. In both cases the scheme is able to track the position of the ice sheet margin with high precision.

A moving-point approach to model shallow ice sheets: a study case with radially symmetrical ice sheets

Predicting the evolution of ice sheets requires numerical models able to accurately track the migration of ice sheet continental margins or grounding lines. We introduce a physically based moving-point approach for the flow of ice sheets based on the conservation of local masses. This allows the ice sheet margins to be tracked explicitly. Our approach is also well suited to capture waiting-time behaviour efficiently. A finite-difference moving-point scheme is derived and applied in a simplified context (continental radially symmetrical shallow ice approximation). The scheme, which is inexpensive, is verified by comparing the results with steady states obtained from an analytic solution and with exact moving-margin transient solutions. In both cases the scheme is able to track the position of the ice sheet margin with high accuracy.

Spatial expansion and population structure of the neotropical malaria vector, Anopheles darlingi (Diptera: Culicidae)

Extensive population structuring is known to occur in Anopheles darlingi, the primary malaria vector of the Neotropics. We analysed the phylogeographic structure of the species using the mitochondrial cytochrome oxidase I marker. Diversity is divided into six main population groups in South America: Colombia, central Amazonia, southern Brazil, south-eastern Brazil, and two groups in north-east Brazil. The ancestral distribution of the taxon is hypothesized to be central Amazonia, and there is evidence of expansion from this region during the late Pleistocene. The expansion was not a homogeneous front, however, with at least four subgroups being formed due to geographic barriers. As the species spread, populations became isolated from each other by the Amazon River and the coastal mountain ranges of south-eastern Brazil and the Andes. Analyses incorporating distances around these barriers suggest that the entire South American range of An. darlingi is at mutation-dispersal-drift equilibrium. Because the species is distributed throughout such a broad area, the limited dispersal across some landscape types promotes differentiation between otherwise proximate populations. Moreover, samples from the An. darlingi holotype location in Rio de Janeiro State are substantially derived from all other populations, implying that there may be additional genetic differences of epidemiological relevance. The results obtained contribute to our understanding of gene flow in this species and allow the formulation of human mosquito health protocols in light of the potential population differences in vector capacity or tolerance to control strategies. (C) 2009 The Linnean Society of London, Biological Journal of the Linnean Society, 2009, 97, 854-866.