A depth-integrated 2D coastal and estuarine model with conformal boundary-fitted mesh generation

Details are given of the development and application of a 2D depth-integrated, conformal boundary-fitted, curvilinear model for predicting the depth-mean velocity field and the spatial concentration distribution in estuarine and coastal waters. A numerical method for conformal mesh generation, based on a boundary integral equation formulation, has been developed. By this method a general polygonal region with curved edges can be mapped onto a regular polygonal region with the same number of horizontal and vertical straight edges and a multiply connected region can be mapped onto a regular region with the same connectivity. A stretching transformation on the conformally generated mesh has also been used to provide greater detail where it is needed close to the coast, with larger mesh sizes further offshore, thereby minimizing the computing effort whilst maximizing accuracy. The curvilinear hydrodynamic and solute model has been developed based on a robust rectilinear model. The hydrodynamic equations are approximated using the ADI finite difference scheme with a staggered grid and the solute transport equation is approximated using a modified QUICK scheme. Three numerical examples have been chosen to test the curvilinear model, with an emphasis placed on complex practical applications

Evaluation of a boundary integral representation for the conformal mapping of the unit disk onto a simply-connected domain

A representation of the conformal mapping g of the interior or exterior of the unit circle onto a simply-connected domain Ω as a boundary integral in terms ofƒ|∂Ω is obtained, whereƒ :=g -l. A product integration scheme for the approximation of the boundary integral is described and analysed. An ill-conditioning problem related to the domain geometry is discussed. Numerical examples confirm the conclusions of this discussion and support the analysis of the quadrature scheme.

Comparison of the open-closed separatrix in a global magnetospheric simulation with observations: the role of the ring current

The development of global magnetospheric models, such as Space Weather Modeling Framework (SWMF), which can accurately reproduce and track space weather processes has high practical utility. We present an interval on 5 June 1998, where the location of the polar cap boundary, or open-closed field line boundary (OCB), can be determined in the ionosphere using a combination of instruments during a period encompassing a sharp northward to southward interplanetary field turning. We present both point- and time-varying comparisons of the observed and simulated boundaries in the ionosphere and find that when using solely the coupled ideal magnetohydrodynamic magnetosphere-ionosphere model, the rate of change of the OCB to a southward turning of the interplanetary field is significantly faster than that computed from the observational data. However, when the inner magnetospheric module is incorporated, the modeling framework both qualitatively, and often quantitatively, reproduces many elements of the studied interval prior to an observed substorm onset. This result demonstrates that the physics of the inner magnetosphere is critical in shaping the boundary between open and closed field lines during periods of southward interplanetary magnetic field (IMF) and provides significant insight into the 3-D time-dependent behavior of the Earth's magnetosphere in response to a northward-southward IMF turning. We assert that during periods that do not include the tens of minutes surrounding substorm expansion phase onset, the coupled SWMF model may provide a valuable and reliable tool for estimating both the OCB and magnetic field topology over a wide range of latitudes and local times.

Lateral boundary contributions to wave-activity invariants and nonlinear stability theorems for balanced dynamics

The slow advective-timescale dynamics of the atmosphere and oceans is referred to as balanced dynamics. An extensive body of theory for disturbances to basic flows exists for the quasi-geostrophic (QG) model of balanced dynamics, based on wave-activity invariants and nonlinear stability theorems associated with exact symmetry-based conservation laws. In attempting to extend this theory to the semi-geostrophic (SG) model of balanced dynamics, Kushner & Shepherd discovered lateral boundary contributions to the SG wave-activity invariants which are not present in the QG theory, and which affect the stability theorems. However, because of technical difficulties associated with the SG model, the analysis of Kushner & Shepherd was not fully nonlinear. This paper examines the issue of lateral boundary contributions to wave-activity invariants for balanced dynamics in the context of Salmon's nearly geostrophic model of rotating shallow-water flow. Salmon's model has certain similarities with the SG model, but also has important differences that allow the present analysis to be carried to finite amplitude. In the process, the way in which constraints produce boundary contributions to wave-activity invariants, and additional conditions in the associated stability theorems, is clarified. It is shown that Salmon's model possesses two kinds of stability theorems: an analogue of Ripa's small-amplitude stability theorem for shallow-water flow, and a finite-amplitude analogue of Kushner & Shepherd's SG stability theorem in which the ‘subsonic’ condition of Ripa's theorem is replaced by a condition that the flow be cyclonic along lateral boundaries. As with the SG theorem, this last condition has a simple physical interpretation involving the coastal Kelvin waves that exist in both models. Salmon's model has recently emerged as an important prototype for constrained Hamiltonian balanced models. The extent to which the present analysis applies to this general class of models is discussed.

An exact local conservation theorem for finite-amplitude disturbances to non-parallel shear flows, with remarks on Hamiltonian structure and on Arnol'd's stability theorems

Disturbances of arbitrary amplitude are superposed on a basic flow which is assumed to be steady and either (a) two-dimensional, homogeneous, and incompressible (rotating or non-rotating) or (b) stably stratified and quasi-geostrophic. Flow over shallow topography is allowed in either case. The basic flow, as well as the disturbance, is assumed to be subject neither to external forcing nor to dissipative processes like viscosity. An exact, local ‘wave-activity conservation theorem’ is derived in which the density A and flux F are second-order ‘wave properties’ or ‘disturbance properties’, meaning that they are O(a2) in magnitude as disturbance amplitude a [rightward arrow] 0, and that they are evaluable correct to O(a2) from linear theory, to O(a3) from second-order theory, and so on to higher orders in a. For a disturbance in the form of a single, slowly varying, non-stationary Rossby wavetrain, $\overline{F}/\overline{A}$ reduces approximately to the Rossby-wave group velocity, where (${}^{-}$) is an appropriate averaging operator. F and A have the formal appearance of Eulerian quantities, but generally involve a multivalued function the correct branch of which requires a certain amount of Lagrangian information for its determination. It is shown that, in a certain sense, the construction of conservable, quasi-Eulerian wave properties like A is unique and that the multivaluedness is inescapable in general. The connection with the concepts of pseudoenergy (quasi-energy), pseudomomentum (quasi-momentum), and ‘Eliassen-Palm wave activity’ is noted. The relationship of this and similar conservation theorems to dynamical fundamentals and to Arnol'd's nonlinear stability theorems is discussed in the light of recent advances in Hamiltonian dynamics. These show where such conservation theorems come from and how to construct them in other cases. An elementary proof of the Hamiltonian structure of two-dimensional Eulerian vortex dynamics is put on record, with explicit attention to the boundary conditions. The connection between Arnol'd's second stability theorem and the suppression of shear and self-tuning resonant instabilities by boundary constraints is discussed, and a finite-amplitude counterpart to Rayleigh's inflection-point theorem noted

A high frequency $hp$ boundary element method for scattering by convex polygons

In this paper we propose and analyze a hybrid $hp$ boundary element method for the solution of problems of high frequency acoustic scattering by sound-soft convex polygons, in which the approximation space is enriched with oscillatory basis functions which efficiently capture the high frequency asymptotics of the solution. We demonstrate, both theoretically and via numerical examples, exponential convergence with respect to the order of the polynomials, moreover providing rigorous error estimates for our approximations to the solution and to the far field pattern, in which the dependence on the frequency of all constants is explicit. Importantly, these estimates prove that, to achieve any desired accuracy in the computation of these quantities, it is sufficient to increase the number of degrees of freedom in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods.

Regulatory hotspots are associated with plant gene expression under varying soil phosphorus supply in Brassica rapa

Gene expression is a quantitative trait that can be mapped genetically in structured populations to identify expression quantitative trait loci (eQTL). Genes and regulatory networks underlying complex traits can subsequently be inferred. Using a recently released genome sequence, we have defined cis- and trans-eQTL and their environmental response to low phosphorus (P) availability within a complex plant genome and found hotspots of trans-eQTL within the genome. Interval mapping, using P supply as a covariate, revealed 18,876 eQTL. trans-eQTL hotspots occurred on chromosomes A06 and A01 within Brassica rapa; these were enriched with P metabolism-related Gene Ontology terms (A06) as well as chloroplast-and photosynthesis-related terms (A01). We have also attributed heritability components to measures of gene expression across environments, allowing the identification of novel gene expression markers and gene expression changes associated with low P availability. Informative gene expression markers were used to map eQTL and P use efficiency-related QTL. Genes responsive to P supply had large environmental and heritable variance components. Regulatory loci and genes associated with P use efficiency identified through eQTL analysis are potential targets for further characterization and may have potential for crop improvement.

Distribution of calcium (Ca) and magnesium (Mg) in the leaves of Brassica rapa under varying exogenous Ca and Mg supply

Background and Aims Leafy vegetable Brassica crops are an important source of dietary calcium (Ca) and magnesium (Mg) and represent potential targets for increasing leaf Ca and Mg concentrations through agronomy or breeding. Although the internal distribution of Ca and Mg within leaves affects the accumulation of these elements, such data are not available for Brassica. The aim of this study was to characterize the internal distribution of Ca and Mg in the leaves of a vegetable Brassica and to determine the effects of altered exogenous Ca and Mg supply on this distribution. Methods Brassica rapa ssp. trilocularis ‘R-o-18’ was grown at four different Ca:Mg treatments for 21 d in a controlled environment. Concentrations of Ca and Mg were determined in fully expanded leaves using inductively coupled plasma-mass spectrometry (ICP-MS). Internal distributions of Ca and Mg were determined in transverse leaf sections at the base and apex of leaves using energy-dispersive X-ray spectroscopy (EDS) with cryo-scanning electron microscopy (cryo-SEM). Key Results Leaf Ca and Mg concentrations were greatest in palisade and spongy mesophyll cells, respectively, although this was dependent on exogenous supply. Calcium accumulation in palisade mesophyll cells was enhanced slightly under high Mg supply; in contrast, Mg accumulation in spongy mesophyll cells was not affected by Ca supply. Conclusions The results are consistent with Arabidopsis thaliana and other Brassicaceae, providing phenotypic evidence that conserved mechanisms regulate leaf Ca and Mg distribution at a cellular scale. The future study of Arabidopsis gene orthologues in mutants of this reference B. rapa genotype will improve our understanding of Ca and Mg homeostasis in plants and may provide a model-to-crop translation pathway for targeted breeding.

Effects of non-uniform crosswind fields on scintillometry measurements

The effects of a non-uniform wind field along the path of a scintillometer are investigated. Theoretical spectra are calculated for a range of scenarios where the crosswind varies in space or time and compared to the ‘ideal’ spectrum based on a constant uniform crosswind. It is verified that the refractive-index structure parameter relation with the scintillometer signal remains valid and invariant for both spatially and temporally-varying crosswinds. However, the spectral shape may change significantly preventing accurate estimation of the crosswind speed from the peak of the frequency spectrum and retrieval of the structure parameter from the plateau of the power spectrum. On comparison with experimental data, non-uniform crosswind conditions could be responsible for previously unexplained features sometimes seen in observed spectra. By accounting for the distribution of crosswind, theoretical spectra can be generated that closely replicate the observations, leading to a better understanding of the measurements. Spatial variability of wind speeds should be expected for paths other than those that are parallel to the surface and over flat, homogenous areas, whilst fluctuations in time are important for all sites.

Evidence from Meteosat imagery of the interaction of sting jets with the boundary layer

Meteosat infra-red imagery for the Great Storm of October 1987 is analysed to show a series of very shallow arc-shaped and smaller chevron-shaped cloud features that were associated with damaging surface winds in the dry-slot region of this extra-tropical cyclone. Hypotheses are presented that attribute these low-level cloud features to boundary-layer convergence lines ahead of wind maxima associated with the downward transport of high momentum from overrunning, so-called sting-jet, flows originating in the storm's main cloud head. Copyright © 2004 Royal Meteorological Society.

Importance of resolution and model configuration when downscaling extreme precipitation

Dynamical downscaling is frequently used to investigate the dynamical variables of extra-tropical cyclones, for example, precipitation, using very high-resolution models nested within coarser resolution models to understand the processes that lead to intense precipitation. It is also used in climate change studies, using long timeseries to investigate trends in precipitation, or to look at the small-scale dynamical processes for specific case studies. This study investigates some of the problems associated with dynamical downscaling and looks at the optimum configuration to obtain the distribution and intensity of a precipitation field to match observations. This study uses the Met Office Unified Model run in limited area mode with grid spacings of 12, 4 and 1.5 km, driven by boundary conditions provided by the ECMWF Operational Analysis to produce high-resolution simulations for the Summer of 2007 UK flooding events. The numerical weather prediction model is initiated at varying times before the peak precipitation is observed to test the importance of the initialisation and boundary conditions, and how long the simulation can be run for. The results are compared to raingauge data as verification and show that the model intensities are most similar to observations when the model is initialised 12 hours before the peak precipitation is observed. It was also shown that using non-gridded datasets makes verification more difficult, with the density of observations also affecting the intensities observed. It is concluded that the simulations are able to produce realistic precipitation intensities when driven by the coarser resolution data.

The invisible hand guiding technology: crossing the boundary of technology

This paper examines attitudes towards Radio Frequency Identification (RFID) technology and explores the wider concerns of the ever increasing prospect of social tagging. Capturing vignettes and narratives from a sample of study participants, the paper highlights concerns about adopting RFID implements now and in the future. The views captured through qualitative methodology act as the platform for a wider argument concerning the human rights and privacy intrusion concerns over IT applications. Intended as an insight into the reality of technology impact, this paper lists a series of questions for leaders to consider over matters of human rights specifically concerning RFID adoption. The authors conclude that caution, naivety and fear are the underlying reasons for society accepting RFIDs without question and that RFIDs will be a part of everyday working and domestic life in the near future.

A high frequency boundary element method for scattering by a class of nonconvex obstacles

In this paper we propose and analyse a hybrid numerical-asymptotic boundary element method for the solution of problems of high frequency acoustic scattering by a class of sound-soft nonconvex polygons. The approximation space is enriched with carefully chosen oscillatory basis functions; these are selected via a study of the high frequency asymptotic behaviour of the solution. We demonstrate via a rigorous error analysis, supported by numerical examples, that to achieve any desired accuracy it is sufficient for the number of degrees of freedom to grow only in proportion to the logarithm of the frequency as the frequency increases, in contrast to the at least linear growth required by conventional methods. This appears to be the first such numerical analysis result for any problem of scattering by a nonconvex obstacle. Our analysis is based on new frequency-explicit bounds on the normal derivative of the solution on the boundary and on its analytic continuation into the complex plane.

Boundary condition effects in the simulation study of equilibrium properties of magnetic dipolar fluids

In this paper we investigate the equilibrium properties of magnetic dipolar (ferro-) fluids and discuss finite-size effects originating from the use of different boundary conditions in computer simulations. Both periodic boundary conditions and a finite spherical box are studied. We demonstrate that periodic boundary conditions and subsequent use of Ewald sum to account for the long-range dipolar interactions lead to a much faster convergence (in terms of the number of investigated dipolar particles) of the magnetization curve and the initial susceptibility to their thermodynamic limits. Another unwanted effect of the simulations in a finite spherical box geometry is a considerable sensitivity to the container size. We further investigate the influence of the surface term in the Ewald sum-that is, due to the surrounding continuum with magnetic permeability mu(BC)-on the convergence properties of our observables and on the final results. The two different ways of evaluating the initial susceptibility, i.e., (1) by the magnetization response of the system to an applied field and (2) by the zero-field fluctuation of the mean-square dipole moment of the system, are compared in terms of speed and accuracy.