Circular Nets with Spherical Parameter Lines and Terminating Laplace Sequences

The focus is on circular nets with one or two families of spherical parameter lines, which are treated in M\"obius geometry. These circular nets provide a discretisation of surfaces with one or two families of spherical curvature lines. The special cases of planar, circular and linear parameter lines are also investigated. A Lie-geometric discretisation in terms of principal contact element nets is also presented. Its properties are analogous to the classical properties of surfaces with one or two families of spherical curvature lines. Circular nets with two families of spherical parameter lines have geometric properties that are related to Darboux cyclides. Circular nets with one or two families of spherical parameter lines are examples of Q-nets with terminating Laplace sequences. More generally, this article considers Q-nets that are inscribed in quadrics and that have terminating Laplace sequences.Comment: 50 pages, 8 figure

Spatio-temporal variation in wave power and implications for electricity supply

Wave energy resources are intermittent and variable over both spatial and temporal scales. This is of concern when considering the supply of power to the electricity grid. This paper investigates whether deploying arrays of devices across multiple spatially separated sites can reduce intermittency of supply and step changes in generated power, thereby smoothing the contribution of wave energy to power supply. The primary focus is on the southwest UK; SWAN wave model hindcast data are analysed to assess the correlation of the resource across multiple sites and the variability of power levels with wave directionality. Power matrices are used to calculate step changes in the generated power with increasing numbers of sites. This is extended to national and European scales using ECMWF hindcast data to analyse the impacts of generating power at multiple sites over wider areas. Results show that at all scales the step change in generated power and the percentage of time with zero generation decreases with increasing numbers of sites before plateauing. This has positive implications for performance of electricity grids with high levels of renewable penetration

The effects of a Severn Barrage on wave conditions in the Bristol Channel

The study investigates the impact that construction of a Severn Barrage in the Severn Estuary, on the west coast of the UK, might have on local wave conditions. Implementation of a barrage will impact on tidal currents and water elevations in the wider region. There is strong tidal modulation of wave conditions under the natural regime and therefore barrage-induced changes to tidal conditions could affect wave modulation in the region. This paper uses Swan, an open source 3rd generation spectral wave model, to investigate the possible impacts of construction of a barrage on tidal modulation of the wave conditions. It is found that current variations, rather than water level variations, are the dominant factor in tidal modulation of wave conditions. Barrage implementation does not substantially change the modulation of the wave period or direction. However, barrage implementation does affect the tidal modulation of wave heights in the area of interest. The tidal modulation of the wave heights is generally reduced compared to the natural case; the peaks in the wave heights on an incoming tide are slightly lowered and there is lesser attenuation in wave heights on the outgoing tide. This modulation leads to net changes in the wave heights over one tidal cycle. For all of the tested wave conditions, this net change is small for the majority of the tested domain, namely to within ±5% of the no barrage case. There are some areas of greater change, most notably larger net increases in the wave heights near the North Somerset coast where the post-construction net wave height increase over a tidal cycle approach 20% of the pre-construction conditions. These changes do not impact coastal flooding because the wave height increase is not co-incident with high tide. Importantly, the maximum wave height is not increased and thus the likelihood of extreme events is not increased. The area of greatest reduction is between Swansea and Porthcawl. Changes over a neap tidal cycle show similar patterns of net change, but the modulation over the tidal cycle is different; primarily the magnitude of modulation is half that for the spring tide case and the shape is altered in some locations

A comparison of numerical modelling techniques for tidal stream turbine analysis

To fully understand the performance of tidal stream turbines for the creation of ocean ren wable energy, a range of computational models is required. We review and compare results from several models at different length scales. Models under review include blade element momentum theory (BEMT), blade element actuation disk RANS-CFD, blade- resolved RANS-CFD and coastal models based on the shallow water equations. Three sets of experimental results are used for model validation

A randomized, blinded, controlled trial investigating the gastrointestinal health effects of drinking water quality.

A double-blinded, randomized, controlled trial was carried out in in Melbourne, Australia, to determine the contribution of drinking water to gastroenteritis. Melbourne is one of the few major cities in the world that draws drinking water from a protected forest catchment with minimal water treatment (chlorination only). Six hundred families were randomly allocated to receive either real or sham water treatment units (WTUs) installed in their kitchen. Real units were designed to remove viruses, bacteria, and protozoa. Study participants completed a weekly health diary reporting gastrointestinal symptoms during the 68-week observation period. There were 2,669 cases of highly credible gastroenteritis (HCG) during the study (0.80 cases/person/year). The ratio of HCG episode rates for the real WTU group compared to the sham WTU group was 0.99 (95% confidence interval, 0.85-1.15, p = 0.85). We collected 795 fecal specimens from participants with gastroenteritis, and pathogens were not more significantly common in the sham WTU group. We found no evidence of waterborne disease in Melbourne. The application of this methodology to other water supplies will provide a better understanding of the relationship between human health and water quality

The influence of waves on morphodynamic impacts of energy extraction at a tidal stream turbine site in the Pentland Firth

Extraction of energy from tidal streams has the potential to impact on the morphodynamics of areas such as sub-tidal sandbanks via alteration of hydrodynamics. Marine sediment transport is forced by both wave and tidal currents. Past work on tidal stream turbine impacts has largely ignored the contribution of waves. Here, a fully coupled hydrodynamic, spectral wave and sediment transport model is used to assess the importance of including waves in simulations of turbine impact on seabed morphodynamics. Assessment of this is important due to the additional expense of including waves in simulations. Focus is given to a sandbank in the Inner Sound of the Pentland Firth. It is found that inclusion of wave action alters hydrodynamics, although extent of alteration is dependant of wave direction. Magnitude of sediment transport is increased when waves are included in the simulations and this has implications for morphological and volumetric changes. Volumetric changes are substantially increased when wave action is included: the impact of including waves is greater than the impact of including tidal stream turbines. Therefore it is recommended that at tidal turbine array sites exposed to large swell or wind-seas, waves should be considered for inclusion in simulations of physical impact

Nets of Lines with the Combinatorics of the Square Grid and with Touching Inscribed Conics

In the projective plane, we consider congruences of straight lines with the combinatorics of the square grid and with all elementary quadrilaterals possessing touching inscribed conics. The inscribed conics of two combinatorially neighbouring quadrilaterals have the same touching point on their common edge-line. We suggest that these nets are a natural projective generalisation of incircular nets. It is shown that these nets are planar Koenigs nets. Moreover, we show that general Koenigs nets are characterised by the existence of a 1-parameter family of touching inscribed conics. It is shown that the lines of any grid of quadrilaterals with touching inscribed conics are tangent to a common conic. These grids can be constructed via polygonal chains that are inscribed in conics. The special case of billiards in conics corresponds to incircular nets.DFG, 195170736, TRR 109: Diskretisierung in Geometrie und DynamikTU Berlin, Open-Access-Mittel – 202

Traditional turbulence methods and novel visualisation techniques for coastal flow model in order to deploy tidal stream turbines

Characteristics of flow in the coastal regions are strongly influenced by the topography of the seabed and understanding of these features is necessary before installation of tidal stream turbines (TST). In this paper, the bathymetry of a potential TST deployment site is surveyed using an echosounder and the resulting data is used in the development of the geometric model. The steady state k-ɛ and transient Large Eddy Simulation (LES) turbulence methods are employed. The stream surface visualisation method employed has important inherent characteristics that can enhance the visual perception of complex flow structures [1]. In this method lighting and shading reinforce the perception of shape and depth, images or textures can be mapped to the surface primitives providing additional visual information, colour and transparency can be used to convey additional data attributes. The results of all cases are compared with the flow data transect gathered by Acoustic Doppler Current Profiler (ADCP). It has been understood that the k-ɛ method can predict the flow pattern with relatively good accuracy near the main features of the domain and the LES model has the ability to simulate some important flow patterns because of the bathymetry