A correction to the enhanced bottom drag parameterisation of tidal turbines

Hydrodynamic modelling is an important tool for the development of tidal stream energy projects. Many hydrodynamic models incorporate the effect of tidal turbines through an enhanced bottom drag. In this paper we show that although for coarse grid resolutions (kilometre scale) the resulting force exerted on the flow agrees well with the theoretical value, the force starts decreasing with decreasing grid sizes when these become smaller than the length scale of the wake recovery. This is because the assumption that the upstream velocity can be approximated by the local model velocity, is no longer valid. Using linear momentum actuator disc theory however, we derive a relationship between these two velocities and formulate a correction to the enhanced bottom drag formulation that consistently applies a force that remains closed to the theoretical value, for all grid sizes down to the turbine scale. In addition, a better understanding of the relation between the model, upstream, and actual turbine velocity, as predicted by actuator disc theory, leads to an improved estimate of the usefully extractable energy. We show how the corrections can be applied (demonstrated here for the models MIKE 21 and Fluidity) by a simple modification of the drag coefficient

Wave packet approach to transport in mesoscopic systems

Wave packets provide a well established and versatile tool for studying time-dependent effects in molecular physics. Here, we demonstrate the application of wave packets to mesoscopic nanodevices at low temperatures. The electronic transport in the devices is expressed in terms of scattering and transmission coefficients, which are efficiently obtained by solving an initial value problem (IVP) using the time-dependent Schroedinger equation. The formulation as an IVP makes non-trivial device topologies accessible and by tuning the wave packet parameters one can extract the scattering properties for a large range of energies.Comment: 12 pages, 4 figure

Shock-resolved Navier–Stokes simulation of the Richtmyer–Meshkov instability start-up at a light–heavy interface

The single-mode Richtmyer–Meshkov instability is investigated using a first-order perturbation of the two-dimensional Navier–Stokes equations about a one-dimensional unsteady shock-resolved base flow. A feature-tracking local refinement scheme is used to fully resolve the viscous internal structure of the shock. This method captures perturbations on the shocks and their influence on the interface growth throughout the simulation, to accurately examine the start-up and early linear growth phases of the instability. Results are compared to analytic models of the instability, showing some agreement with predicted asymptotic growth rates towards the inviscid limit, but significant discrepancies are noted in the transient growth phase. Viscous effects are found to be inadequately predicted by existing models

Surface structure of i-Al(68)Pd(23)Mn(9): An analysis based on the T*(2F) tiling decorated by Bergman polytopes

A Fibonacci-like terrace structure along a 5fold axis of i-Al(68)Pd(23)Mn(9) monograins has been observed by T.M. Schaub et al. with scanning tunnelling microscopy (STM). In the planes of the terraces they see patterns of dark pentagonal holes. These holes are well oriented both within and among terraces. In one of 11 planes Schaub et al. obtain the autocorrelation function of the hole pattern. We interpret these experimental findings in terms of the Katz-Gratias-de Boisseu-Elser model. Following the suggestion of Elser that the Bergman clusters are the dominant motive of this model, we decorate the tiling T*(2F) by the Bergman polytopes only. The tiling T*(2F) allows us to use the powerful tools of the projection techniques. The Bergman polytopes can be easily replaced by the Mackay polytopes as the decoration objects. We derive a picture of ``geared'' layers of Bergman polytopes from the projection techniques as well as from a huge patch. Under the assumption that no surface reconstruction takes place, this picture explains the Fibonacci-sequence of the step heights as well as the related structure in the terraces qualitatively and to certain extent even quantitatively. Furthermore, this layer-picture requires that the polytopes are cut in order to allow for the observed step heights. We conclude that Bergman or Mackay clusters have to be considered as geometric building blocks of the i-AlPdMn structure rather than as energetically stable entities

Infrared Photometry of Starless Dense Cores

Deep JHKs photometry was obtained towards eight dense molecular cores and J-H vs. H-Ks color-color plots are presented. Our photometry, sensitive to the detection of a 1 solar mass, 1 X 10^6 year old star through approx. 35 - 50 magnitudes of visual extinction, shows no indication of the presence of star/disk systems based on J-H vs. H-Ks colors of detected objects. The stars detected towards the cores are generally spatially anti-correlated with core centers suggesting a background origin, although we cannot preclude the possibility that some stars detected at H and Ks alone, or Ks alone, are not low mass stars or brown dwarfs (< 0.3 Solar Masses) behind substantial amounts of visual extinction (e.g. 53 magnitudes for L183B). Lower limits to optical extinctions are estimated for the detected background stars, with high extinctions being encountered, in the extreme case ranging up to at least Av = 46, and probably higher. The extinction data are used to estimate cloud masses and densities which are comparable to those determined from molecular line studies. Variations in cloud extinctions are consistent with a systematic nature to cloud density distributions and column density variations and extinctions are found to be consistent with submillimeter wave continuum studies of similar regions. The results suggest that some cores have achieved significant column density contrasts (approx. 30) on sub-core scales (approx. 0.05 pc) without having formed known stars.Comment: 44 pages including tables and figures, accepted ApJ, March 24, 200

Space-times admitting a three-dimensional conformal group

Perfect fluid space-times admitting a three-dimensional Lie group of conformal motions containing a two-dimensional Abelian Lie subgroup of isometries are studied. Demanding that the conformal Killing vector be proper (i.e., not homothetic nor Killing), all such space-times are classified according to the structure of their corresponding three-dimensional conformal Lie group and the nature of their corresponding orbits (that are assumed to be non-null). Each metric is then explicitly displayed in coordinates adapted to the symmetry vectors. Attention is then restricted to the diagonal case, and exact perfect fluid solutions are obtained in both the cases in which the fluid four-velocity is tangential or orthogonal to the conformal orbits, as well as in the more general "tilting" case.Comment: Latex 34 page