An experimental investigation of the recirculation zone formed downstream of a forward facing step

An experimental investigation of the recirculation zone formed downstream of a forward facing step immersed in a turbulent boundary layer has been undertaken using particle image velocimetry. Bluff body flow is observed with the fixed separation point located at the leading edge of the step. The recirculation region dimensions are characterised over a range of Reynolds numbers (1400–19 000), with Reh based on the step height and the free stream velocity. Turbulent perturbations are produced in the free shear layer which develops between the recirculating flow close to the step and the free stream flow. Contour maps of amplification factor, streamwise perturbation velocity and Reynolds stresses are constructed, providing insight into optimal placement of structures within such topographical features. The mechanisms affecting the reattachment distance, namely the turbulent mixing within the boundary layer and the velocity deficit in the boundary layer, are discussed

Characterisation of a horizontal axis wind turbine’s tip and root vortices

The vortical near wake of a model horizontal axis wind turbine has been investigated experimentally in a water channel. The objective of this work is to study vortex interaction and stability of the helical vortex filaments within a horizontal axis wind turbine wake. The experimental model is a geometrically scaled version of the Tjæreborg wind turbine, which existed in western Denmark in the late 1980s. Here, the turbine was tested in both the upwind and downwind configurations. Qualitative flow visualisations using hydrogen bubble, particle streakline and planar laser-induced fluorescence techniques were combined with quantitative data measurements taken using planar particle image velocimetry. Vortices were identified using velocity gradient tensor invariants. Parameters that describe the helical vortex wake, such as the helicoidal pitch, and vortex circulation, were determined for three tip speed ratios. Particular attention is given here to the root vortex, which has been investigated minimally to date. Signatures of the coherent tip vortices are seen throughout the measurement domain; however, the signature of the root vortex is only evident much closer to the rotor plane, irrespective of the turbine configuration. It is postulated that the root vortex diffuses rapidly due to the effects of the turbine support geometries

On-line Ramsey numbers of paths and cycles

Consider a game played on the edge set of the infinite clique by two players, Builder and Painter. In each round, Builder chooses an edge and Painter colours it red or blue. Builder wins by creating either a red copy of $G$ or a blue copy of $H$ for some fixed graphs $G$ and $H$. The minimum number of rounds within which Builder can win, assuming both players play perfectly, is the on-line Ramsey number $\tilde{r}(G,H)$. In this paper, we consider the case where $G$ is a path $P_k$. We prove that $\tilde{r}(P_3, P_{\ell+1}) = \lceil 5\ell/4 \rceil = \tilde{r}(P_3, C_\ell)$ for all $\ell \ge 5$, and determine $\tilde{r}(P_4, P_{\ell+1}$) up to an additive constant for all $\ell \ge 3$. We also prove some general lower bounds for on-line Ramsey numbers of the form $\tilde{r}(P_{k+1},H)$.Comment: Preprin

Complementarity in Wormhole Chromodynamics

The electric charge of a wormhole mouth and the magnetic flux ``linked'' by the wormhole are non-commuting observables, and so cannot be simultaneously diagonalized. We use this observation to resolve some puzzles in wormhole electrodynamics and chromodynamics. Specifically, we analyze the color electric field that results when a colored object traverses a wormhole, and we discuss the measurement of the wormhole charge and flux using Aharonov-Bohm interference effects. We suggest that wormhole mouths may obey conventional quantum statistics, contrary to a recent proposal by Strominger.Comment: 12 pages and 2 figures, phyzzx, CALT-68-188

Vortex-induced vibration of a square-section cylinder with incidence angle variation

Vortex-induced vibration (VIV) occurs when vortex shedding from a body results in fluctuating forces that, in turn, cause the body to vibrate. This can result in undesired large-amplitude vibrations leading to structural damage or catastrophic failure. While much has been done on the VIV of a circular cylinder less has been done on other canonical bluff bodies, such as rectangular cylinders. The present experimental work studied the VIV of a square cross-section cylinder in a water channel, with three different incidence angles (α 15 , 30 and 45 ). The influence of geometry on the body’s oscillation amplitude and frequency response, and its wake structure over a range of reduced velocity were investigated. The oscillations were measured at a low mass damping ratio of m ζ 0.013 , which was comparable to the circular cylinder system with m ζ 0.013 studied by Khalak & Williamson (1997)1. The comparison showed that the incidence angle change had a significant impact on amplitude response. For α 15 the maximum non-dimensional amplitude was A 1.11, 10% larger than the circular case, as shown in figure 1 (a). Asymmetric amplitudes with respect to the cylinder’s equilibrium position in still water were observed in α 15 and 30 cases, due to the one-sided nature of the mean lift force. Compared with the circular cyinder, the square cylinder locked on to the structural natural frequency in water over a smaller reduced velocity regime. An oscillation frequency drop was found in the α 15 case, during which the cylinder experienced its largest amplitude response. The wake structure for each case in the different flow regimes was determined using particle image velocimetry and will also be presented

The interaction between flow-induced vibration mechanisms of a square cylinder with varying angles of attack

This study examines the influence of angle of attack of a square section cylinder on the cylinder’s flow-induced vibration, where the direction of the vibration is transverse to the oncoming flow. Our experiments, which traversed the velocity–angle of attack parameter space in considerable breadth and depth, show that a low-mass ratio body can undergo combinations of both vortex-induced vibration and galloping. When the body has an angle of attack that makes it symmetric to the flow, such as when it assumes the square or diamond orientation, the two mechanisms remain independent. However, when symmetry is lost we find a mixed mode response with a new branch of vortex-induced oscillations that exceeds the amplitudes resulting from the two phenomena independently. The oscillations of this higher branch have amplitudes larger than the ‘upper branch’ of vortex-induced vibrations and at half the frequency. For velocities above this resonant region, the frequency splits into two diverging branches. Analysis of the amplitude response reveals that the transition between galloping and vortex-induced vibrations occurs over a narrow range of angle of incidence. Despite the rich set of states found in the parameter space the vortex shedding modes remain very similar to those found previously in vortex-induced vibration

Security of quantum key distribution with imperfect devices

We prove the security of the Bennett-Brassard (BB84) quantum key distribution protocol in the case where the source and detector are under the limited control of an adversary. Our proof applies when both the source and the detector have small basis-dependent flaws, as is typical in practical implementations of the protocol. We derive a general lower bound on the asymptotic key generation rate for weakly basis-dependent eavesdropping attacks, and also estimate the rate in some special cases: sources that emit weak coherent states with random phases, detectors with basis-dependent efficiency, and misaligned sources and detectors.Comment: 22 pages. (v3): Minor changes. (v2): Extensively revised and expanded. New results include a security proof for generic small flaws in the source and the detecto