Vortex shedding from tapered, triangular plates: taper and aspect ratio effects

Further experiments on features of the vortex shedding from tapered flat plates normal to an airstream are described. The work extends that of Castro and Rogers (2002) and concentrates on the study of the effects of varying the spanwise aspect ratio for a fixed shape plate, by appropriate adjustment of end-plates, and of the nature of the shedding as the degree of taper becomes very large, so that the body is more like a triangular plate—e.g. an isosceles triangle—than a slightly tapered plate. With the taper ratio TR defined as the ratio of plate length to average cross-stream width, the paper concentrates on the range 0.58<TR<60. Reynolds numbers, based on the average plate width, exceed 104. It is confirmed that for a small enough taper ratio the geometrical three-dimensionality is sufficiently strong that all signs of periodic vortex shedding cease. For all other cases, however, the flow at different locations along the span can vary substantially, depending on taper. There appear to be at least four different regimes, each appropriate for a different range of taper ratio. These various regimes are described

Building hyperbolic metrics suited to closed curves and applications to lifting simply

Let $\gamma$ be an essential closed curve with at most $k$ self-intersections on a surface $\mathcal{S}$ with negative Euler characteristic. In this paper, we construct a hyperbolic metric $\rho$ for which $\gamma$ has length at most $M \cdot \sqrt{k}$, where $M$ is a constant depending only on the topology of $\mathcal{S}$. Moreover, the injectivity radius of $\rho$ is at least $1/(2\sqrt{k})$. This yields linear upper bounds in terms of self-intersection number on the minimum degree of a cover to which $\gamma$ lifts as a simple closed curve (i.e. lifts simply). We also show that if $\gamma$ is a closed curve with length at most $L$ on a cusped hyperbolic surface $\mathcal{S}$, then there exists a cover of $\mathcal{S}$ of degree at most $N \cdot L \cdot e^{L/2}$ to which $\gamma$ lifts simply, for $N$ depending only on the topology of $\mathcal{S}$.Comment: 18 pages, 7 figures. Comments welcome

On the flow along swept leading edges

Flight tests on the Handley Page suction wing showed that turbulence, generated at the wing root, can propagate along the leading edge and cause the whole flow to be turbulent. The flow on the attachment line of a swept wing was studied in a low speed wind tunnel with particular reference to the problem of turbulent contamination. The critical Reynolds number, R9L, of the attachment line boundary layer for the spanwise spread of turbulence was found to be about 100 for sweep angles in the range 40°- 60°. A device was developed to act as a barrier to the turbulent root flow 30 that a clean laminar flow could exist outboard. This device was shown to be effective up to an Re of at least 170. With the aid of this bump experiments were Possible on L laminar boundary layer at Reynolds numbers above the lower critical value. A spark was used to introduce spots of turbulence into the attachment line boundary layer and the propagation speeds of the leading and trailing edges were measured. The spots expanded, the leading edge moving faster than the trailing edge, at high Reynolds numbers, and contracted at low values. The behaviour of Tollmien-Schlichting waves was also investigated by exciting the flow with sound emanating from a small hole on the attachment line. Measurements of the perturbation phase and amplitude were made downstream of the source and although accurate values of wave length and propagation speed could be found no difficulties were experienced in evaluating the amplification ratio. Nevertheless, all small disturbances decayed at a sufficient distance from the source hole up to the highest Reynolds number tested of 170

Reduced TCA Flux in Diabetic Myotubes: Determined by Single Defects?

The diabetic phenotype is complex, requiring elucidation of key initiating defects. Diabetic myotubes express a primary reduced tricarboxylic acid (TCA) cycle flux but at present it is unclear in which part of the TCA cycle the defect is localised. In order to localise the defect we studied ATP production in isolated mitochondria from substrates entering the TCA cycle at various points. ATP production was measured by luminescence with or without concomitant ATP utilisation by hexokinase in mitochondria isolated from myotubes established from eight lean and eight type 2 diabetic subjects. The ATP production of investigated substrate combinations was significantly reduced in mitochondria isolated from type 2 diabetic subjects compared to lean. However, when ATP synthesis rates at different substrate combinations were normalized to the corresponding individual pyruvate-malate rate, there was no significant difference between groups. These results show that the primary reduced TCA cycle flux in diabetic myotubes is not explained by defects in specific part of the TCA cycle but rather results from a general downregulation of the TCA cycle