The wakes behind square cylinders with variation in incidence angle are computed over a range of Reynolds numbers to elucidate the three-dimensional stability and dynamics up to a Reynolds number of Re = 300, based on the projected height of the inclined square cylinder. Three-dimensional instability modes are predicted and computed using a linear stability analysis technique and three-dimensional simulations, respectively. Depending on the incidence angle, the flow is found to transition to three-dimensional flow through either a mode A instability, or a subharmonic mode C instability. The mode A instability is predicted as the firstoccurring instability at incidence angles smaller than 12 • and greater than 26 • , with the mode C instability predicted between these incidence angles. At a zero-degree angle of incidence, the wake instabilities closely match modes A, B and a quasiperiodic mode predicted in earlier studies behind square and circular cylinders. With increasing angle of incidence, the three-dimensional wake transition Reynolds number first increases from Re = 164 as the mode A instability weakens, before decreasing again beyond an incidence angle of 12 • as the wake becomes increasingly unstable to the mode C instability, and then again to the mode A instability as the incidence angle approaches 45 • . A spanwise autocorrelation analysis from computations over a cylinder span 20 times the square cross-section side length reveals that beyond the onset of three-dimensional instabilities, the vortex street breaks down with patterns consistent with spatio-temporal chaos. This effect was more pronounced at higher incidence angles.

Despite little supporting evidence, there appears to be an implicit assumption that the wakes of two-dimensional bluff bodies undergo transition to three-dimensional flow and eventually turbulence, through the same sequence of transitions as observed for a circular cylinder wake. Previous studies of a square cylinder wake support this assumption. In this paper, the transition to three-dimensional wake flow is examined for an elongated cylinder with an aerodynamic leading edge and square trailing edge. The three-dimensional instability modes are determined as a function of aspect ratio ($\hbox{\it AR}\,{=}\,$length to width). Floquet analysis reveals that three distinct instabilities occur. These are referred to as Modes A, B$^\prime$ and S$^\prime$ through analogy with the modes for circular and square cylinders. For aspect ratios less than approximately 7.5, Mode A is the most unstable mode. For aspect ratios greater than this, the most unstable mode switches to Mode B$^\prime$. This has the same spatio-temporal symmetry as Mode B for a circular cylinder, but a spanwise wavelength and near-wake features more in common with Mode S for a square cylinder. The dominant wavelength for this mode is approximately two cylinder thicknesses, much longer than for Mode B for a circular cylinder. It is found that the critical Reynolds number for the onset of the Mode A instability varies approximately with the square root of the aspect ratio. On the other hand, the critical Reynolds number for Mode B$^\prime$ is almost independent of aspect ratio. For large aspect ratios, the separation in Reynolds number between the critical Reynolds numbers is substantial; for instance, for $\hbox{\it AR}\,{=}\,17.5$, these values are approximately 450 and 700. In fact, for this aspect ratio, the third instability mode, Mode S$^\prime$, is more unstable than Mode A. These results suggest that the transition scenario for elongated bluff bodies may be distinctly different to short bodies such as circular or square cylinders. At the very least, the dominant spanwise wavelength in the turbulent wake is likely to be much longer than that for a circular cylinder wake. In addition, the reversal of the ordering of occurrence of the two modes with the different spatial symmetries is likely to affect the development of spatio-temporal chaos as a precursor to fully turbulent flow.In conjunction with prior work, the current results indicate that nearly all three-dimensional instabilities of the vortex street can be identified as one of only a handful of transition modes.

The elliptic instability of a Batchelor vortex subject to a stationary strain field is considered by theoretical and numerical means in the regime of large Reynolds number and small axial flow. In the theory, the elliptic instability is described as a resonant coupling of two quasi-neutral normal modes (Kelvin modes) of the Batchelor vortex of azimuthal wavenumbers m and m + 2 with the underlying strain field. The growth rate associated with these resonances is computed for different values of the azimuthal wavenumbers as the axial flow parameter is varied. We demonstrate that the resonant Kelvin modes m = 1 and m = −1 which are the most unstable in the absence of axial flow become damped as the axial flow is increased. This is shown to be due to the appearance of a critical layer which damps one of the resonant Kelvin modes. However, the elliptic instability does not disappear. Other combinations of Kelvin modes m = −2 and m = 0, then m = −3 and m = −1 are shown to become progressively unstable for increasing axial flow. A complete instability diagram is obtained as a function of the axial flow parameter for several values of the strain rate and Reynolds number.The numerical study considers a system of two counter-rotating Batchelor vortices in which the strain field felt by each vortex is due to the other vortex. The characteristics of the most unstable linear modes developing on the frozen base flow are computed by direct numerical simulations for two axial flow parameters and compared to the theory. In both cases, a very good agreement is obtained for the most unstable modes. Less unstable modes are also identified in the numerics and shown to correspond to peculiar resonances involving Kelvin modes from branches of different labels.

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A tethered cylinder may be considered an extension of the widely studied problem of a hydro-elastically mounted cylinder. Here we numerically investigate the flow past a positively buoyant tethered cylinder for a range of mass ratios and tether length ratios at a Reynolds numberRe= 200. The results are found to be qualitatively similar to related experimental work performed at significantly higher Reynolds numbers. Two important findings are related in this paper. First, we find that the action of the tethered cylinder oscillating at an angle to the flow induces a mean lift coefficient. Second, a critical mass ratio (m*crit) is found below which large-amplitude oscillations are noted, similar to that previously reported for the case of a hydro-elastically mounted cylinder. For short tether lengths, (m*crit) is significantly greater than that found for a hydro-elastically mounted cylinder. As the tether length increases, the (m*crit) decreases and asymptotes to that of a hydro-elastically mounted cylinder as the tether length approaches infinity.

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a b s t r a c tWhile there is clear recognition of the need to incorporate sustainable development into university curricula, there is limited research that examines how to achieve that integration or evaluates its impacts on student learning. This paper responds to these knowledge gaps through a case study of curriculum renewal that involved embedding sustainability into a first year engineering curriculum. The initiative was guided by a deliberative and dynamic model for curriculum renewal that brought together internal and external stakeholders through a structured sequence of facilitated workshops and meetings. That process identified sustainability-related knowledge and skills relevant for first year engineering, and faculty members teaching in the first year program were guided through a process of curriculum renewal to meet those needs. The process through which the whole of curriculum renewal was undertaken is innovative and provides a case study of precedent in the field of education for sustainability. The study demonstrates the contribution that can be made by a web-based sustainability portal in supporting curriculum renewal. Learning and teaching outcomes were evaluated through 'before and after surveys' of the first year engineering students. Statistically significant increases in student's self-reported knowledge of sustainability were measured as a result of exposure to the renewed first year curriculum and this confirmed the value of the initiative in terms of enhancing student learning. While applied in this case to engineering, the process to achieve integration of sustainability into the curriculum approach is likely to have value for other academic disciplines. Considering student performance on assignments and exam questions relating to sustainability would provide a stronger basis for future research to understand the impact of initiatives like this on student learning.