Spreading of two-dimensional axisymmetric vortices exposed to a rotating strain field

Copyright © 2009 Cambridge University PressThis paper examines the evolution of an axisymmetric two-dimensional vortex in a steadily rotating strain field and the dynamical interactions that can enhance vortex spreading through resonant behaviour. Starting with a point vortex localized at the origin, the applied strain field generates a cat's eye topology in the co-rotating streamfunction, localized around a radius rext. Now the vortex is allowed to spread viscously: initially rext lies outside the vortex, but as it spreads, vorticity is advected into the cat's eyes, leading to a local flattening of the mean profile of the vortex and so to enhanced mixing and spreading of the vortex. Together with this is a feedback: the response of the vortex to the external strain depends on the modified profile. The feedback is particularly strong when rext coincides with the radius rcat at which the vortex can support cat's eyes of infinitesimal width. There is a particular time at which this occurs, as these radii change with the viscous spread of the vortex: rext moves inwards and rcat outwards. This resonance behaviour leads to increased mixing of vorticity, along with a rapid stretching of vorticity contours and a sharp increase in the amplitude of the non-axisymmetric components. The dynamical feedback and enhanced diffusion are studied for viscously spreading vortices by means of numerical simulations of their time evolution, parameterized only by the Reynolds number R and the dimensionless strength A of the external strain field

Diffusion and the formation of vorticity staircases in randomly strained two-dimensional vortices

Copyright © 2009 Cambridge University PressThe spreading and diffusion of two-dimensional vortices subject to weak external random strain fields is examined. The response to such a field of given angular frequency depends on the profile of the vortex and can be calculated numerically. An effective diffusivity can be determined as a function of radius and may be used to evolve the profile over a long time scale, using a diffusion equation that is both nonlinear and non-local. This equation, containing an additional smoothing parameter, is simulated starting with a Gaussian vortex. Fine scale steps in the vorticity profile develop at the periphery of the vortex and these form a vorticity staircase. The effective diffusivity is high in the steps where the vorticity gradient is low: between the steps are barriers characterized by low effective diffusivity and high vorticity gradient. The steps then merge before the vorticity is finally swept out and this leaves a vortex with a compact core and a sharp edge. There is also an increase in the effective diffusion within an encircling surf zone. In order to understand the properties of the evolution of the Gaussian vortex, an asymptotic model first proposed by Balmforth, Llewellyn Smith & Young (J. Fluid Mech., vol. 426, 2001, p. 95) is employed. The model is based on a vorticity distribution that consists of a compact vortex core surrounded by a skirt of relatively weak vorticity. Again simulations show the formation of fine scale vorticity steps within the skirt, followed by merger. The diffusion equation we develop has a tendency to generate vorticity steps on arbitrarily fine scales; these are limited in our numerical simulations by smoothing the effective diffusivity over small spatial scales

Response to Miles and Mezzich:“Medicine in crisis and a crisis in semantics”

Miles and Mezzich offer a welcome and comprehensive account of historical recent developments in healthcare and the role of its practice models. They identify a ‘crisis’ in medicine, which seems to have occurred in part because the science of medicine has been over-emphasised and the importance of compassion and care de-emphasised.  As they point out, this crisis has been perceived to have evolved over the past one hundred years. Evidence Based Medicine (EBM) is suggested to be inadequate to solve the crisis and it may be the case that EBM, in fact, has precipitated it because it ignores patients qua persons. It is also suggested that Patient Centred Care (PCC) seeks to address the imbalance, but that this is inadequate, too. Between these existing views it is claimed that Person Centred Medicine (PCM) solves the crisis by giving persons and evidence their proper roles and relative importances</jats:p

Neutral modes of a two-dimensional vortex and their link to persistent cat's eyes

Copyright © 2008 American Institute of Physics. This article may be downloaded for personal use only. Any other use requires prior permission of the author and the American Institute of Physics. The following article appeared in Physics of Fluids 20 (2008) and may be found at http://link.aip.org/link/?PHFLE6/20/027101/1This paper considers the relaxation of a smooth two-dimensional vortex to axisymmetry after the application of an instantaneous, weak external strain field. In this limit the disturbance decays exponentially in time at a rate that is linked to a pole of the associated linear inviscid problem (known as a Landau pole). As a model of a typical vortex distribution that can give rise to cat's eyes, here distributions are examined that have a basic Gaussian shape but whose profiles have been artificially flattened about some radius rc. A numerical study of the Landau poles for this family of vortices shows that as rc is varied so the decay rate of the disturbance moves smoothly between poles as the decay rates of two Landau poles cross. Cat's eyes that occur in the nonlinear evolution of a vortex lead to an axisymmetric azimuthally averaged profile with an annulus of approximately uniform vorticity, rather like the artificially flattened profiles investigated. Based on the stability of such profiles it is found that finite thickness cat's eyes can persist (i.e., the mean profile has a neutral mode) at two distinct radii, and in the limit of a thin flattened region the result that vanishingly thin cat's eyes only persist at a single radius is recovered. The decay of nonaxisymmetric perturbations to these flattened profiles for larger times is investigated and a comparison made with the result for a Gaussian profile

Competence and competency in higher education, simple terms yet with complex meanings: Theoretical and practical issues for university teachers and assessors implementing Competency-Based Education (CBE)

There are different and conflicting definitions of competence, competency, and competency-based learning. Consequently, multiple interpretations and understandings are held by educators in respect of what these terms mean, when applied to their own teaching and assessment practices. Whilst UK and American universities are increasingly adopting competency-based learning, unless informed and considered discussion has taken place amongst staff about their individual understandings and interpretations, any development of new, competency-based assessment processes and procedures, is problematic. This paper provides an overview of the main issues involved in defining competency and assessing competence, along with recommendations for action. The purpose is to stimulate reflection and discussion, so that teaching staff can arrive at a common understanding and interpretation of the terminology of competency-based education, so that they may develop appropriate, authentic and fair assessment processes

A modified route to unsymmetrically substituted triphenylenes, new functionalised derivatives and twins, and the smallest reported triphenylene mesogen

We report the unexpected observation of columnar mesophase formation in a simple 2,7-dibromotetramethoxytriphenylene – by far the most lightly substituted discotic mesogen in this class. This derivative was prepared alongside the 3,6-dibromotriphenylene isomer to demonstrate an alternative, modified synthetic strategy that permits late-stage interchange of alkyl chain substituents. The new method is employed alongside the original route to deliver several new materials, including a conjugated ferrocene-triphenylene-ferrocene triad, a BODIPY-triphenylene-BODIPY triad and a new nematic twin linked through imine bridges

Evaluation of a combination of SIFT-MS and multivariate data analysis for the diagnosis of Mycobacterium bovis in wild badgers

The currently accepted gold standard tuberculosis (TB) detection method for veterinary applications is that of culturing from a tissue sample post mortem. The test is accurate, but growing Mycobacterium bovis is difficult and the process can take up to 12 weeks to return a diagnosis. In this paper we evaluate a much faster screening approach based on serum headspace analysis using selected ion flow tube mass spectrometry (SIFT-MS). SIFT-MS is a rapid, quantitative gas analysis technique, with sample analysis times of as little as a few seconds. Headspace from above serum samples from wild badgers, captured as part of a randomised trial, was analysed. Multivariate classification algorithms were then employed to extract a simple TB diagnosis from the complex multivariate response provided by the SIFT-MS instrument. This is the first time that such multivariate analysis has been applied to SIFT-MS data. An accuracy of TB discrimination of approximately 88% true positive was achieved which shows promise, but the corresponding false positive rate of 38% indicates that there is more work to do before this approach could replace the culture test. Recommendations for future work that could increase the performance are therefore proposed