An instability mechanism for particulate pipe flow

We present linear stability analysis for a simple model of particle-laden pipe flow. The model consists of a continuum approximation for the particles two-way coupled to the fluid velocity field via Stokes drag (Saffman 1962). We extend previous analysis in a channel (Klinkenberg et al. 2011) to allow for the initial distribution of particles to be inhomogeneous and in particular consider the effect of allowing the particles to be preferentially located around one radius in accordance with experimental observations. This simple modification of the problem is enough to alter the stability properties of the flow, and in particular can lead to a linear instability at experimentally realistic parameters. The results are compared to the experimental work of Matas et al. (2004a) and are shown to be consistent with the reported flow regimes.Comment: 15 pages, 11 figure

Minimal seeds for shear flow turbulence: using nonlinear transient growth to touch the edge of chaos

We propose a general strategy for determining the minimal finite amplitude isturbance to trigger transition to turbulence in shear flows. This involves constructing a variational problem that searches over all disturbances of fixed initial amplitude, which respect the boundary conditions, incompressibility and the Navier--Stokes equations, to maximise a chosen functional over an asymptotically long time period. The functional must be selected such that it identifies turbulent velocity fields by taking significantly enhanced values compared to those for laminar fields. We illustrate this approach using the ratio of the final to initial perturbation kinetic energies (energy growth) as the functional and the energy norm to measure amplitudes in the context of pipe flow. Our results indicate that the variational problem yields a smooth converged solution providing the amplitude is below the threshold amplitude for transition. This optimal is the nonlinear analogue of the well-studied (linear) transient growth optimal. At and above this threshold, the optimising search naturally seeks out disturbances that trigger turbulence by the end of the period, and convergence is then practically impossible. The first disturbance found to trigger turbulence as the amplitude is increased identifies the `minimal seed' for the given geometry and forcing (Reynolds number). We conjecture that it may be possible to select a functional such that the converged optimal below threshold smoothly converges to the minimal seed at threshold. This seems at least approximately true for our choice of energy growth functional and the pipe flow geometry chosen here.Comment: 27 pages, 19 figures, submitted to JF

A nonlinear approach to transition in subcritical plasmas with sheared flow

In many plasma systems, introducing a small background shear flow is enough to stabilize the system linearly. The nonlinear dynamics are much less sensitive to sheared flows than the average linear growthrates, and very small amplitude perturbations can lead to sustained turbulence. We explore the general problem of characterizing how and when the transition from near-laminar states to sustained turbulence occurs; a model of the interchange instability being used as a concrete example. These questions are fundamentally nonlinear, and the answers must go beyond the linear transient amplification of small perturbations. Two methods that account for nonlinear interactions are therefore explored here. The first method explored is edge tracking, which identifies the boundary between the basins of attraction of the laminar and turbulent states. Here, the edge is found to be structured around an exact, localized, traveling wave solution; a solution that is qualitatively similar to avalanche-like bursts seen in the turbulent regime. The second method is an application of nonlinear, non-modal stability theory which allows us to identify the smallest disturbances which can trigger turbulence (the minimal seed for the problem) and hence to quantify how stable the laminar regime is. The results obtained from these fully nonlinear methods provides confidence in the derivation of a semi-analytic approximation for the minimal seed

Relative periodic orbits in transitional pipe flow

A dynamical system description of the transition process in shear flows with no linear instability starts with a knowledge of exact coherent solutions, among them travelling waves (TWs) and relative periodic orbits (RPOs). We describe a numerical method to find such solutions in pipe flow and apply it in the vicinity of a Hopf bifurcation from a TW which looks to be especially relevant for transition. The dominant structural feature of the RPO solution is the presence of weakly modulated streaks. This RPO, like the TW from which it bifurcates, sits on the laminar-turbulent boundary separating initial conditions which lead to turbulence from those which immediately relaminarise

Simple advecting structures and the edge of chaos in subcritical tokamak plasmas

In tokamak plasmas, sheared flows perpendicular to the driving temperature gradients can strongly stabilize linear modes. While the system is linearly stable, regimes with persistent nonlinear turbulence may develop, i.e. the system is subcritical. A perturbation with small but finite amplitude may be sufficient to push the plasma into a regime where nonlinear effects are dominant and thus allow sustained turbulence. The minimum threshold for nonlinear instability to be triggered provides a criterion for assessing whether a tokamak is likely to stay in the quiescent (laminar) regime. At the critical amplitude, instead of transitioning to the turbulent regime or decaying to a laminar state, the trajectory will map out the edge of chaos. Surprisingly, a quasi-traveling-wave solution is found as an attractor on this edge manifold. This simple advecting solution is qualitatively similar to, but simpler than, the avalanche-like bursts seen in earlier turbulent simulations and provides an insight into how turbulence is sustained in subcritical plasma systems. For large flow shearing rate, the system is only convectively unstable, and given a localised initial perturbation, will eventually return to a laminar state at a fixed spatial location

Do UK universities communicate their brands effectively through their websites?

This paper attempts to explore the effectiveness of UK universities’ websites. The area of branding in higher education has received increasing academic investigation, but little work has researched how universities demonstrate their brand promises through their websites. The quest to differentiate through branding can be challenging in the university context, however. It is argued that those institutions that have a strong distinctive image will be in a better position to face a changing future. Employing a multistage methodology, the web pages of twenty UK universities were investigated by using a combination of content and multivariable analysis. Results indicated ‘traditional values’ such as teaching and research were often well communicated in terms of online brand but ‘emotional values’ like social responsibility and the universities’ environments were less consistently communicated, despite their increased topicality. It is therefore suggested that emotional values may offer a basis for possible future online differentiation

‘Brands in Higher Education ; Challenges and Potential Strategies’

This study explores the challenges of university branding and the qualities that make university branding different from commercial branding in terms of cultural issues, branding concepts and frameworks and brands architecture. The literature about branding in the university sector is described and viewed in the context of exploratory interviews with fifty five university managers. The results present the differences between university and commercial brandings as well as culture, brand concepts and brand architecture,. The study was conducted in UK universities, but similar issues in many other countries means that the results are comparable internationally. Overall, the findings presented in this research offer a valuable contribution to our understanding of the complexities of higher education branding

TLR9-Dependent and Independent Pathways Drive Activation of the Immune System by Propionibacterium Acnes

Propionibacterium acnes is usually a relatively harmless commensal. However, under certain, poorly understood conditions it is implicated in the etiology of specific inflammatory diseases. In mice, P. acnes exhibits strong immunomodulatory activity leading to splenomegaly, intrahepatic granuloma formation, hypersensitivity to TLR ligands and endogenous cytokines, and enhanced resistance to infection. All these activities reach a maximum one week after P. acnes priming and require IFN-γ and TLR9. We report here the existence of a markedly delayed (1–2 weeks), but phenotypically similar TLR9-independent immunomodulatory response to P. acnes. This alternative immunomodulation is also IFN-γ dependent and requires functional MyD88. From our experiments, a role for MyD88 in the IFN-γ-mediated P. acnes effects seems unlikely and the participation of the known MyD88-dependent receptors, including TLR5, Unc93B-dependent TLRs, IL-1R and IL-18R in the development of the alternative response has been excluded. However, the crucial role of MyD88 can partly be attributed to TLR2 and TLR4 involvement. Either of these two TLRs, activated by bacteria and/or endogenously generated ligands, can fulfill the required function. Our findings hint at an innate immune sensitizing mechanism, which is potentially operative in both infectious and sterile inflammatory disorders