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Theoretical simulations have shown that magnetic fields play an important role in massive star formation: they can suppress fragmentation in the star forming cloud, enhance accretion via disc and regulate outflows and jets. However, models require specific magnetic configurations and need more observational constraints to properly test the impact of magnetic fields. We investigate the magnetic field structure of the massive protostar IRAS18089-1732, analysing 6.7 GHz CH3OH maser MERLIN observations. IRAS18089-1732 is a well studied high mass protostar, showing a hot core chemistry, an accretion disc and a bipolar outflow. An ordered magnetic field oriented around its disc has been detected from previous observations of polarised dust. This gives us the chance to investigate how the magnetic field at the small scale probed by masers relates to the large scale field probed by the dust.
Studies were made to find evidence of louping-ill virus infection in free-living red grouse and relate this to their breeding success. In areas where ticks were abundant 61 (84%) adult grouse had antibody to the virus compared with 1 (10%) in areas where ticks were relatively scarce. Of 162 chicks tested 25 were shown to be viraemic. Infected chicks were of significantly less weight than comparably aged uninfected birds and the probability that they died was much greater than that of uninfected birds. It is concluded that the relatively poor breeding success in areas of high tick numbers was principally due to infection with louping-ill virus. The susceptibility of the red grouse to infection is discussed.
The influence of colostrum-derived antibody to louping-ill virus on the course of experimental infection was investigated in lambs. Lambs that had high titres of antibody were refractory to infection. Lambs that had low titres of antibody did not develop a viraemia but either showed an antibody reaction or were sensitized as judged by the immune response, which was typical of an anamnestic response, after rechallenge. Animals that had no antibody 34–20 days before challenge had either no or very slight viraemia, but did develop an antibody response with titres as high as those of control lambs by day 21. Lambs that had been negative for longer periods responded in a similar fashion to controls.
These findings are discussed in relation to the occurrence of disease in lambs kept in louping-ill endemic areas. It is concluded that in such areas infections of lambs are likely to be of minor importance as a cause of mortality and of little epidemiological significance.
The complex pathogen–host–vector system of the tick-borne louping-ill virus causes economic losses to sheep and red grouse in upland United Kingdom. This paper examines the spatial distribution, incidence and effect of control measures on louping-ill virus in the Bowland Fells of Lancashire. Seroprevalence in sheep at the beginning of the study varied within the area and was affected significantly by the frequency of acaricide treatment. There was a clear decrease over 5 years in the effective force of infection on farms implementing a vaccination programme, irrespective of acaricide treatment regime, however, only one third of farms apparently eliminated infection. On farms where vaccination did not occur or where vaccination was carried out intermittently, the estimated force of infection was variable or possibly increased. Thus, as befits a complex host–pathogen system, reductions in prevalence were not as dramatic as predicted; we discuss the potential explanations for these observations.
In Scotland, between 1995 and 2000 there were between 4 and 10 cases of illness per 100000 population per year identified as being caused by Escherichia coli O157, whereas in England and Wales there were between 1 and 2 cases per 100000 population per year. Within Scotland there is significant regional variation. A cluster of high rate areas was identified in the Northeast of Scotland and a cluster of low rate areas in central-west Scotland. Temporal trends follow a seasonal pattern whilst spatial effects appeared to be distant rather than local. The best-fit model identified a significant spatial trend with case rate increasing from West to East, and from South to North. No statistically significant spatial interaction term was found. In the models fitted, the cattle population density, the human population density, and the number of cattle per person were variously significant. The findings suggest that rural/urban exposures are important in sporadic infections.
The transition of laminar flow, with its clean layers of flow tubes, to strongly mixed, irregular turbulent flow is one of the principal problems of modern hydrodynamics. It is certain that this fundamental change in type of motion of the fluid is traceable to an instability in the laminar flow, for laminar flows of themselves would always be possible solutions of the hydrodynamic equations.
– W. Tollmien (1935)
In this chapter we wish to consider the stability of steady two-dimensional or axisymmetric flows with parallel streamlines. Flows of this type were first studied experimentally by Reynolds (1883), who observed that instability could occur in quite different ways depending on the form of the basic velocity distribution. Thus, when the velocity profile is of the form shown in Fig. 4.1(a) he observed that ‘eddies showed themselves reluctantly and irregularly’ whereas when the profile is as shown in Fig. 4.1(b) the ‘eddies appeared in the middle regularly and readily’. From these observations he was led to consider the role of viscosity in flows of this type. By comparing the flow of a viscous fluid with that of an inviscid fluid, both flows being assumed to have the same basic velocity distribution, he was led to formulate two fundamental hypotheses which can be stated as follows:
First Hypothesis. The inviscid fluid may be unstable and the viscous fluid stable. The effect of viscosity is then purely stabilizing. […]
Yet not every solution of the equations of motion, even if it is exact, can actually occur in Nature. The flows that occur in Nature must not only obey the equations of fluid dynamics, but also be stable.
– L. D. Landau & E. M. Lifshitz (1959)
The essential problems of hydrodynamic stability were recognized and formulated in the nineteenth century, notably by Helmholtz, Kelvin, Rayleigh and Reynolds. It is difficult to introduce these problems more clearly than in Osborne Reynolds's (1883) own description of his classic series of experiments on the instability of flow in a pipe.
The … experiments were made on three tubes …. The diameters of these were nearly 1 inch, ½ inch and ¼ inch. They were all … fitted with trumpet mouthpieces, so that the water might enter without disturbance. The water was drawn through the tubes out of a large glass tank, in which the tubes were immersed, arrangements being made so that a streak or streaks of highly coloured water entered the tubes with the clear water.
The general results were as follows:–
(1) When the velocities were sufficiently low, the streak of colour extended in a beautiful straight line through the tube, Fig. 1.1 (a).
(2) If the water in the tank had not quite settled to rest, at sufficiently low velocities, the streak would shift about the tube, but there was no appearance of sinuosity. […]
Hydrodynamic stability is of fundamental importance in fluid mechanics and is concerned with the problem of transition from laminar to turbulent flow. Drazin and Reid emphasise throughout the ideas involved, the physical mechanisms, the methods used, and the results obtained, and, wherever possible, relate the theory to both experimental and numerical results. A distinctive feature of the book is the large number of problems it contains. These problems not only provide exercises for students but also provide many additional results in a concise form. This new edition of this celebrated introduction differs principally by the inclusion of detailed solutions for those exercises, and by the addition of a Foreword by Professor J. W. Miles.
For nearly a century now, hydrodynamic stability has been recognized as one of the central problems of fluid mechanics. It is concerned with when and how laminar flows break down, their subsequent development, and their eventual transition to turbulence. It has many applications in engineering, in meteorology and oceanography, and in astrophysics and geophysics. Some of these applications are mentioned, but the book is written from the point of view intrinsic to fluid mechanics and applied mathematics. Thus, although we have emphasized the analytical aspects of the theory, we have also tried, wherever possible, to relate the theory to experimental and numerical results.
Our aim in writing this book has been twofold. Firstly, in Chapters 1–4, to describe the fundamental ideas, methods, and results in three major areas of the subject: thermal convection, rotating and curved flows, and parallel shear flows. Secondly, to provide an introduction to some aspects of the subject which are of current research interest. These include some of the more recent developments in the asymptotic theory of the Orr–Sommerfeld equation in Chapter 5, some applications of the linear stability theory in Chapter 6 and finally, in Chapter 7, a discussion of some of the fundamental ideas involved in current work on the nonlinear theory of hydrodynamic stability.
Each chapter ends with a number of problems which often extend or supplement the main text as well as provide exercises to help the reader understand the topics.