Andrew Walton

This is the fourth volume in a four-part series on fluid dynamics: Part 1. Classical Fluid Dynamics Part 2. Asymptotic Problems of Fluid Dynamics Part 3. Boundary Layers Part 4. Hydrodynamic Stability Theory The series is designed to give a comprehensive and coherent description of fluid dynamics, starting with chapters on classical theory suitable for an introductory undergraduate lecture course, and then progressing through more advanced material up to the level of modern research in the field. Part 4 is devoted to hydrodynamic stability theory which aims at predicting the conditions under which the laminar state of a flow turns into a turbulent state. The phenomenon of laminar-turbulent transition remains one of the main challenges of modern physics. The resolution of this problem is important not only from a theoretical viewpoint but also for practical applications. For instance, in the flow past a passenger aircraft wing, the laminar-turbulent transition causes a fivefold increase in the viscous drag. The book starts with the classical results of the theory which include the global stability analysis followed by the derivation of the Orr-Sommerfeld equation. The properties of this equation are discussed using, as examples, plane Poiseuille flow and the Blasius boundary layer. In addition, we discuss 'inviscid flow' instability governed by the Rayleigh equation, Kelvin-Helmholtz instability, crossflow instability, and centrifugal instability, taking the form of Taylor-Görtler vortices. However, in this presentation our main attention regards recent developments in the theory. These include linear and nonlinear critical layer theory, the theory of receptivity of the boundary layer to external perturbations, weakly nonlinear stability theory of Landau and Stuart, and vortex-wave interaction theory. The latter allows us to describe self-sustaining nonlinear perturbations within a viscous fluid.

Introducing Political Philosophy is a thought-provoking introduction that invites readers to consider and analyse the philosophical controversies that underpin several prominent areas of political debate. The opening chapter familiarises students with the aims and methods of political philosophy. It explains the tools required to practice the discipline, and discusses how to apply these to political arguments. Each of the fifteen subsequent chapters focuses on a distinct area of public policy, such as affirmative action, humanitarian intervention, immigration, and parental leave. The authors introduce students to the moral questions that lie at the heart of these political disputes, as well as to some of the relevant academic literature. The authors believe that the best way to learn about political philosophy is to see it in action. By arguing for a position in each chapter and defending it against criticisms, they demonstrate to students how political philosophy can inform our analysis of public policy. Introducing Political Philosophy is available for students and institutions to purchase in a variety of formats, and is supported by online resources. The e-book offers a mobile experience and convenient access along with hyperlinks a list of web-links, and self-test questions, helping to test your knowledge and understanding of policy areas, and the philosophical arguments that influence them: www.oxfordtextbooks.co.uk/ebooks. · Student resources: a curated list of websites help you to deepen your knowledge of policy areas, and self-test questions help you to critically evaluate key points from each chapter. · Lecturer resources include: seminar activities to encourage student engagement, discussion and debate; guidance on using the teaching activities; a teaching guide explaining how to get the most out of the book's inside-out approach; and customisable PowerPoint slides on key topics, thinkers, and concepts to aid effective teaching preparation.

This collection of poems - some playful, others serious - is intended to highlight the destruction of our environment at the hands of capitalism. I have also put forward the alternative, a society where wealth is shared, rather than hoarded, and used for the common good. A planet where the vast majority of its citizens - the 99% - are in control, not a tiny elite, to allow us to plan our economy to solve environmental threats.