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Seldom does a physical system, particularly one as apparently simple as the flow of a Newtonian fluid between concentric rotating cylinders, retain the interest of scientists, applied mathematicians and engineers for very long. Yet, as this volume goes to press it has been nearly 70 years since G. I. Taylor's outstanding experimental and theoretical study of the linear stability of this flow was published, and a century since the first experiments were performed on rotating cylinder viscometers. Since then, the study of this system has progressed enormously, but new features of the flow patterns are still being uncovered. Interesting variations on the basic system abound. Connections with open flows are being made. More complex fluids are used in some experiments. The vigor of the research going on in this particular example of nonequilibrium systems was very apparent at the NATO Advanced Research Workshop on "Ordered and Turbulent Patterns in Taylor Couette Flow," held in Columbus, Ohio, USA May 22-24, 1991. A primary goal of this ARW was to bring together those interested in pattern formation in the classic Taylor Couette problem with those looking at variations on the basic system and with those interested in related systems, in order to better define the interesting areas for the future, the open questions, and the features common (and not common) to closed and open systems. This volume contains many of the contributions presented during the workshop.
Seldom does a physical system, particularly one as apparently simple as the flow of a Newtonian fluid between concentric rotating cylinders, retain the interest of scientists, applied mathematicians and engineers for very long. Yet, as this volume goes to press it has been nearly 70 years since G. I. Taylor's outstanding experimental and theoretical study of the linear stability of this flow was published, and a century since the first experiments were performed on rotating cylinder viscometers. Since then, the study of this system has progressed enormously, but new features of the flow patterns are still being uncovered. Interesting variations on the basic system abound. Connections with open flows are being made. More complex fluids are used in some experiments. The vigor of the research going on in this particular example of nonequilibrium systems was very apparent at the NATO Advanced Research Workshop on "Ordered and Turbulent Patterns in Taylor Couette Flow," held in Columbus, Ohio, USA May 22-24, 1991. A primary goal of this ARW was to bring together those interested in pattern formation in the classic Taylor Couette problem with those looking at variations on the basic system and with those interested in related systems, in order to better define the interesting areas for the future, the open questions, and the features common (and not common) to closed and open systems. This volume contains many of the contributions presented during the workshop.
The role of high performance computing in current research on transitional and turbulent flows is undoubtedly very important. This review volume provides a good platform for leading experts and researchers in various fields of fluid mechanics dealing with transitional and turbulent flows to synergistically exchange ideas and present the state of the art in the fields.Contributed by eminent researchers, the book chapters feature keynote lectures, panel discussions and the best invited contributed papers.
This book is a complete revision of the part of Monin & Yaglom's famous two-volume work "Statistical Fluid Mechanics: Mechanics of Turbulence" that deals with the theory of laminar-flow instability and transition to turbulence. It includes the considerable advances in the subject that have been made in the last 15 years or so. It is intended as a textbook for advanced graduate courses and as a reference for research students and professional research workers. The first two Chapters are an introduction to the mathematics, and the experimental results, for the instability of laminar (or inviscid) flows to infinitesimal (in practice "small") disturbances. The third Chapter develops this linear theory in more detail and describes its application to particular problems. Chapters 4 and 5 deal with instability to finite-amplitude disturbances: much of the material has previously been available only in research papers.
This book presents the new discovery of the origin of turbulence from Navier–Stokes equations. The fully developed turbulence is found to be composed of singularities of flow field. The mechanisms of flow stability and turbulent transition are described using the energy gradient theory, which states all the flow instability and breakdown resulted from the gradient of the total mechanical energy normal to the flow direction. This approach is universal for flow instability in Newtonian flow and non-Newtonian flow. The theory has been used to solve several problems, such as plane and pipe Poiseuille flows, plane Couette flow, Taylor–Couette flow, flows in straight coaxial annulus, flows in curved pipes and ducts, thermal convection flow, viscoelastic flow, and magnet fluid flow, etc. The theory is in agreement with results from numerical simulations and experiments. The analytical method used in this book is novel and is different from the traditional approaches. This book includes the fundamental basics of flow stability and turbulent transition, the essentials of the energy gradient theory, and the applications of the theory to several practical problems. This book is suitable for researchers and graduate students.
The Taylor-Couette system is one of the most studied examples of fluid flow exhibiting the spontaneous formation of dynamical structures. In this book, the variety of time independent solutions with periodic spatial structure is numerically investigated by solution of the Navier-Stokes equations.
Spatio-temporal patterns appear almost everywhere in nature, and their description and understanding still raise important and basic questions. However, if one looks back 20 or 30 years, definite progress has been made in the modeling of insta bilities, analysis of the dynamics in their vicinity, pattern formation and stability, quantitative experimental and numerical analysis of patterns, and so on. Universal behaviors of complex systems close to instabilities have been determined, leading to the wide interdisciplinarity of a field that is now referred to as nonlinear science or science of complexity, and in which initial concepts of dissipative structures or synergetics are deeply rooted. In pioneering domains related to hydrodynamics or chemical instabilities, the interactions between experimentalists and theoreticians, sometimes on a daily basis, have been a key to progress. Everyone in the field praises the role played by the interactions and permanent feedbacks between ex perimental, numerical, and analytical studies in the achievements obtained during these years. Many aspects of convective patterns in normal fluids, binary mixtures or liquid crystals are now understood and described in this framework. The generic pres ence of defects in extended systems is now well established and has induced new developments in the physics of laser with large Fresnel numbers. Last but not least, almost 40 years after his celebrated paper, Turing structures have finally been ob tained in real-life chemical reactors, triggering anew intense activity in the field of reaction-diffusion systems.
An exciting new direction in hydrodynamic stability theory and the transition to turbulence is concerned with the role of disconnected states or finite amplitude solutions in the evolution of disorder in fluid flows. This volume contains refereed papers presented at the IUTAM/LMS sponsored symposium on "Non-Uniqueness of Solutions to the Navier-Stokes equations and their Connection with Laminar-Turbulent Transition" held in Bristol 2004. Theoreticians and experimentalists gathered to discuss developments in understanding both the onset and collapse of disordered motion in shear flows such as those found in pipes and channels. The central objective of the symposium was to discuss the increasing amount of experimental and numerical evidence for finite amplitude solutions to the Navier-Stokes equations and to set the work into a modern theoretical context. The participants included many of the leading authorities in the subject and this volume captures much of the flavour of the resulting stimulating and lively discussions.
This IMA Volume in Mathematics and its Applications PATTERN FORMATION IN CONTINUOUS AND COUPLED SYSTEMS is based on the proceedings of a workshop with the same title, but goes be yond the proceedings by presenting a series of mini-review articles that sur vey, and provide an introduction to, interesting problems in the field. The workshop was an integral part of the 1997-98 IMA program on "EMERG ING APPLICATIONS OF DYNAMICAL SYSTEMS." I would like to thank Martin Golubitsky, University of Houston (Math ematics) Dan Luss, University of Houston (Chemical Engineering), and Steven H. Strogatz, Cornell University (Theoretical and Applied Mechan ics) for their excellent work as organizers of the meeting and for editing the proceedings. I also take this opportunity to thank the National Science Foundation (NSF), and the Army Research Office (ARO), whose financial support made the workshop possible. Willard Miller, Jr., Professor and Director v PREFACE Pattern formation has been studied intensively for most of this cen tury by both experimentalists and theoreticians, and there have been many workshops and conferences devoted to the subject. In the IMA workshop on Pattern Formation in Continuous and Coupled Systems held May 11-15, 1998 we attempted to focus on new directions in the patterns literature.