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Structures And Bifurcations In Fluid Flows
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Book Synopsis Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics by : Tian Ma
Download or read book Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics written by Tian Ma and published by American Mathematical Soc.. This book was released on 2005 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents a geometric theory for incompressible flow and its applications to fluid dynamics. The main objective is to study the stability and transitions of the structure of incompressible flows and its applications to fluid dynamics and geophysical fluid dynamics. The development of the theory and its applications goes well beyond its original motivation of the study of oceanic dynamics. The authors present a substantial advance in the use of geometric and topological methods to analyze and classify incompressible fluid flows. The approach introduces genuinely innovative ideas to the study of the partial differential equations of fluid dynamics. One particularly useful development is a rigorous theory for boundary layer separation of incompressible fluids. The study of incompressible flows has two major interconnected parts. The first is the development of a global geometric theory of divergence-free fields on general two-dimensional compact manifolds. The second is the study of the structure of velocity fields for two-dimensional incompressible fluid flows governed by the Navier-Stokes equations or the Euler equations. Motivated by the study of problems in geophysical fluid dynamics, the program of research in this book seeks to develop a new mathematical theory, maintaining close links to physics along the way. In return, the theory is applied to physical problems, with more problems yet to be explored. The material is suitable for researchers and advanced graduate students interested in nonlinear PDEs and fluid dynamics.
Book Synopsis An Introduction to the Geometry and Topology of Fluid Flows by : Renzo L. Ricca
Download or read book An Introduction to the Geometry and Topology of Fluid Flows written by Renzo L. Ricca and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 346 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leading experts present a unique, invaluable introduction to the study of the geometry and typology of fluid flows. From basic motions on curves and surfaces to the recent developments in knots and links, the reader is gradually led to explore the fascinating world of geometric and topological fluid mechanics. Geodesics and chaotic orbits, magnetic knots and vortex links, continual flows and singularities become alive with more than 160 figures and examples. In the opening article, H. K. Moffatt sets the pace, proposing eight outstanding problems for the 21st century. The book goes on to provide concepts and techniques for tackling these and many other interesting open problems.
Book Synopsis An Introduction to the Geometry and Topology of Fluid Flows by : Renzo L. Ricca
Download or read book An Introduction to the Geometry and Topology of Fluid Flows written by Renzo L. Ricca and published by Springer Science & Business Media. This book was released on 2001-11-30 with total page 364 pages. Available in PDF, EPUB and Kindle. Book excerpt: Leading experts present a unique, invaluable introduction to the study of the geometry and typology of fluid flows. From basic motions on curves and surfaces to the recent developments in knots and links, the reader is gradually led to explore the fascinating world of geometric and topological fluid mechanics. Geodesics and chaotic orbits, magnetic knots and vortex links, continual flows and singularities become alive with more than 160 figures and examples. In the opening article, H. K. Moffatt sets the pace, proposing eight outstanding problems for the 21st century. The book goes on to provide concepts and techniques for tackling these and many other interesting open problems.
Book Synopsis Bifurcation Analysis of Fluid Flows by : Henk A. Dijkstra
Download or read book Bifurcation Analysis of Fluid Flows written by Henk A. Dijkstra and published by Cambridge University Press. This book was released on 2023-06-30 with total page 343 pages. Available in PDF, EPUB and Kindle. Book excerpt: A better understanding of the mechanisms leading a fluid system to exhibit turbulent behavior is one of the grand challenges of the physical and mathematical sciences. Over the last few decades, numerical bifurcation methods have been extended and applied to a number of flow problems to identify critical conditions for fluid instabilities to occur. This book provides a state-of-the-art account of these numerical methods, with much attention to modern linear systems solvers and generalized eigenvalue solvers. These methods also have a broad applicability in industrial, environmental and astrophysical flows. The book is a must-have reference for anyone working in scientific fields where fluid flow instabilities play a role. Exercises at the end of each chapter and Python code for the bifurcation analysis of canonical fluid flow problems provide practice material to get to grips with the methods and concepts presented in the book.
Book Synopsis Fluid-Structure Interactions by : Michael P. Paidoussis
Download or read book Fluid-Structure Interactions written by Michael P. Paidoussis and published by Academic Press. This book was released on 2013-12-07 with total page 885 pages. Available in PDF, EPUB and Kindle. Book excerpt: The first of two books concentrating on the dynamics of slender bodies within or containing axial flow, Fluid-Structure Interaction, Volume 1 covers the fundamentals and mechanisms giving rise to flow-induced vibration, with a particular focus on the challenges associated with pipes conveying fluid. This volume has been thoroughly updated to reference the latest developments in the field, with a continued emphasis on the understanding of dynamical behaviour and analytical methods needed to provide long-term solutions and validate the latest computational methods and codes. In this edition, Chapter 7 from Volume 2 has also been moved to Volume 1, meaning that Volume 1 now mainly treats the dynamics of systems subjected to internal flow, whereas in Volume 2 the axial flow is in most cases external to the flow or annular. - Provides an in-depth review of an extensive range of fluid-structure interaction topics, with detailed real-world examples and thorough referencing throughout for additional detail - Organized by structure and problem type, allowing you to dip into the sections that are relevant to the particular problem you are facing, with numerous appendices containing the equations relevant to specific problems - Supports development of long-term solutions by focusing on the fundamentals and mechanisms needed to understand underlying causes and operating conditions under which apparent solutions might not prove effective
Book Synopsis Mathematical Theory of Evolutionary Fluid-Flow Structure Interactions by : Barbara Kaltenbacher
Download or read book Mathematical Theory of Evolutionary Fluid-Flow Structure Interactions written by Barbara Kaltenbacher and published by Springer. This book was released on 2018-06-21 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of coupled partial differential equation models, which describe complex dynamical systems occurring in modern scientific applications such as fluid/flow-structure interactions. The first chapter provides a general description of a fluid-structure interaction, which is formulated within a realistic framework, where the structure subject to a frictional damping moves within the fluid. The second chapter then offers a multifaceted description, with often surprising results, of the case of the static interface; a case that is argued in the literature to be a good model for small, rapid oscillations of the structure. The third chapter describes flow-structure interaction where the compressible Navier-Stokes equations are replaced by the linearized Euler equation, while the solid is taken as a nonlinear plate, which oscillates in the surrounding gas flow. The final chapter focuses on a the equations of nonlinear acoustics coupled with linear acoustics or elasticity, as they arise in the context of high intensity ultrasound applications.
Book Synopsis Wave Packets and Their Bifurcations in Geophysical Fluid Dynamics by : Huijun Yang
Download or read book Wave Packets and Their Bifurcations in Geophysical Fluid Dynamics written by Huijun Yang and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 253 pages. Available in PDF, EPUB and Kindle. Book excerpt: The material in this book is based predominantly on my recent work. It is the first monograph on the subject, though some support material may overlap other monographs. The investigation of wave packets and their bi furcations is very interesting, and useful theoretically and in practice, not only in geophysical fluid dynamics, which is the field to which the theory is being applied here, but also in other fields in mathematics and the natural sciences. I hope that the applied mathematician will find reading this book worthwhile, especially the material on the behavior of highly nonlinear dy namic systems. However, it is my belief that applying the concepts and methods developed here to other fields will be both interesting and con structive, since there are numerous phenomena in other areas of physics that share the characteristics of those in geophysical fluid dynamics. The theory developed here provides an effective tool to investigate the structure and the structural changes of dynamic systems in physics. Applications of the theory in geophysical fluid dynamics are an example of its usefulness and effectiveness. Some of the results presented here give us more insight into the nature of geophysical fluids. Moreover, the material is presented systematically and developmentally. Necessary basic knowledge is provided to make the book more readable for graduate students and researchers in such fields as applied mathematics, geophysical fluid dynamics, atmospheric sciences, and physical oceanogra phy.
Book Synopsis Heat Transfer and Fluid Flow in Biological Processes by : Sid M. Becker
Download or read book Heat Transfer and Fluid Flow in Biological Processes written by Sid M. Becker and published by Academic Press. This book was released on 2014-12-31 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: Heat Transfer and Fluid Flow in Biological Processes covers emerging areas in fluid flow and heat transfer relevant to biosystems and medical technology. This book uses an interdisciplinary approach to provide a comprehensive prospective on biofluid mechanics and heat transfer advances and includes reviews of the most recent methods in modeling of flows in biological media, such as CFD. Written by internationally recognized researchers in the field, each chapter provides a strong introductory section that is useful to both readers currently in the field and readers interested in learning more about these areas. Heat Transfer and Fluid Flow in Biological Processes is an indispensable reference for professors, graduate students, professionals, and clinical researchers in the fields of biology, biomedical engineering, chemistry and medicine working on applications of fluid flow, heat transfer, and transport phenomena in biomedical technology. - Provides a wide range of biological and clinical applications of fluid flow and heat transfer in biomedical technology - Covers topics such as electrokinetic transport, electroporation of cells and tissue dialysis, inert solute transport (insulin), thermal ablation of cancerous tissue, respiratory therapies, and associated medical technologies - Reviews the most recent advances in modeling techniques
Download or read book Advances in Applied Mechanics written by and published by Elsevier. This book was released on 2007-04-04 with total page 355 pages. Available in PDF, EPUB and Kindle. Book excerpt: The major developments in the fields of fluid and solid mechanics are scattered throughout an array of technical journals, often making it difficult to find what the real advances are, especially for a researcher new to the field or an individual interested in discovering the state-of-the-art in connection with applications. The Advances in Applied Mechanics book series draws together recent significant advances in various topics in applied mechanics. Published since 1948, Advances in Applied Mechanics aims to provide authoritative review articles on topics in the mechanical sciences, primarily of interest to scientists and engineers working in the various branches of mechanics, but also of interest to the many who use the results of investigations in mechanics in various application areas such as aerospace, chemical, civil, environmental, mechanical and nuclear engineering. Advances in Applied Mechanics continues to be a publication of high visibility and impact. Review articles are provided by active, leading scientists in the field by invitation of the editors. Many of the articles published have become classics within their fields. Volume 41 in the series contains articles on topological fluid mechanics, electrospinning, vortex dynamics and self-assembly. - Covers all fields of the mechanical sciences - Highlights classical and modern areas of mechanics that are ready for review - Provides comprehensive coverage of the field in question
Book Synopsis Elements of Applied Bifurcation Theory by : Yuri Kuznetsov
Download or read book Elements of Applied Bifurcation Theory written by Yuri Kuznetsov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 648 pages. Available in PDF, EPUB and Kindle. Book excerpt: Providing readers with a solid basis in dynamical systems theory, as well as explicit procedures for application of general mathematical results to particular problems, the focus here is on efficient numerical implementations of the developed techniques. The book is designed for advanced undergraduates or graduates in applied mathematics, as well as for Ph.D. students and researchers in physics, biology, engineering, and economics who use dynamical systems as model tools in their studies. A moderate mathematical background is assumed, and, whenever possible, only elementary mathematical tools are used. This new edition preserves the structure of the first while updating the context to incorporate recent theoretical developments, in particular new and improved numerical methods for bifurcation analysis.
Book Synopsis Engineering Fluid Dynamics by : C. Kleinstreuer
Download or read book Engineering Fluid Dynamics written by C. Kleinstreuer and published by Cambridge University Press. This book was released on 1997-02-28 with total page 562 pages. Available in PDF, EPUB and Kindle. Book excerpt: A practical approach to the study of fluid mechanics at the graduate level.
Book Synopsis Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics by : Alexander Gelfgat
Download or read book Computational Modelling of Bifurcations and Instabilities in Fluid Dynamics written by Alexander Gelfgat and published by Springer. This book was released on 2018-07-06 with total page 524 pages. Available in PDF, EPUB and Kindle. Book excerpt: Instabilities of fluid flows and the associated transitions between different possible flow states provide a fascinating set of problems that have attracted researchers for over a hundred years. This book addresses state-of-the-art developments in numerical techniques for computational modelling of fluid instabilities and related bifurcation structures, as well as providing comprehensive reviews of recently solved challenging problems in the field.
Book Synopsis Internal Fluid Flow by : Alfred John Ward-Smith
Download or read book Internal Fluid Flow written by Alfred John Ward-Smith and published by Oxford University Press, USA. This book was released on 1980 with total page 604 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems by : Eusebius Doedel
Download or read book Numerical Methods for Bifurcation Problems and Large-Scale Dynamical Systems written by Eusebius Doedel and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Institute for Mathematics and its Applications (IMA) devoted its 1997-1998 program to Emerging Applications of Dynamical Systems. Dynamical systems theory and related numerical algorithms provide powerful tools for studying the solution behavior of differential equations and mappings. In the past 25 years computational methods have been developed for calculating fixed points, limit cycles, and bifurcation points. A remaining challenge is to develop robust methods for calculating more complicated objects, such as higher- codimension bifurcations of fixed points, periodic orbits, and connecting orbits, as well as the calcuation of invariant manifolds. Another challenge is to extend the applicability of algorithms to the very large systems that result from discretizing partial differential equations. Even the calculation of steady states and their linear stability can be prohibitively expensive for large systems (e.g. 10_3- -10_6 equations) if attempted by simple direct methods. Several of the papers in this volume treat computational methods for low and high dimensional systems and, in some cases, their incorporation into software packages. A few papers treat fundamental theoretical problems, including smooth factorization of matrices, self -organized criticality, and unfolding of singular heteroclinic cycles. Other papers treat applications of dynamical systems computations in various scientific fields, such as biology, chemical engineering, fluid mechanics, and mechanical engineering.
Book Synopsis Ordered and Turbulent Patterns in Taylor-Couette Flow by : C. David Andereck
Download or read book Ordered and Turbulent Patterns in Taylor-Couette Flow written by C. David Andereck and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Methods In Equivariant Bifurcations And Dynamical Systems by : Pascal Chossat
Download or read book Methods In Equivariant Bifurcations And Dynamical Systems written by Pascal Chossat and published by World Scientific Publishing Company. This book was released on 2000-02-28 with total page 422 pages. Available in PDF, EPUB and Kindle. Book excerpt: This invaluable book presents a comprehensive introduction to bifurcation theory in the presence of symmetry, an applied mathematical topic which has developed considerably over the past twenty years and has been very successful in analysing and predicting pattern formation and other critical phenomena in most areas of science where nonlinear models are involved, like fluid flow instabilities, chemical waves, elasticity and population dynamics.The book has two aims. One is to expound the mathematical methods of equivariant bifurcation theory. Beyond the classical bifurcation tools, such as center manifold and normal form reductions, the presence of symmetry requires the introduction of the algebraic and geometric formalism of Lie group theory and transformation group methods. For the first time, all these methods in equivariant bifurcations are presented in a coherent and self-consistent way in a book.The other aim is to present the most recent ideas and results in this theory, in relation to applications. This includes bifurcations of relative equilibria and relative periodic orbits for compact and noncompact group actions, heteroclinic cycles and forced symmetry-breaking perturbations. Although not all recent contributions could be included and a choice had to be made, a rather complete description of these new developments is provided. At the end of every chapter, exercises are offered to the reader.
Book Synopsis Computational Fluid-Structure Interaction by : Yuri Bazilevs
Download or read book Computational Fluid-Structure Interaction written by Yuri Bazilevs and published by John Wiley & Sons. This book was released on 2013-01-25 with total page 444 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Fluid-Structure Interaction: Methods and Applications takes the reader from the fundamentals of computational fluid and solid mechanics to the state-of-the-art in computational FSI methods, special FSI techniques, and solution of real-world problems. Leading experts in the field present the material using a unique approach that combines advanced methods, special techniques, and challenging applications. This book begins with the differential equations governing the fluid and solid mechanics, coupling conditions at the fluid–solid interface, and the basics of the finite element method. It continues with the ALE and space–time FSI methods, spatial discretization and time integration strategies for the coupled FSI equations, solution techniques for the fully-discretized coupled equations, and advanced FSI and space–time methods. It ends with special FSI techniques targeting cardiovascular FSI, parachute FSI, and wind-turbine aerodynamics and FSI. Key features: First book to address the state-of-the-art in computational FSI Combines the fundamentals of computational fluid and solid mechanics, the state-of-the-art in FSI methods, and special FSI techniques targeting challenging classes of real-world problems Covers modern computational mechanics techniques, including stabilized, variational multiscale, and space–time methods, isogeometric analysis, and advanced FSI coupling methods Is in full color, with diagrams illustrating the fundamental concepts and advanced methods and with insightful visualization illustrating the complexities of the problems that can be solved with the FSI methods covered in the book. Authors are award winning, leading global experts in computational FSI, who are known for solving some of the most challenging FSI problems Computational Fluid-Structure Interaction: Methods and Applications is a comprehensive reference for researchers and practicing engineers who would like to advance their existing knowledge on these subjects. It is also an ideal text for graduate and senior-level undergraduate courses in computational fluid mechanics and computational FSI.
