Topological Fluid Mechanics

Author : Mitchell A. Berger,Renzo L. Ricca,Louis H. Kauffman,Boris Khesin,H. Keith Moffatt,De Witt Sumners
Publisher : Springer
Page : 223 pages
File Size : 48,5 Mb
Release : 2009-05-28
Category : Science
ISBN : 9783642008375

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Lectures on Topological Fluid Mechanics by Mitchell A. Berger,Renzo L. Ricca,Louis H. Kauffman,Boris Khesin,H. Keith Moffatt,De Witt Sumners Pdf

Helmholtz's seminal paper on vortex motion (1858) marks the beginning of what is now called topological fluid mechanics.After 150 years of work, the field has grown considerably. In the last several decades unexpected developments have given topological fluid mechanics new impetus, benefiting from the impressive progress in knot theory and geometric topology on the one hand, and in mathematical and computational fluid dynamics on the other. This volume contains a wide-ranging collection of up-to-date, valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics, including topological vortex dynamics and magnetohydrodynamics, integrability issues, Hamiltonian structures and singularity formation, to DNA tangles and knotted DNAs in sedimentation. A substantial introductory chapter on knots and links, covering elements of modern braid theory and knot polynomials, as well as more advanced topics in knot classification, provides an invaluable addition to this material.

Author : Renzo L. Ricca
Publisher : Springer Science & Business Media
Page : 346 pages
File Size : 41,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9789401004466

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An Introduction to the Geometry and Topology of Fluid Flows by Renzo L. Ricca Pdf

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.

Author : International Union of Theoretical and Applied Mechanics
Publisher : Cambridge University Press
Page : 394 pages
File Size : 41,8 Mb
Release : 1990-04-12
Category : Mathematics
ISBN : 0521381452

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Topological Fluid Mechanics by International Union of Theoretical and Applied Mechanics Pdf

There has been developing interest in the aspects of fluid mechanics and of magnetohydrodynamics that can be properly described as topological, rather than exclusively analytical in character. This book contains the proceedings of the IUTAM symposium on Topological Fluid Mechanics held at Cambridge UK, 13-18 August, 1989. Topics covered include the kinematic and dynamical problems in laminar and turbulent flows, as well as the range of problems that arise from the magnetohydrodynamics of highly conducting flows. The papers presented cover all approaches; theoretical, computational and experimental, and each paper has been edited by a member of the International Scientific Committee.

Author : H.K. Moffatt,G.M. Zaslavsky,P. Comte,M. Tabor
Publisher : Springer Science & Business Media
Page : 597 pages
File Size : 50,8 Mb
Release : 2013-03-09
Category : Science
ISBN : 9789401735506

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Topological Aspects of the Dynamics of Fluids and Plasmas by H.K. Moffatt,G.M. Zaslavsky,P. Comte,M. Tabor Pdf

This volume contains papers arising out of the program of the Institute for Theoretical Physics (ITP) of the University of California at Santa Bar bara, August-December 1991, on the subject "Topological Fluid Dynamics". The first group of papers cover the lectures on Knot Theory, Relaxation un der Topological Constraints, Kinematics of Stretching, and Fast Dynamo Theory presented at the initial Pedagogical Workshop of the program. The remaining papers were presented at the subsequent NATO Advanced Re search Workshop or were written during the course of the program. We wish to acknowledge the support of the NATO Science Committee in making this workshop possible. The scope of "Topological Fluid Dynamics" was defined by an earlier Symposium of the International Union of Theoretical and Applied Mechan ics (IUTAM) held in Cambridge, England in August, 1989, the Proceedings of which were published (Eds. H.K. Moffatt and A. Tsinober) by Cambridge University Press in 1990. The proposal to hold an ITP program on this sub ject emerged from that Symposium, and we are grateful to John Greene and Charlie Kennel at whose encouragement the original proposal was formu lated. Topological fluid dynamics covers a range of problems, particularly those involving vortex tubes and/or magnetic flux tubes in nearly ideal fluids, for which topological structures can be identified and to some extent quantified.

Author : Mitchell A. Berger,Louis H. Kauffman,Boris Khesin,H. Keith Moffatt,De Witt Sumners
Publisher : Springer Science & Business Media
Page : 240 pages
File Size : 45,6 Mb
Release : 2009-05-05
Category : Mathematics
ISBN : 9783642008368

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Lectures on Topological Fluid Mechanics by Mitchell A. Berger,Louis H. Kauffman,Boris Khesin,H. Keith Moffatt,De Witt Sumners Pdf

This volume contains a wide-ranging collection of valuable research papers written by some of the most eminent experts in the field. Topics range from fundamental aspects of mathematical fluid mechanics to DNA tangles and knotted DNAs in sedimentation.

Author : Vladimir Shtern
Publisher : Cambridge University Press
Page : 589 pages
File Size : 41,9 Mb
Release : 2018-02-08
Category : Technology & Engineering
ISBN : 9781108418621

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Cellular Flows by Vladimir Shtern Pdf

This book discusses flow cells, their emergence, multiplication, coalescence, disappearance, and physical reasons for their metamorphoses.

Author : Vladimir I. Arnold,Boris A. Khesin
Publisher : Springer Science & Business Media
Page : 376 pages
File Size : 44,6 Mb
Release : 2008-01-08
Category : Mathematics
ISBN : 9780387225890

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Topological Methods in Hydrodynamics by Vladimir I. Arnold,Boris A. Khesin Pdf

The first monograph to treat topological, group-theoretic, and geometric problems of ideal hydrodynamics and magnetohydrodynamics from a unified point of view. It describes the necessary preliminary notions both in hydrodynamics and pure mathematics with numerous examples and figures. The book is accessible to graduates as well as pure and applied mathematicians working in hydrodynamics, Lie groups, dynamical systems, and differential geometry.

Author : Henry Keith Moffatt,Arkady Tsinober
Publisher : Unknown
Page : 805 pages
File Size : 40,9 Mb
Release : 1990
Category : Electronic
ISBN : OCLC:636805340

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Topological Fluid Mechanics by Henry Keith Moffatt,Arkady Tsinober Pdf

Author : Victor G. Zvyagin,Dmitry A. Vorotnikov
Publisher : Walter de Gruyter
Page : 245 pages
File Size : 51,7 Mb
Release : 2008-09-25
Category : Mathematics
ISBN : 9783110208283

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Topological Approximation Methods for Evolutionary Problems of Nonlinear Hydrodynamics by Victor G. Zvyagin,Dmitry A. Vorotnikov Pdf

The authors present functional analytical methods for solving a class of partial differential equations. The results have important applications to the numerical treatment of rheology (specific examples are the behaviour of blood or print colours) and to other applications in fluid mechanics. A class of methods for solving problems in hydrodynamics is presented.

Author : Gary Webb
Publisher : Springer
Page : 301 pages
File Size : 45,8 Mb
Release : 2018-02-05
Category : Science
ISBN : 9783319725116

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Magnetohydrodynamics and Fluid Dynamics: Action Principles and Conservation Laws by Gary Webb Pdf

This text focuses on conservation laws in magnetohydrodynamics, gasdynamics and hydrodynamics. A grasp of new conservation laws is essential in fusion and space plasmas, as well as in geophysical fluid dynamics; they can be used to test numerical codes, or to reveal new aspects of the underlying physics, e.g., by identifying the time history of the fluid elements as an important key to understanding fluid vorticity or in investigating the stability of steady flows. The ten Galilean Lie point symmetries of the fundamental action discussed in this book give rise to the conservation of energy, momentum, angular momentum and center of mass conservation laws via Noether’s first theorem. The advected invariants are related to fluid relabeling symmetries – so-called diffeomorphisms associated with the Lagrangian map – and are obtained by applying the Euler-Poincare approach to Noether’s second theorem. The book discusses several variants of helicity including kinetic helicity, cross helicity, magnetic helicity, Ertels’ theorem and potential vorticity, the Hollman invariant, and the Godbillon Vey invariant. The book develops the non-canonical Hamiltonian approach to MHD using the non-canonical Poisson bracket, while also refining the multisymplectic approach to ideal MHD and obtaining novel nonlocal conservation laws. It also briefly discusses Anco and Bluman’s direct method for deriving conservation laws. A range of examples is used to illustrate topological invariants in MHD and fluid dynamics, including the Hopf invariant, the Calugareanu invariant, the Taylor magnetic helicity reconnection hypothesis for magnetic fields in highly conducting plasmas, and the magnetic helicity of Alfvén simple waves, MHD topological solitons, and the Parker Archimedean spiral magnetic field. The Lagrangian map is used to obtain a class of solutions for incompressible MHD. The Aharonov-Bohm interpretation of magnetic helicity and cross helicity is discussed. In closing, examples of magnetosonic N-waves are used to illustrate the role of the wave number and group velocity concepts for MHD waves. This self-contained and pedagogical guide to the fundamentals will benefit postgraduate-level newcomers and seasoned researchers alike.

Author : Bijan Mohammadi,Olivier Pironneau
Publisher : OUP Oxford
Page : 296 pages
File Size : 55,6 Mb
Release : 2009-09-24
Category : Mathematics
ISBN : 9780191574214

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Applied Shape Optimization for Fluids by Bijan Mohammadi,Olivier Pironneau Pdf

The fields of computational fluid dynamics (CFD) and optimal shape design (OSD) have received considerable attention in the recent past, and are of practical importance for many engineering applications. This new edition of Applied Shape Optimization for Fluids deals with shape optimization problems for fluids, with the equations needed for their understanding (Euler and Navier Strokes, but also those for microfluids) and with the numerical simulation of these problems. It presents the state of the art in shape optimization for an extended range of applications involving fluid flows. Automatic differentiation, approximate gradients, unstructured mesh adaptation, multi-model configurations, and time-dependent problems are introduced, and their implementation into the industrial environments of aerospace and automobile equipment industry explained and illustrated. With the increases in the power of computers in industry since the first edition, methods which were previously unfeasible have begun giving results, namely evolutionary algorithms, topological optimization methods, and level set algortihms. In this edition, these methods have been treated in separate chapters, but the book remains primarily one on differential shape optimization. This book is essential reading for engineers interested in the implementation and solution of optimization problems using commercial packages or in-house solvers and graduates and researchers in applied mathematics, aerospace, or mechanical engineering, fluid dynamics, and CFD. More generally, anyone needing to understand and solve design problems or looking for new exciting areas for research and development in this area will find this book useful, especially in applying the methodology to practical problems.

Author : Ira M. Cohen,Pijush K. Kundu
Publisher : Academic Press
Page : 904 pages
File Size : 50,6 Mb
Release : 2007-12-05
Category : Technology & Engineering
ISBN : 9780080555836

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Fluid Mechanics by Ira M. Cohen,Pijush K. Kundu Pdf

Fluid mechanics, the study of how fluids behave and interact under various forces and in various applied situations—whether in the liquid or gaseous state or both—is introduced and comprehensively covered in this widely adopted text. Fully revised and updated with the addition of a new chapter on biofluid mechanics, Fluid Mechanics, Fourth Edition is suitable for both a first or second course in fluid mechanics at the graduate or advanced undergraduate level. The leading advanced general text on fluid mechanics, Fluid Mechanics, 4e guides students from the fundamentals to the analysis and application of fluid mechanics, including compressible flow and such diverse applications as hydraulics and aerodynamics. Updates to several chapters and sections, including Boundary Layers, Turbulence, Geophysical Fluid Dynamics, Thermodynamics and Compressibility. Fully revised and updated chapter on Computational Fluid Dynamics. New chapter on Biofluid Mechanics by Professor Portonovo Ayyaswamy, the Asa Whitney Professor of Dynamical Engineering at the University of Pennsylvania. New Visual Resources appendix provides a list of fluid mechanics films available for viewing online. Additional worked-out examples and end-of-chapter problems. Updated online Solutions Manual for adopting instructors.

Author : Pijush K. Kundu,Ira M. Cohen,David R Dowling
Publisher : Academic Press
Page : 919 pages
File Size : 52,5 Mb
Release : 2012
Category : Science
ISBN : 9780123821003

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Fluid Mechanics by Pijush K. Kundu,Ira M. Cohen,David R Dowling Pdf

Suitable for both a first or second course in fluid mechanics at the graduate or advanced undergraduate level, this book presents the study of how fluids behave and interact under various forces and in various applied situations - whether in the liquid or gaseous state or both.

Author : Richard W. Johnson
Publisher : Springer Science & Business Media
Page : 1962 pages
File Size : 55,6 Mb
Release : 1998-08-18
Category : Technology & Engineering
ISBN : 3540646124

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The Handbook of Fluid Dynamics by Richard W. Johnson Pdf

Providing professionals in the field with a comprehensive guide and resource, this book balances three traditional areas of fluid mechanics - theoretical, computational, and experimental - and expounds on basic science and engineering techniques. Each chapter discusses the primary issues related to the topic in question, outlines expert approaches, and supplies references for further information.

Author : Tian Ma,Shouhong Wang
Publisher : American Mathematical Soc.
Page : 248 pages
File Size : 54,9 Mb
Release : 2005
Category : Differential equations, Partial
ISBN : 9780821836934

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Geometric Theory of Incompressible Flows with Applications to Fluid Dynamics by Tian Ma,Shouhong Wang Pdf

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.