Tubes, Sheets and Singularities in Fluid Dynamics

Tubes, Sheets and Singularities in Fluid Dynamics

Author: K. Bajer

Publisher: Springer Science & Business Media

Published: 2006-04-11

Total Pages: 392

ISBN-13: 030648420X

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Modern experiments and numerical simulations show that the long-known coherent structures in turbulence take the form of elongated vortex tubes and vortex sheets. The evolution of vortex tubes may result in spiral structures which can be associated with the spectral power laws of turbulence. The mutual stretching of skewed vortex tubes, when they are close to each other, causes rapid growth of vorticity. Whether this process may or may not lead to a finite-time singularity is one of the famous open problems of fluid dynamics. This book contains the proceedings of the NATO ARW and IUTAM Symposium held in Zakopane, Poland, 2-7 September 2001. The papers presented, carefully reviewed by the International Scientific Committee, cover various aspects of the dynamics of vortex tubes and sheets and of their analogues in magnetohydrodynamics and in quantum turbulence. The book should be a useful reference for all researchers and students of modern fluid dynamics.


Lectures on Topological Fluid Mechanics

Lectures on Topological Fluid Mechanics

Author: Mitchell A. Berger

Publisher: Springer Science & Business Media

Published: 2009-05-05

Total Pages: 240

ISBN-13: 3642008364

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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.


Boundary Integral and Singularity Methods for Linearized Viscous Flow

Boundary Integral and Singularity Methods for Linearized Viscous Flow

Author: C. Pozrikidis

Publisher: Cambridge University Press

Published: 1992-02-28

Total Pages: 276

ISBN-13: 9780521406932

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In addition to theory, this study focuses on practical application and computer implementation in a coherent introduction to boundary integrals, boundary element and singularity methods for steady and unsteady flow at zero Reynolds numbers.


Theoretical Fluid Dynamics

Theoretical Fluid Dynamics

Author: Achim Feldmeier

Publisher: Springer Nature

Published: 2020-03-17

Total Pages: 580

ISBN-13: 3030310221

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This textbook gives an introduction to fluid dynamics based on flows for which analytical solutions exist, like individual vortices, vortex streets, vortex sheets, accretions disks, wakes, jets, cavities, shallow water waves, bores, tides, linear and non-linear free-surface waves, capillary waves, internal gravity waves and shocks. Advanced mathematical techniques ("calculus") are introduced and applied to obtain these solutions, mostly from complex function theory (Schwarz-Christoffel theorem and Wiener-Hopf technique), exterior calculus, singularity theory, asymptotic analysis, the theory of linear and nonlinear integral equations and the theory of characteristics. Many of the derivations, so far contained only in research journals, are made available here to a wider public.


Fundamentals of Fluid Mechanics

Fundamentals of Fluid Mechanics

Author: Patrick Chassaing

Publisher: Springer Nature

Published: 2023-01-24

Total Pages: 579

ISBN-13: 3031100867

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This textbook provides a coherent and structured overview of fluid mechanics, a discipline concerned with many natural phenomena and at the very heart of the most diversified industrial applications and human activities. The balance between phenomenological analysis, physical conceptualization and mathematical formulation serve both as a unifying educational marker and as a methodological guide to the three parts of the work. The thermo-mechanical motion equations of a homogeneous single-phase fluid are established, from which flow models (perfect fluid, viscous) and motion classes (isovolume, barotropic, irrotational, etc.) are derived. Incompressible, potential flows and compressible flows, both in an isentropic evolution and shock, of an ideal inviscid fluid are addressed in the second part. The viscous fluid is the subject of the last one, with the creeping motion regime and the laminar, dynamic and thermal boundary layer. Historical perspectives are included whenever they enrich the understanding of modern concepts. Many examples, chosen for their pedagogical relevance, are dealt with in exercises. The book is intended as a teaching tool for undergraduate students, wishing to acquire a first command of fluid mechanics, as well as graduates in advanced courses and engineers in other fields, concerned with completing what is sometimes a scattered body of knowledge.


The Mathematical Foundations of Mixing

The Mathematical Foundations of Mixing

Author: Rob Sturman

Publisher: Cambridge University Press

Published: 2006-09-21

Total Pages: 303

ISBN-13: 1139459201

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Mixing processes occur in many technological and natural applications, with length and time scales ranging from the very small to the very large. The diversity of problems can give rise to a diversity of approaches. Are there concepts that are central to all of them? Are there tools that allow for prediction and quantification? The authors show how a variety of flows in very different settings possess the characteristic of streamline crossing. This notion can be placed on firm mathematical footing via Linked Twist Maps (LTMs), which is the central organizing principle of this book. The authors discuss the definition and construction of LTMs, provide examples of specific mixers that can be analyzed in the LTM framework and introduce a number of mathematical techniques which are then brought to bear on the problem of fluid mixing. In a final chapter, they present a number of open problems and new directions.


Singularities: Formation, Structure and Propagation

Singularities: Formation, Structure and Propagation

Author: J. Eggers

Publisher: Cambridge University Press

Published: 2015-09-10

Total Pages: 471

ISBN-13: 1107098416

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This book explores a wide range of singular phenomena, providing mathematical tools for understanding them and highlighting their common features.


Advances in Applied Mechanics

Advances in Applied Mechanics

Author:

Publisher: Academic Press

Published: 2012-01-25

Total Pages: 265

ISBN-13: 0123808774

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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. - Highlights classical and modern areas of mechanics that are ready for review - Provides comprehensive coverage of the field in question