Mathematical Aspects of Vortex Dynamics
Author : Russel E. Caflisch
Publisher : SIAM
Page : 240 pages
File Size : 27,21 MB
Release : 1989-01-01
Category : Science
ISBN : 9780898712353
Vortex Dynamics
Author : P. G. Saffman
Publisher : Cambridge University Press
Page : 332 pages
File Size : 35,33 MB
Release : 1995-02-24
Category : Mathematics
ISBN : 9780521477390
Book Description
Vortex dynamics is a natural paradigm for the field of chaotic motion and modern dynamical system theory. However, this volume focuses on those aspects of fluid motion that are primarily controlled by the vorticity and are such that the effects of the other fluid properties are secondary.
Vorticity and Vortex Dynamics
Author : Jie-Zhi Wu
Publisher : Springer Science & Business Media
Page : 776 pages
File Size : 15,23 MB
Release : 2007-04-20
Category : Technology & Engineering
ISBN : 3540290281
Book Description
This book is a comprehensive and intensive monograph for scientists, engineers and applied mathematicians, as well as graduate students in fluid dynamics. It starts with a brief review of fundamentals of fluid dynamics, with an innovative emphasis on the intrinsic orthogonal decomposition of fluid dynamic process, by which one naturally identifies the content and scope of vorticity and vortex dynamics. This is followed by a detailed presentation of vorticity dynamics as the basis of later development. In vortex dynamics part the book deals with the formation, motion, interaction, stability, and breakdown of various vortices. Typical vortex structures are analyzed in laminar, transitional, and turbulent flows, including stratified and rotational fluids. Physical understanding of vertical flow phenomena and mechanisms is the first priority throughout the book. To make the book self-contained, some mathematical background is briefly presented in the main text, but major prerequisites are systematically given in appendices. Material usually not seen in books on vortex dynamics is included, such as geophysical vortex dynamics, aerodynamic vortical flow diagnostics and management.
Mathematical Aspects of Fluid Mechanics
Author : James C. Robinson
Publisher : Cambridge University Press
Page : 275 pages
File Size : 27,72 MB
Release : 2012-10-18
Category : Mathematics
ISBN : 1139577212
Book Description
The rigorous mathematical theory of the equations of fluid dynamics has been a focus of intense activity in recent years. This volume is the product of a workshop held at the University of Warwick to consolidate, survey and further advance the subject. The Navier–Stokes equations feature prominently: the reader will find new results concerning feedback stabilisation, stretching and folding, and decay in norm of solutions to these fundamental equations of fluid motion. Other topics covered include new models for turbulent energy cascade, existence and uniqueness results for complex fluids and certain interesting solutions of the SQG equation. The result is an accessible collection of survey articles and more traditional research papers that will serve both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.
Theoretical Approaches to Turbulence
Author : D.L. Dwoyer
Publisher : Springer Science & Business Media
Page : 377 pages
File Size : 42,33 MB
Release : 2012-12-06
Category : Science
ISBN : 1461210925
Book Description
Turbulence is the lIDst natural nDde of fluid lIDtion, and has been the subject of scientific study for all Dst a century. During this period, various ideas and techniques have evolved to nDdel turbulence. Following Saffman, these theoretical approaches can be broadly divided into four overlapping categories -- (1) analytical lIDdelling, (2) physical lIDdelling, (3) phenomenologicalllDdelling, and (4) nurerical lIDdelling. With the purpose of stmtnarizing our =ent understanding of these theoretical approaches to turbulence, recognized leaders (fluid dynamicists, mathematicians and physicists) in the field were invited to participate in a formal workshop during October 10-12, 1984, sponsored by The Institute for CooIputer Applications in Science and Engineering and NASA Langley Research Center. Kraiciman, McCcxnb, Pouquet and Spiegel represented the category of analytical nDdelling, while Landahl and Saffman represented physical lIDdelling. The contributions of Latmder and Spalding were in the category of phenanenological lIDdelling, and those of Ferziger and Reynolds in the area of nurericalllDdelling. Aref, Cholet, Lumley, Moin, Pope and Temam served on the panel discussions. With the care and cooperation of the participants, the workshop achieved its purpose, and we believe that its proceedings published in this vol\. llre has lasting scientific value. The tone of the workshop was set by two introductory talks by Bushnell and ChaImm. Buslmell presented the engineering viewpoint while Chapman reviewed from a historical perspective developments in the study of turbulence. The remaining talks dealt with specific aspects of the theoretical approaches to fluid turbulence.
Vorticity and Incompressible Flow
Author : Andrew J. Majda
Publisher : Cambridge University Press
Page : 562 pages
File Size : 40,53 MB
Release : 2002
Category : Mathematics
ISBN : 9780521639484
Book Description
This book is a comprehensive introduction to the mathematical theory of vorticity and incompressible flow ranging from elementary introductory material to current research topics. While the contents center on mathematical theory, many parts of the book showcase the interaction between rigorous mathematical theory, numerical, asymptotic, and qualitative simplified modeling, and physical phenomena. The first half forms an introductory graduate course on vorticity and incompressible flow. The second half comprise a modern applied mathematics graduate course on the weak solution theory for incompressible flow.
Liutex and Its Applications in Turbulence Research
Author : Chaoqun Liu
Publisher : Academic Press
Page : 460 pages
File Size : 15,99 MB
Release : 2020-10-29
Category : Technology & Engineering
ISBN : 0128190248
Book Description
Liutex and Its Applications in Turbulence Research reviews the history of vortex definition, provides an accurate mathematical definition of vortices, and explains their applications in flow transition, turbulent flow, flow control, and turbulent flow experiments. The book explains the term "Rortex" as a mathematically defined rigid rotation of fluids or vortex, which could help solve many longstanding problems in turbulence research. The accurate mathematical definition of the vortex is important in a range of industrial contexts, including aerospace, turbine machinery, combustion, and electronic cooling systems, so there are many areas of research that can benefit from the innovations described here. This book provides a thorough survey of the latest research in generalized and flow-thermal, unified, law-of-the-wall for wall-bounded turbulence. Important theory and methodologies used for developing these laws are described in detail, including: the classification of the conventional turbulent boundary layer concept based on proper velocity scaling; the methodology for identification of the scales of velocity, temperature, and length needed to establish the law; and the discovery, proof, and strict validations of the laws, with both Reynolds and Prandtl number independency properties using DNS data. The establishment of these statistical laws is important to modern fluid mechanics and heat transfer research, and greatly expands our understanding of wall-bounded turbulence. - Provides an accurate mathematical definition of vortices - Provides a thorough survey of the latest research in generalized and flow-thermal, unified, law-of-the-wall for wall-bounded turbulence - Explains the term "Rortex as a mathematically defined rigid rotation of fluids or vortex - Covers the statistical laws important to modern fluid mechanics and heat transfer research, and greatly expands our understanding of wall-bounded turbulence
Fluid Vortices
Author : Sheldon Green
Publisher : Springer Science & Business Media
Page : 905 pages
File Size : 30,54 MB
Release : 2012-12-06
Category : Technology & Engineering
ISBN : 940110249X
Book Description
Fluid Vortices is a comprehensive, up-to-date, research-level overview covering all salient flows in which fluid vortices play a significant role. The various chapters have been written by specialists from North America, Europe and Asia, making for unsurpassed depth and breadth of coverage. Topics addressed include fundamental vortex flows (mixing layer vortices, vortex rings, wake vortices, vortex stability, etc.), industrial and environmental vortex flows (aero-propulsion system vortices, vortex-structure interaction, atmospheric vortices, computational methods with vortices, etc.), and multiphase vortex flows (free-surface effects, vortex cavitation, and bubble and particle interactions with vortices). The book can also be recommended as an advanced graduate-level supplementary textbook. The first nine chapters of the book are suitable for a one-term course; chapters 10--19 form the basis for a second one-term course.
Quantized Vortex Dynamics and Superfluid Turbulence
Author : C.F. Barenghi
Publisher : Springer
Page : 459 pages
File Size : 29,35 MB
Release : 2008-01-11
Category : Technology & Engineering
ISBN : 3540455426
Book Description
This book springs from the programme Quantized Vortex Dynamics and Sup- ?uid Turbulence held at the Isaac Newton Institute for Mathematical Sciences (University of Cambridge) in August 2000. What motivated the programme was the recognition that two recent developments have moved the study of qu- tized vorticity, traditionally carried out within the low-temperature physics and condensed-matter physics communities, into a new era. The ?rst development is the increasing contact with classical ?uid dynamics and its ideas and methods. For example, some current experiments with - lium II now deal with very classical issues, such as the measurement of velocity spectra and turbulence decay rates. The evidence from these experiments and many others is that super?uid turbulence and classical turbulence share many features. The challenge is now to explain these similarities and explore the time scales and length scales over which they hold true. The observed classical aspects have also attracted attention to the role played by the ?ow of the normal ?uid, which was somewhat neglected in the past because of the lack of direct ?ow visualization. Increased computing power is also making it possible to study the coupled motion of super?uid vortices and normal ?uids. Another contact with classical physics arises through the interest in the study of super?uid vortex - connections. Reconnections have been studied for some time in the contexts of classical ?uid dynamics and magneto-hydrodynamics (MHD), and it is useful to learn from the experience acquired in other ?elds.
Vortex Methods
Author : Georges-Henri Cottet
Publisher : Cambridge University Press
Page : 0 pages
File Size : 28,75 MB
Release : 2008-04-24
Category : Science
ISBN : 9780521061704
Book Description
Vortex methods have matured in recent years, offering an interesting alternative to finite difference and spectral methods for high resolution numerical solutions of the Navier Stokes equations. In the past three decades, research into the numerical analysis aspects of vortex methods has provided a solid mathematical background for understanding the accuracy and stability of the method. At the same time vortex methods retain their appealing physical character, which was the motivation for their introduction. This book presents and analyzes vortex methods as a tool for the direct numerical simulation of impressible viscous flows. It will interest graduate students and researchers in numerical analysis and fluid mechanics and also serve as an ideal textbook for courses in fluid dynamics.
