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Theory of Concentrated Vortices

An Introduction

  • Book
  • © 2007

Overview

Authors:
  1. S.V. Alekseenko

    1. Russian Academy of Sciences, Siberian Branch, Institute of Thermophysics, Russia

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  2. P.A. Kuibin

    1. Russian Academy of Sciences, Siberian Branch, Institute of Thermophysics, Russia

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  3. V.L. Okulov

    1. Russian Academy of Sciences, Siberian Branch, Institute of Thermophysics, Russia

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  • Clear and concise introduction to the theory of concentrated vortices
  • Presents basic elements of vortex motion: waves, shear flows, helical motion (twisters)
  • Nonlinearity effects are analyzed such as vortex breakdown, self-induced motion of vortices such as vortex rings, helical vortices and real swirl flows

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Table of contents (7 chapters)

  1. Front Matter

    Pages I-8
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  2. Equations and laws of vortex motion

    • S.V. Alekseenko, P.A. Kuibin, V.L. Okulov
    Pages 9-68

  3. Vortex filaments

    • S.V. Alekseenko, P.A. Kuibin, V.L. Okulov
    Pages 69-110

  4. Models of vortex structures

    • S.V. Alekseenko, P.A. Kuibin, V.L. Okulov
    Pages 111-153

  5. Stability and waves on columnar vortices

    • S.V. Alekseenko, P.A. Kuibin, V.L. Okulov
    Pages 155-234

  6. Dynamics of vortex filaments

    • S.V. Alekseenko, P.A. Kuibin, V.L. Okulov
    Pages 235-308

  7. Dynamics of two-dimensional vortex structures

    • S.V. Alekseenko, P.A. Kuibin, V.L. Okulov
    Pages 309-378

  8. Experimental observation of concentrated vortices in vortex apparatus

    • S.V. Alekseenko, P.A. Kuibin, V.L. Okulov
    Pages 379-466

  9. Back Matter

    Pages 467-487
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Keywords

About this book

Vortex motion is one of the basic states of a flowing continuum. Intere- ingly, in many cases vorticity is space-localized, generating concentrated vortices. Vortex filaments having extremely diverse dynamics are the most characteristic examples of such vortices. Notable examples, in particular, include such phenomena as self-inducted motion, various instabilities, wave generation, and vortex breakdown. These effects are typically ma- fested as a spiral (or helical) configuration of a vortex axis. Many publications in the field of hydrodynamics are focused on vortex motion and vortex effects. Only a few books are devoted entirely to v- tices, and even fewer to concentrated vortices. This work aims to highlight the key problems of vortex formation and behavior. The experimental - servations of the authors, the impressive visualizations of concentrated vortices (including helical and spiral) and pictures of vortex breakdown primarily motivated the authors to begin this work. Later, the approach based on the helical symmetry of swirl flows was developed, allowing the authors to deduce simplified mathematical models and to describe many vortex phenomena. The major portion of this book consists of theoretical studies of vortex dynamics. The final chapter presents detailed results of experimentally observed concentrated vortices that provide the basis for analysis and stimulate development of vortex theory. The mathematical description of the dynamics of concentrated vortices is hindered by the requirement to consider three-dimensional and nonlinear effects, singularity, and various instabilities. For each particular problem, very different coordinate frames and equation systems must be used.

Reviews

From the reviews:

"The book contains a comprehensive overview and authoritative coverage of the wide field of concentrated vortices observed in nature and technique. It familiarizes readers with the methods for research of their kinematics and dynamics. … this book also covers recent achievements in the fields of stability analysis, waves on vortices and vortex breakdown. Scientists working in the areas of applied mathematics, and in theoretical and/or computational fluid dynamics will benefit from this book, which may serve both as a reference monograph and a textbook." (Felix Kaplanski, Zentralblatt MATH, Vol. 1132 (10), 2008)

Authors and Affiliations

  • Russian Academy of Sciences, Siberian Branch, Institute of Thermophysics, Russia

    S.V. Alekseenko, P.A. Kuibin, V.L. Okulov

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