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The N-Vortex Problem Analytical Techniques

Bibliographic Details
Main Author: Newton, Paul K.
Format: eBook
Language:English
Published: New York, NY Springer New York 2001, 2001
Edition:1st ed. 2001
Series:Applied Mathematical Sciences
Subjects:
Classical And Continuum Physics
Continuum Mechanics
Computational Intelligence
Manifolds And Cell Complexes
Physics
Manifolds (mathematics)
Applications Of Mathematics
Mathematics
Online Access:
Collection: Springer Book Archives -2004 - Collection details see MPG.ReNa
Table of Contents:
  • Preface
  • 1 Introduction
  • 1.1 Vorticity Dynamics
  • 1.2 Hamiltonian Dynamics
  • 1.3 Summary of Basic Questions
  • 1.4 Exercises
  • 2 N Vortices in the Plane
  • 2.1 General Formulation
  • 2.2 N = 3
  • 2.3 N = 4
  • 2.4 Bibliographic Notes
  • 2.5 Exercises
  • 3 Domains with Boundaries
  • 3.1 Green’s Function of the First Kind
  • 3.2 Method of Images
  • 3.3 Conformai Mapping Techniques
  • 3.4 Breaking Integrability
  • 3.5 Bibliographic Notes
  • 3.6 Exercises
  • 4 Vortex Motion on a Sphere
  • 4.1 General Formulation
  • 4.2 Dynamics of Three Vortices
  • 4.3 Phase Plane Dynamics
  • 4.4 3-Vortex Collapse
  • 4.5 Stereographic Projection
  • 4.6 Integrable Streamline Topologies
  • 4.7 Boundaries
  • 4.8 Bibliographic Notes
  • 4.9 Exercises
  • 5 Geometric Phases
  • 5.1 Geometric Phases in Various Contexts
  • 5.2 Phase Calculations For Slowly Varying Systems
  • 5.3 Definition of the Adiabatic Hannay Angle
  • 5.4 3-Vortex Problem
  • 5.5 Applications
  • 5.6 Exercises
  • 6 Statistical Point Vortex Theories
  • 6.1 Basics of Statistical Physics
  • 6.2 Statistical Equilibrium Theories
  • 6.3 Maximum Entropy Theories
  • 6.4 Nonequilibrium Theories
  • 6.5 Exercises
  • 7 Vortex Patch Models
  • 7.1 Introduction to Vortex Patches
  • 7.2 The Kida-Neu Vortex
  • 7.3 Time-Dependent Strain
  • 7.4 Melander-Zabusky-Styczek Model
  • 7.5 Geometric Phase for Corotating Patches
  • 7.6 Viscous Shear Layer Model
  • 7.7 Bibliographic Notes
  • 7.8 Exercises
  • 8 Vortex Filament Models
  • 8.1 Introduction to Vortex Filaments and the LIE
  • 8.2 DaRios-Betchov Intrinsic Equations
  • 8.3 Hasimoto’s Transformation
  • 8.4 LIA Invariants
  • 8.5 Vortex-Stretching Models
  • 8.6 Nearly Parallel Filaments
  • 8.7 The Vorton Model
  • 8.8 Exercises
  • References

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