The N-Vortex Problem

Analytical Techniques

Paul K. Newton (Autor)

Buch | Hardcover

420 Seiten

2001 | 2001 ed.
Springer-Verlag New York Inc.
9780387952260 (ISBN)

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Suitable for applied mathematicians, physicists, and engineers interested in either nonlinear dynamics or classical mechanics and fluid dynamics. This book describes the Hamiltonian aspects of vortex dynamics.

For applied mathematicians, physicists, and engineers interested in either nonlinear dynamics or classical mechanics and fluid dynamics. Describes the Hamiltonian aspects of vortex dynamics so that it may serve as an entry into the large literature on integrable and non-integrable vortex problems.

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.

Reihe/Serie	Applied Mathematical Sciences ; 145
Zusatzinfo	XVIII, 420 p.
Verlagsort	New York, NY
Sprache	englisch
Maße	156 x 234 mm
Themenwelt	Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
	Naturwissenschaften ► Physik / Astronomie ► Mechanik
	Naturwissenschaften ► Physik / Astronomie ► Strömungsmechanik
ISBN-13	9780387952260 / 9780387952260
Zustand	Neuware