Introduction to Hamiltonian Fluid Dynamics and Stability Theory

AvGordon E Swaters

Inbunden, Engelska, 1999

Del i serien Monographs and Surveys in Pure and Applied Mathematics

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Beskrivning

Hamiltonian fluid dynamics and stability theory work hand-in-hand in a variety of engineering, physics, and physical science fields. Until now, however, no single reference addressed and provided background in both of these closely linked subjects. Introduction to Hamiltonian Fluid Dynamics and Stability Theory does just that-offers a comprehensive introduction to Hamiltonian fluid dynamics and describes aspects of hydrodynamic stability theory within the context of the Hamiltonian formalism.The author uses the example of the nonlinear pendulum-giving a thorough linear and nonlinear stability analysis of its equilibrium solutions-to introduce many of the ideas associated with the mathematical argument required in infinite dimensional Hamiltonian theory needed for fluid mechanics. He examines Andrews' Theorem, derives and develops the Charney-Hasegawa-Mima (CMH) equation, presents an account of the Hamiltonian structure of the Korteweg-de Vries (KdV) equation, and discusses the stability theory associated with the KdV soliton.The book's tutorial approach and plentiful exercises combine with its thorough presentations of both subjects to make Introduction to Hamiltonian Fluid Dynamics and Stability Theory an ideal reference, self-study text, and upper level course book.

Produktinformation

Utgivningsdatum:1999-09-29
Mått:156 x 234 x 20 mm
Vikt:690 g
Format:Inbunden
Språk:Engelska
Serie:Monographs and Surveys in Pure and Applied Mathematics
Antal sidor:288
Förlag:Taylor & Francis Inc
ISBN:9781584880233

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Teknik: allmänt inom Naturvetenskap och teknik
Klassisk mekanik inom Naturvetenskap och teknik
Fysik inom Naturvetenskap och teknik

Mer om författaren

Swaters, Gordon E

Recensioner i media

"…a refreshingly non-technical style…this is a well-written introduction to Hamiltonian fluid dynamics and basic stability results."--S. Reich, Edinburgh Mathematical Society, Vol. 44

Innehållsförteckning

IntroductionThe Nonlinear PendulumModel FormulationCanonical Hamiltonian FormulationLeast Action PrincipleSymplectic Hamiltonian FormulationMathematical Properties of the J MatrixPoisson Bracket FormulationSteady Solutions of a Canonical Hamiltonian SystemLinear Stability of a Steady SolutionNonlinear Stability of a Steady SolutionThe Two Dimensional Euler EquationsVorticity Equation FormulationHamiltonian Structure for Partial Differential EquationsHamiltonian Structure of the Euler EquationsReduction of the Canonical Poisson BracketCasimir Functionals and Noether's TheoremExercisesStability of Steady Euler FlowsSteady Solutions of the Vorticity EquationLinear Stability ProblemNormal Mode Equations for Parallel Shear FlowsLinear Stability TheoremsNonlinear Stability TheoremsAndrews' TheoremFlows with Special SymmetriesExercisesThe Charney-Hasegawa-Mima EquationA Derivation of the CHM EquationHamiltonian StructureSteady SolutionsStability of Steady SolutionsSteadily-Travelling SolutionsExercisesThe KdV EquationA Derivation of the KdV EquationHamiltonian StructurePeriodic and Soliton SolutionsVariational PrinciplesLinear Stability Nonlinear StabilityExercises