Gordon E Swaters

Introduction to Hamiltonian Fluid Dynamics and Stability Theory (eBook, ePUB)

• Format: ePub

Produktbeschreibung

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.

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Produktdetails

• Verlag: Taylor & Francis eBooks
• Seitenzahl: 288
• Erscheinungstermin: 22. Januar 2019
• Englisch
• ISBN-13: 9781351436960
• Artikelnr.: 54969586

Autorenporträt

Swaters, Gordon E

Inhaltsangabe

Introduction The Nonlinear Pendulum Model Formulation Canonical Hamiltonian
Formulation Least Action Principle Symplectic Hamiltonian Formulation
Mathematical Properties of the J Matrix Poisson Bracket Formulation Steady
Solutions of a Canonical Hamiltonian System Linear Stability of a Steady
Solution Nonlinear Stability of a Steady Solution The Two Dimensional Euler
Equations Vorticity Equation Formulation Hamiltonian Structure for Partial
Differential Equations Hamiltonian Structure of the Euler Equations
Reduction of the Canonical Poisson Bracket Casimir Functionals and
Noether's Theorem Exercises Stability of Steady Euler Flows Steady
Solutions of the Vorticity Equation Linear Stability Problem Normal Mode
Equations for Parallel Shear Flows Linear Stability Theorems Nonlinear
Stability Theorems Andrews' Theorem Flows with Special Symmetries Exercises
The Charney-Hasegawa-Mima Equation A Derivation of the CHM Equation
Hamiltonian Structure Steady Solutions Stability of Steady Solutions
Steadily-Travelling Solutions Exercises The KdV Equation A Derivation of
the KdV Equation Hamiltonian Structure Periodic and Soliton Solutions
Variational Principles Linear Stability Nonlinear Stability Exercises