Introduction to Hamiltonian Fluid Dynamics and Stability Theory

ISBN-13: 9781584880233 / Angielski / Twarda / 1999 / 288 str.

Gordon E. Swaters

Opis

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.

Recenzje

"…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

Spis treści

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

O autorze

Swaters, Gordon E