Introduction to Hamiltonian Fluid Dynamics and Stability Theory

Introduction to Hamiltonian Fluid Dynamics and Stability Theory

by Gordon E Swaters

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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

Product Details

ISBN-13: 9781351436960
Publisher: CRC Press
Publication date: 01/22/2019
Sold by: Barnes & Noble
Format: NOOK Book
Pages: 288
File size: 10 MB

About the Author

Swaters, Gordon E

Table of Contents

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
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
The Charney-Hasegawa-Mima Equation
A Derivation of the CHM Equation
Hamiltonian Structure
Steady Solutions
Stability of Steady Solutions
Steadily-Travelling Solutions
The KdV Equation
A Derivation of the KdV Equation
Hamiltonian Structure
Periodic and Soliton Solutions
Variational Principles
Linear Stability Nonlinear Stability

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