Introduction to Hamiltonian Fluid Dynamics and Stability Theory

Introduction to Hamiltonian Fluid Dynamics and Stability Theory offers a comprehensive introduction to Hamiltonian fluid dynamics and describes aspects of hydrodynamic stability theory within the context of the Hamiltonian formalism.

List of contents

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

About the author

Swaters, Gordon E

Summary

Introduction to Hamiltonian Fluid Dynamics and Stability Theory offers a comprehensive introduction to Hamiltonian fluid dynamics and describes aspects of hydrodynamic stability theory within the context of the Hamiltonian formalism.

Product details

• Authors: Gordon E Swaters, Gordon E. Swaters
• Assisted by: Haim Brezis (Editor of the series), Ronald G. Douglas (Editor of the series), Alan Jeffrey (Editor of the series)
• Publisher: Taylor and Francis
• Languages: English
• Product format: Hardback
• Released: 29.09.1999
• EAN: 9781584880233
• ISBN: 978-1-58488-023-3
• No. of pages: 288
• Weight: 690 g
• Series: Monographs and Surveys in Pure and Applied Mathematics
• Subjects: Natural sciences, medicine, IT, technology > Mathematics > Miscellaneous; TECHNOLOGY & ENGINEERING / Mechanical, MATHEMATICS / Applied, SCIENCE / Mechanics / Fluids, SCIENCE / Physics / Optics & Light, Optical physics, Fluid mechanics, Mechanics of fluids, Maths for scientists, Maths for engineers, Physics: Fluid mechanics, Engineering: Mechanics of fluids