Introduction to Hamiltonian Fluid Dynamics and Stability Theory

✍ Scribed by Swaters, Gordon E.

• Publisher: Routledge
• Year: 2018
• Tongue: English
• Leaves: 287
• Series: Monographs and Surveys in Pure and Applied Mathematics.
• Category: Library

✦ Table of Contents

Cover
Half Title
Title Page
Copyright Page
Dedication
Table of Contents
About the author
Acknowledgments
1: Introduction
2: The nonlinear pendulum
2.1 Model formulation
2.2 Canonical Hamiltonian formulation
2.3 Least Action Principle
2.4 Symplectic Hamiltonian formulation
2.5 Mathematical properties of the J matrix
2.6 Poisson bracket formulation
2.7 Steady solutions of a canonical Hamiltonian system
2.8 Linear stability of a steady solution
2.9 Nonlinear stability of a steady solution
3: The two dimensional Euler equations
3.1 Vorticity equation formulation 3.2 Hamiltonian structure for partial differential equations3.3 Hamiltonian structure of the Euler equations
3.4 Reduction of the canonical Poisson bracket
3.5 Casimir functionals
3.6 Noether's Theorem
3.7 Exercises
4: Stability of steady Euler flows
4.1 Steady solutions of the vorticity equation
4.2 Linear stability problem
4.3 Normal mode equations for parallel shear flows
4.4 Linear stability theorems
4.5 Nonlinear stability theorems
4.6 Andrews's Theorem
4.7 Flows with special symmetries
4.8 Exercises
5: The Charney-Hasegawa-Mima equation 5.1 A derivation of the CHM equation5.2 Hamiltonian structure
5.3 Steady solutions
5.4 Stability of steady solutions
5.5 Steadily-travelling solutions
5.6 Exercises
6: The KdV equation
6.1 A derivation of the KdV equation
6.2 Hamiltonian structure
6.3 Periodic and soliton solutions
6.4 Variational principles
6.5 Linear stability
6.6 Nonlinear stability
6.7 Exercises
References
Index