Swaters (mathematical sciences and Director of the Applied Mathematics Institute, U. of Alberta, Canada) provides an introduction to Hamiltonian fluid dynamics and describes aspects of hydrodynamic stability theory within the context of Hamiltonian formalism. He uses the example of the nonlinear pendulum to introduce many of the ideas associated with the mathematical argument required in infinite dimension Hamiltonian theory needed for fluid mechanics. Topics include Andrew' Theorem, derivation and development of the Charney-Hasegawa-Mima (CMH) equation, an account of the Hamiltonian structure of the Korteweg de Vries (KdV) equation, and discussion of the stability theory associated with the KdV soliton. Adopts a tutorial approach and makes use of plentiful exercises. Annotation c. Book News, Inc., Portland, OR (booknews.com)
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.
