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.
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