Introduction to Hamiltonian Fluid Dynamics and Stability Theory

Introduction to Hamiltonian Fluid Dynamics and Stability Theory
Author :
Publisher : Routledge
Total Pages : 290
Release :
ISBN-10 : 9781351436960
ISBN-13 : 1351436961
Rating : 4/5 (60 Downloads)

Book Synopsis Introduction to Hamiltonian Fluid Dynamics and Stability Theory by : Gordon E Swaters

Download or read book Introduction to Hamiltonian Fluid Dynamics and Stability Theory written by Gordon E Swaters and published by Routledge. This book was released on 2019-01-22 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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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These notes are based on a one-quarter (i. e. very short) course in fluid mechanics taught in the Department of Mathematics of the University of California, Ber