The book describes Fluid Dynamics, Magnetohydrodynamics, and Classical Thermodynamics as branches of Lagrange’s Analytical Mechanics. The approach presented is markedly different from the treatment given to them in traditional text books. A Hamilton-Type Variational Principle as the proper mathematical technique for the theoretical description of the dynamic state of any fluid is formulated. The scheme is completed proposing a new group of variations regarding the evolution parameter.
This revised, updated edition provides a comprehensive and rigorous description of the application of Hamilton’s principle to continuous media. To introduce terminology and initial concepts, it begins with what is called the first problem of the calculus of variations. For both historical and pedagogical reasons, it first discusses the application of the principle to systems of particles, including conservative and non-conservative systems and systems with constraints. The foundations of mechanics of continua are introduced in the context of inner product spaces. With this basis, the application of Hamilton’s principle to the classical theories of fluid and solid mechanics are covered. Then recent developments are described, including materials with microstructure, mixtures, and continua with singular surfaces.
Hamilton's principle of mechanics governs the motion of the geophysical fluids. As a statement of dynamical law, it has the following practical advantages over the more conventional Eulerian formulation of fluid dynamics: This paper will demonstrate how Hamilton's principle permits useful numerical approximations to the equations governing the motion of a shallow rotating fluid blob. Salmon (1982) used a similar model system for a numerical study of the ocean's main thermocline. However, the methods described here are distinctly superior to those of the earlier paper. The new methods generalize easily to continuously stratified and multi-layer flows.
This revised, updated edition provides a comprehensive and rigorous description of the application of Hamilton's principle to continuous media. To introduce terminology and initial concepts, it begins with what is called the first problem of the calculus of variations. For both historical and pedagogical reasons, it first discusses the application of the principle to systems of particles, including conservative and non-conservative systems and systems with constraints. The foundations of mechanics of continua are introduced in the context of inner product spaces. With this basis, the application of Hamilton's principle to the classical theories of fluid and solid mechanics are covered. Then recent developments are described, including materials with microstructure, mixtures, and continua with singular surfaces. Presents a comprehensive, rigorous description of the application of Hamilton's principle to continuous media; Includes recent applications of the principle to continua with microstructure, mixtures, and media with surfaces of discontinuity; Discusses foundations of continuum mechanics and variational methods therein in the context of linear vector spaces.
Given a conservative dynamical system of classical physics, how does one find a variational principle for it? Is there a canonical recipe for such a principle? The case of particle mechanics was settled by Lagrange in 1788; this text treats continuous systems. Recipes devised are algebraic in nature, and this book develops all the mathematical tools found necessary after the minute examination of the adiabatic fluid dynamics in the introduction. These tools include: Lagrangian and Hamiltonian formalisms, Legendre transforms, dual spaces of Lie algebras and associated 2-cocycles; and linearized and Z2-graded versions of all of these. The following typical physical systems, together with their Hamiltonian structures, are discussed: Classical Magnetohydro-dynamics with its Hall deformation; Multifluid Plasma; Superfluid He-4 (both irrotational and rotating) and 3He-A; Quantum fluids; Yang-Mills MHD; Spinning fluids; Spin Glass; Extended YM Plasma; A Lattice Gas. Detailed motivations, easy-to-follow arguments, open problems, and over 300 exercises help the reader. Request Inspection Copy
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.
Energy Optimization in Process Systems and Fuel Cells, Second Edition covers the optimization and integration of energy systems, with a particular focus on fuel cell technology. With rising energy prices, imminent energy shortages, and increasing environmental impacts of energy production, energy optimization and systems integration is critically important. The book applies thermodynamics, kinetics and economics to study the effect of equipment size, environmental parameters, and economic factors on optimal power production and heat integration. Author Stanislaw Sieniutycz, highly recognized for his expertise and teaching, shows how costs can be substantially reduced, particularly in utilities common in the chemical industry. This second edition contains substantial revisions, with particular focus on the rapid progress in the field of fuel cells, related energy theory, and recent advances in the optimization and control of fuel cell systems. - New information on fuel cell theory, combined with the theory of flow energy systems, broadens the scope and usefulness of the book - Discusses engineering applications including power generation, resource upgrading, radiation conversion, and chemical transformation in static and dynamic systems - Contains practical applications of optimization methods that help solve the problems of power maximization and optimal use of energy and resources in chemical, mechanical, and environmental engineering
This self-contained book provides an introduction to the flow-oscillator modeling of vortex-induced bluff-body oscillations. One of the great challenges in engineering science also happens to be one of engineering design – the modeling, analysis and design of vibrating structures driven by fluid motion. The literature on fluid–structure interaction is vast, and it can be said to comprise a large fraction of all papers published in the mechanical sciences. This book focuses on the vortex-induced oscillations of an immersed body, since, although the importance of the subject has long been known, it is only during the past fifty years that there have been concerted efforts to analytically model the general behavior of the coupling between vortex shedding and structural oscillations. At the same time, experimentalists have been gathering data on such interactions in order to help define the various regimes of behavior. This data is critical to our understanding and to those who develop analytical models, as can be seen in this book. The fundamental bases for the modeling developed in this book are the variational principles of analytical dynamics, in particular Hamilton’s principle and Jourdain’s principle, considered great intellectual achievements on par with Newton’s laws of motion. Variational principles have been applied in numerous disciplines, including dynamics, optics and quantum mechanics. Here, we apply variational principles to the development of a framework for the modeling of flow-oscillator models of vortex-induced oscillations.
