Mathematics Applied to Fluid Mechanics and Stability
Author: Donald A. Drew
Publisher: SIAM
Published: 1986-01-01
Total Pages: 316
ISBN-13: 9780898712087
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Author: Donald A. Drew
Publisher: SIAM
Published: 1986-01-01
Total Pages: 316
ISBN-13: 9780898712087
DOWNLOAD EBOOKAuthor: Gordon E Swaters
Publisher: Routledge
Published: 2019-01-22
Total Pages: 290
ISBN-13: 1351436961
DOWNLOAD EBOOKHamiltonian 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.
Author: J. E. Flaherty
Publisher:
Published: 1986
Total Pages: 295
ISBN-13:
DOWNLOAD EBOOKAuthor: P. G. Drazin
Publisher: Cambridge University Press
Published: 2002-09-09
Total Pages: 278
ISBN-13: 1316582876
DOWNLOAD EBOOKInstability of flows and their transition to turbulence are widespread phenomena in engineering and the natural environment, and are important in applied mathematics, astrophysics, biology, geophysics, meteorology, oceanography and physics as well as engineering. This is a textbook to introduce these phenomena at a level suitable for a graduate course, by modelling them mathematically, and describing numerical simulations and laboratory experiments. The visualization of instabilities is emphasized, with many figures, and in references to more still and moving pictures. The relation of chaos to transition is discussed at length. Many worked examples and exercises for students illustrate the ideas of the text. Readers are assumed to be fluent in linear algebra, advanced calculus, elementary theory of ordinary differential equations, complex variables and the elements of fluid mechanics. The book is aimed at graduate students but will also be very useful for specialists in other fields.
Author: A. J. Chorin
Publisher: Springer Science & Business Media
Published: 2012-12-06
Total Pages: 213
ISBN-13: 1468400827
DOWNLOAD EBOOKThese 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, Berkeley during the Spring of 1978. The goal of the course was not to provide an exhaustive account of fluid mechanics, nor to assess the engineering value of various approxima tion procedures. The goals were: (i) to present some of the basic ideas of fluid mechanics in a mathematically attractive manner (which does not mean "fully rigorous"); (ii) to present the physical back ground and motivation for some constructions which have been used in recent mathematical and numerical work on the Navier-Stokes equations and on hyperbolic systems; (iil. ) 'to interest some of the students in this beautiful and difficult subject. The notes are divided into three chapters. The first chapter contains an elementary derivation of the equations; the concept of vorticity is introduced at an early stage. The second chapter contains a discussion of potential flow, vortex motion, and boundary layers. A construction of boundary layers using vortex sheets and random walks is presented; it is hoped that it helps to clarify the ideas. The third chapter contains an analysis of one-dimensional gas iv flow, from a mildly modern point of view. Weak solutions, Riemann problems, Glimm's scheme, and combustion waves are discussed. The style is informal and no attempt was made to hide the authors' biases and interests.
Author: Jose Francisco Rodrigues
Publisher: CRC Press
Published: 2020-10-02
Total Pages: 280
ISBN-13: 1000115232
DOWNLOAD EBOOKThis Research Note presents several contributions and mathematical studies in fluid mechanics, namely in non-Newtonian and viscoelastic fluids and on the Navier-Stokes equations in unbounded domains. It includes review of the mathematical analysis of incompressible and compressible flows and results in magnetohydrodynamic and electrohydrodynamic stability and thermoconvective flow of Boussinesq-Stefan type. These studies, along with brief communications on a variety of related topics comprise the proceedings of a summer course held in Lisbon, Portugal in 1991. Together they provide a set of comprehensive survey and advanced introduction to problems in fluid mechanics and partial differential equations.
Author: P. G. Drazin
Publisher: Cambridge University Press
Published: 2002-09-09
Total Pages: 284
ISBN-13: 9780521009652
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Author: P. G. Drazin
Publisher: Cambridge University Press
Published: 2004-08-05
Total Pages: 630
ISBN-13: 9780521525411
DOWNLOAD EBOOKHydrodynamic stability is of fundamental importance in fluid mechanics and is concerned with the problem of transition from laminar to turbulent flow. Drazin and Reid emphasise throughout the ideas involved, the physical mechanisms, the methods used, and the results obtained, and, wherever possible, relate the theory to both experimental and numerical results. A distinctive feature of the book is the large number of problems it contains. These problems not only provide exercises for students but also provide many additional results in a concise form. This new edition of this celebrated introduction differs principally by the inclusion of detailed solutions for those exercises, and by the addition of a Foreword by Professor J. W. Miles.
Author: Tomáš Bodnár
Publisher: Springer Nature
Published:
Total Pages: 376
ISBN-13: 3031473558
DOWNLOAD EBOOKAuthor: Herbert Amann
Publisher: Birkhäuser
Published: 2016-03-17
Total Pages: 478
ISBN-13: 3034809395
DOWNLOAD EBOOKThe aim of this proceeding is addressed to present recent developments of the mathematical research on the Navier-Stokes equations, the Euler equations and other related equations. In particular, we are interested in such problems as: 1) existence, uniqueness and regularity of weak solutions2) stability and its asymptotic behavior of the rest motion and the steady state3) singularity and blow-up of weak and strong solutions4) vorticity and energy conservation5) fluid motions around the rotating axis or outside of the rotating body6) free boundary problems7) maximal regularity theorem and other abstract theorems for mathematical fluid mechanics.