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Author: Boris A. Trubnikov
Publisher: CRC Press
ISBN: 9780849328749
Category : Science
Languages : en
Pages : 228
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Book Description
For the first time, exact analytical solutions are available for some of the most interesting types of problems arising in physics and applied mathematics. Hydrodynamics of Unstable Media outlines the theory of "quasi-gaseous" unstable media, and demonstrates how the theory can be used to obtain analytical solutions. Until now, the solutions to many of the examples considered in this new book have been numerical or partial solutions. By developing a new theory of hydrodynamics for unstable media, the authors provide a means for scientists and mathematicians to solve problems exactly and analytically. Solutions to some 50 problems are provided! Hydrodynamics of Unstable Media features interdisciplinary discussions by internationally recognized authors.
Author: Boris A. Trubnikov
Publisher: CRC Press
ISBN: 9780849328749
Category : Science
Languages : en
Pages : 228
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Book Description
For the first time, exact analytical solutions are available for some of the most interesting types of problems arising in physics and applied mathematics. Hydrodynamics of Unstable Media outlines the theory of "quasi-gaseous" unstable media, and demonstrates how the theory can be used to obtain analytical solutions. Until now, the solutions to many of the examples considered in this new book have been numerical or partial solutions. By developing a new theory of hydrodynamics for unstable media, the authors provide a means for scientists and mathematicians to solve problems exactly and analytically. Solutions to some 50 problems are provided! Hydrodynamics of Unstable Media features interdisciplinary discussions by internationally recognized authors.
Author: Jean Pierre Hulin
Publisher: North Holland
ISBN:
Category : Science
Languages : en
Pages : 322
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Book Description
The purpose of the 4th meeting of the liquid section of the European Physical Society was to contribute to a better communication between different scientific communities of fundamental and applied sciences dealing with random structures and processes. This should lead to an awareness of the relationship between geometries at different scales and physical behaviors. The papers presented here show how one can go from a microscopic description to a phenomenological one by using hydrodynamical treatments and statistical ones (when disorder is present) as the mediators in this process of change of scales. This permits one to change from the microscopic description of a spreading drop at the nanometer scale to the study of a foam or of the wetting in random materials. In the same way, one can go from the microscopic properties at the interface of two fluids to the macroscopic dispersion behavior or from the interaction between two particles (or between a particle and a surface) to the rheology of a suspension.
Author: George H. Fichtl
Publisher:
ISBN:
Category : Atmospheric circulation
Languages : en
Pages : 180
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Book Description
The stability to small perturbations of shear layer and jet flows (z) in atmospheres with potential temperature (z) is investigated. The problem is reduced to a chardcteristic value problem for the dimensionless wave frequency v which appears in a second-order differential equation with the dependent variable being the horizontal and temporal Fourier transform amplitude of the vertical component of the perturbation momentum vector. Broken-line profiles of E(z) and (z) are used in the analysis of this problem. Integral equations, over the domain of the fluid, which contain both quadratic forms and interfacial contributions, are derived. The interfacial terms vanish for continuous flows, and the theorems of Synge, Howard, and Miles follow. A necessary and sufficient condition for instability is also obtained for continuous flows; however, its usefulness is compromised by integrands which depend on both the basic state flow and the dependent variable of the governing differential equation.
Author: A. Georgescu
Publisher: Springer Science & Business Media
ISBN: 9401718148
Category : Mathematics
Languages : en
Pages : 306
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Book Description
The great number of varied approaches to hydrodynamic stability theory appear as a bulk of results whose classification and discussion are well-known in the literature. Several books deal with one aspect of this theory alone (e.g. the linear case, the influence of temperature and magnetic field, large classes of globally stable fluid motions etc.). The aim of this book is to provide a complete mathe matical treatment of hydrodynamic stability theory by combining the early results of engineers and applied mathematicians with the recent achievements of pure mathematicians. In order to ensure a more operational frame to this theory I have briefly outlined the main results concerning the stability of the simplest types of flow. I have attempted several definitions of the stability of fluid flows with due consideration of the connections between them. On the other hand, as the large number of initial and boundary value problems in hydrodynamic stability theory requires appropriate treat ments, most of this book is devoted to the main concepts and methods used in hydrodynamic stability theory. Open problems are expressed in both mathematical and physical terms.
Author: Felix V. Dolzhansky
Publisher: Springer Science & Business Media
ISBN: 3642310338
Category : Mathematics
Languages : en
Pages : 266
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Book Description
This newly-translated book takes the reader from the basic principles and conservation laws of hydrodynamics to the description of general atmospheric circulation. Among the topics covered are the Kelvin, Ertel and Rossby-Obukhov invariants, quasi-geostrophic equation, thermal wind, singular Helmholtz vortices, derivation of the Navier-Stokes equation, Kolmogorov's flow, hydrodynamic stability, and geophysical boundary layers. Generalizing V. Arnold's approach to hydrodynamics, the author ingeniously brings in an analogy of Coriolis forces acting on fluid with motion of the Euler heavy top and shows how this is used in the analysis of general atmospheric circulation. This book is based on popular graduate and undergraduate courses given by F.V.Dolzhansky at the Moscow Institute of Physics and Technology, and is the result of the author's highly acclaimed work in Moscow's Laboratory of Geophysical Hydrodynamics. Each chapter is full of examples and figures, exercises and hints, motivating and illustrating both theoretical and experimental results. The exposition is comprehensive yet user-friendly in engaging and exploring the broad range of topics for students and researchers in mathematics, physics, meteorology and engineering.
Author: George Pavlov
Publisher: Cambridge Scholars Publishing
ISBN: 1527540634
Category : Science
Languages : en
Pages : 212
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Book Description
This book develops a theory of the nonlinear response of densely charged and neutral media to electric and electromagnetic fields and gradients of hydrodynamic variables. It considers phenomena related to the nonlinear response of the media to plasma echo, transformation of waves, and parametric and second harmonic generation of radiation, and determines exact expressions and calculation methods for Burnett transport coefficients describing heat, mass, momentum and charge flows. It also discusses the use of transport coefficients in hydrodynamic tasks outside the framework of Euler’s theorem on homogeneous functions. It analyses in detail the thermal regimes calculated using linear and non-linear transport coefficients in the cavity of a gas-phase nuclear reactor, and in the shock layer of a spacecraft moving in the atmosphere of Mars during a soft landing on the planet. The book will appeal to researchers, as well as postgraduate and undergraduate students, working and specializing in the field of physics and gas dynamics of densely charged and neutral media characterized by chemical reactions.
Author: P. G. Drazin
Publisher: Cambridge University Press
ISBN: 9780521525411
Category : Mathematics
Languages : en
Pages : 630
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Book Description
Hydrodynamic 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: Nikolay Nikolaevich Fimin
Publisher: World Scientific
ISBN: 9811211175
Category : Science
Languages : en
Pages : 295
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Book Description
This book studies the fundamental concept of hydrodynamics as part of theoretical physics and demonstrates the connection of macroscopic approach with the description of properties of fluid motion and microscopic kinetic theory. It also presents recent investigations in instabilities and turbulence theory.
Author: Akiva M. Yaglom
Publisher: Springer Science & Business Media
ISBN: 9400742371
Category : Technology & Engineering
Languages : en
Pages : 611
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Book Description
This book is a complete revision of the part of Monin & Yaglom's famous two-volume work "Statistical Fluid Mechanics: Mechanics of Turbulence" that deals with the theory of laminar-flow instability and transition to turbulence. It includes the considerable advances in the subject that have been made in the last 15 years or so. It is intended as a textbook for advanced graduate courses and as a reference for research students and professional research workers. The first two Chapters are an introduction to the mathematics, and the experimental results, for the instability of laminar (or inviscid) flows to infinitesimal (in practice "small") disturbances. The third Chapter develops this linear theory in more detail and describes its application to particular problems. Chapters 4 and 5 deal with instability to finite-amplitude disturbances: much of the material has previously been available only in research papers.
Author:
Publisher:
ISBN:
Category : Physics
Languages : en
Pages : 454
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Book Description
