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The Statistical Dynamics Of Turbulence

Author: Jovan Jovanovic
Publisher: Springer Science & Business Media
ISBN: 3662104113
Size: 16.65 MB
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This short but complicated book is very demanding of any reader. The scope and style employed preserve the nature of its subject: the turbulence phe nomena in gas and liquid flows which are believed to occur at sufficiently high Reynolds numbers. Since at first glance the field of interest is chaotic, time-dependent and three-dimensional, spread over a wide range of scales, sta tistical treatment is convenient rather than a description of fine details which are not of importance in the first place. When coupled to the basic conserva tion laws of fluid flow, such treatment, however, leads to an unclosed system of equations: a consequence termed, in the scientific community, the closure problem. This is the central and still unresolved issue of turbulence which emphasizes its chief peculiarity: our inability to do reliable predictions even on the global flow behavior. The book attempts to cope with this difficult task by introducing promising mathematical tools which permit an insight into the basic mechanisms involved. The prime objective is to shed enough light, but not necessarily the entire truth, on the turbulence closure problem. For many applications it is sufficient to know the direction in which to go and what to do in order to arrive at a fast and practical solution at minimum cost. The book is not written for easy and attractive reading.

Non Equilibrium Statistical Mechanics And Turbulence

Author: John Cardy
Publisher: Cambridge University Press
ISBN: 9780521715140
Size: 37.54 MB
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This self-contained volume introduces modern methods of statistical mechanics in turbulence, with three harmonised lecture courses by world class experts.

Statistical Mechanics Of Turbulent Flows

Author: Stefan Heinz
Publisher: Springer Science & Business Media
ISBN: 3662100223
Size: 21.86 MB
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The simulation of technological and environmental flows is very important for many industrial developments. A major challenge related to their modeling is to involve the characteristic turbulence that appears in most of these flows. The traditional way to tackle this question is to use deterministic equations where the effects of turbulence are directly parametrized, i. e. , assumed as functions of the variables considered. However, this approach often becomes problematic, in particular if reacting flows have to be simulated. In many cases, it turns out that appropriate approximations for the closure of deterministic equations are simply unavailable. The alternative to the traditional way of modeling turbulence is to construct stochastic models which explain the random nature of turbulence. The application of such models is very attractive: one can overcome the closure problems that are inherent to deterministic methods on the basis of relatively simple and physically consistent models. Thus, from a general point of view, the use of stochastic methods for turbulence simulations seems to be the optimal way to solve most of the problems related to industrial flow simulations. However, it turns out that this is not as simple as it looks at first glance. The first question concerns the numerical solution of stochastic equations for flows of environmental and technological interest. To calculate industrial flows, 3 one often has to consider a number of grid cells that is of the order of 100 .

Statistical Fluid Mechanics

Author: Andre? Sergeevich Monin
Publisher: Courier Corporation
ISBN: 0486458830
Size: 49.96 MB
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"If ever a book on turbulence could be called definitive," declared Science, "it is this book by two of Russia's most eminent and productive scientists in turbulence, oceanography, and atmospheric physics." Noted for its clarity as well as its comprehensive treatment, this two-volume set serves as text or reference. 1971 edition.

The Statistical Mechanics Of Financial Markets

Author: Johannes Voit
Publisher: Springer Science & Business Media
ISBN: 3662051257
Size: 25.30 MB
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This textbook describes parallels between statistical physics and finance - both those established in the 100-year-long interaction between these disciplines, as well as new research results on capital markets. The random walk, well known in physics, is also the basic model in finance, upon which are built, for example, the Black--Scholes theory of option pricing and hedging, or methods of risk control using diversification. Here the underlying assumptions are discussed using empirical financial data and analogies to physical models such as fluid flows, turbulence, or superdiffusion. On this basis, new theories of derivative pricing and risk control can be formulated. Computer simulations of interacting agent models of financial markets provide insights into the origins of asset price fluctuations. Stock exchange crashes can be modelled in ways analogous to phase transitions and earthquakes. These models allow for predictions. This study edition has been updated with a presentation of several new and significant developments, e.g. the dynamics of volatility smiles and implied volatility surfaces, path integral approaches to option pricing, a new and accurate simulation scheme for options, multifractals, the application of nonextensive statistical mechanics to financial markets, and the minority game. Moreover, the book was scanned for and corrected from errors, both typographical and in presentation.

Statistical Turbulence Modelling For Fluid Dynamics Demystified

Author: Michael Leschziner
Publisher: World Scientific
ISBN: 1783266635
Size: 10.33 MB
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This book is intended for self-study or as a companion of lectures delivered to post-graduate students on the subject of the computational prediction of complex turbulent flows. There are several books in the extensive literature on turbulence that deal, in statistical terms, with the phenomenon itself, as well its many manifestations in the context of fluid dynamics. Statistical Turbulence Modelling for Fluid Dynamics — Demystified differs from these and focuses on the physical interpretation of a broad range of mathematical models used to represent the time-averaged effects of turbulence in computational prediction schemes for fluid flow and related transport processes in engineering and the natural environment. It dispenses with complex mathematical manipulations and instead gives physical and phenomenological explanations. This approach allows students to gain a 'feel' for the physical fabric represented by the mathematical structure that describes the effects of turbulence and the models embedded in most of the software currently used in practical fluid-flow predictions, thus counteracting the ill-informed black-box approach to turbulence modelling. This is done by taking readers through the physical arguments underpinning exact concepts, the rationale of approximations of processes that cannot be retained in their exact form, and essential calibration steps to which the resulting models are subjected by reference to theoretically established behaviour of, and experimental data for, key canonical flows. Contents: Statistical Viewpoint of Turbulence — Motivation and RationaleWhat Makes Turbulence Tick?Reynolds-AveragingFundamentals of Stress / Strain InteractionFundamentals of Near-Wall InteractionsFundamentals of Scalar-Flux / Scalar-Gradient InteractionsThe Eddy ViscosityOne-Equation Eddy-Viscosity ModelsTwo-Equation ModelsWall Functions For Linear Eddy-Viscosity ModelsDefects of Linear Eddy-Viscosity Models, Their Sources and (Imperfect) Corrections Reynolds-Stress-Transport ModellingScalar/Heat-Flux-Ttransport ModellingThe ¯υ2 — ƒ ModelAlgebraic Reynolds-Stress and Non-Linear Eddy-Viscosity Models Readership: Researchers and post-graduate students in the field of fluid dynamics. Key Features:Emphasis on physical and phenomenological interpretationBroad range of models coveredStrong emphasis on understanding the concepts and the rationale behind assumptionsAvoidance of mathematical complexity that does not serve the objective of conveying understanding and insightKeywords:Turbulence Modeling;Rans;Computational Fluid Dynamics;Single Point Closure

Statistical Theory And Modeling For Turbulent Flows

Author: P. A. Durbin
Publisher: John Wiley & Sons
ISBN: 1119957524
Size: 77.49 MB
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Providing a comprehensive grounding in the subject of turbulence, Statistical Theory and Modeling for Turbulent Flows develops both the physical insight and the mathematical framework needed to understand turbulent flow. Its scope enables the reader to become a knowledgeable user of turbulence models; it develops analytical tools for developers of predictive tools. Thoroughly revised and updated, this second edition includes a new fourth section covering DNS (direct numerical simulation), LES (large eddy simulation), DES (detached eddy simulation) and numerical aspects of eddy resolving simulation. In addition to its role as a guide for students, Statistical Theory and Modeling for Turbulent Flows also is a valuable reference for practicing engineers and scientists in computational and experimental fluid dynamics, who would like to broaden their understanding of fundamental issues in turbulence and how they relate to turbulence model implementation. Provides an excellent foundation to the fundamental theoretical concepts in turbulence. Features new and heavily revised material, including an entire new section on eddy resolving simulation. Includes new material on modeling laminar to turbulent transition. Written for students and practitioners in aeronautical and mechanical engineering, applied mathematics and the physical sciences. Accompanied by a website housing solutions to the problems within the book.

Statistical Fluid Mechanics Volume Ii

Author: A. S. Monin
Publisher: Courier Corporation
ISBN: 0486318141
Size: 19.20 MB
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"If ever a field needed a definitive book, it is the study of turbulence; if ever a book on turbulence could be called definitive, it is this book." — Science Written by two of Russia's most eminent and productive scientists in turbulence, oceanography, and atmospheric physics, this two-volume survey is renowned for its clarity as well as its comprehensive treatment. The first volume begins with an outline of laminar and turbulent flow. The remainder of the book treats a variety of aspects of turbulence: its statistical and Lagrangian descriptions, shear flows near surfaces and free turbulence, the behavior of thermally stratified media, and diffusion. Volume Two continues and concludes the presentation. Topics include spectral functions, homogeneous fields, isotropic random fields, isotropic turbulence, self-preservation hypotheses, spectral energy transfer, the Millionshchikov hypothesis, acceleration fields, equations for higher moments and the closure problem, and turbulence in a compressible fluid. Additional subjects include general concepts of the local structure of turbulence at high Reynolds numbers, the theory of fully developed turbulence, the propagation of electromagnetic and acoustic waves through a turbulent medium, and the twinkling of stars. The book closes with a discussion of the functional formulation of the problem of turbulence, presenting the equations for the characteristic functional and methods for their solution.

Atmospheric Turbulence

Author: Adrian F. Tuck
Publisher: OUP Oxford
ISBN: 0191553123
Size: 15.60 MB
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This book, authored by a well-known researcher and expositor in meteorology, focuses on the direct link between molecular dynamics and atmospheric variation. Uniting molecular dynamics, turbulence theory, fluid mechanics and non equilibrium statistical mechanics, it is relevant to the fields of applied mathematics, physics and atmospheric sciences, and focuses on fluid flow and turbulence, as well as on temperature, radiative transfer and chemistry. With extensive references and glossary this is an ideal text for graduates and researchers in meteorology, applied mathematics and physical chemistry.