Download or read book The Statistical Mechanics of Ideal Homogeneous Turbulence written by John V. Shebalin and published by . This book was released on 2002 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plasmas, such as those found in the space environment or in plasma confinement devices, are often modeled as electrically conducting fluids. When fluids and plasmas are energetically stirred, regions of highly nonlinear, chaotic behavior known as turbulence arise. Understanding the fundamental nature of turbulence is a long-standing theoretical challenge. The present work describes a statistical theory concerning a certain class of nonlinear, finite dimensional, dynamical models of turbulence. These models arise when the partial differential equations describing incompressible, ideal (i.e., non-dissipative) homogeneous fluid and magnetofluid (i.e., plasma) turbulence are Fourier transformed into a very large set of ordinary differential equations. These equations define a divergenceless flow in a high-dimensional phase space, which allows for the existence of a Lionville theorem, guaranteeing a distribution function based on constants of the motion (integral invariants).
Download or read book The Statistical Mechanics of Ideal Homogeneous Turbulence written by National Aeronautics and Space Administration (NASA) and published by Createspace Independent Publishing Platform. This book was released on 2018-06-15 with total page 132 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plasmas, such as those found in the space environment or in plasma confinement devices, are often modeled as electrically conducting fluids. When fluids and plasmas are energetically stirred, regions of highly nonlinear, chaotic behavior known as turbulence arise. Understanding the fundamental nature of turbulence is a long-standing theoretical challenge. The present work describes a statistical theory concerning a certain class of nonlinear, finite dimensional, dynamical models of turbulence. These models arise when the partial differential equations describing incompressible, ideal (i.e., nondissipative) homogeneous fluid and magnetofluid (i.e., plasma) turbulence are Fourier transformed into a very large set of ordinary differential equations. These equations define a divergenceless flow in a high-dimensional phase space, which allows for the existence of a Liouville theorem, guaranteeing a distribution function based on constants of the motion (integral invariants). The novelty of these particular dynamical systems is that there are integral invariants other than the energy, and that some of these invariants behave like pseudoscalars under two of the discrete symmetry transformations of physics, parity, and charge conjugation. In this work the 'rugged invariants' of ideal homogeneous turbulence are shown to be the only significant scalar and pseudoscalar invariants. The discovery that pseudoscalar invariants cause symmetries of the original equations to be dynamically broken and induce a nonergodic structure on the associated phase space is the primary result presented here. Applicability of this result to dissipative turbulence is also discussed. Shebalin, John V. Johnson Space Center
Download or read book The Statistical Mechanics of Ideal Homogeneous Turbulence written by John V. Shebalin and published by BiblioGov. This book was released on 2013-07 with total page 136 pages. Available in PDF, EPUB and Kindle. Book excerpt: Plasmas, such as those found in the space environment or in plasma confinement devices, are often modeled as electrically conducting fluids. When fluids and plasmas are energetically stirred, regions of highly nonlinear, chaotic behavior known as turbulence arise. Understanding the fundamental nature of turbulence is a long-standing theoretical challenge. The present work describes a statistical theory concerning a certain class of nonlinear, finite dimensional, dynamical models of turbulence. These models arise when the partial differential equations describing incompressible, ideal (i.e., nondissipative) homogeneous fluid and magnetofluid (i.e., plasma) turbulence are Fourier transformed into a very large set of ordinary differential equations. These equations define a divergenceless flow in a high-dimensional phase space, which allows for the existence of a Liouville theorem, guaranteeing a distribution function based on constants of the motion (integral invariants). The novelty of these particular dynamical systems is that there are integral invariants other than the energy, and that some of these invariants behave like pseudoscalars under two of the discrete symmetry transformations of physics, parity, and charge conjugation. In this work the 'rugged invariants' of ideal homogeneous turbulence are shown to be the only significant scalar and pseudoscalar invariants. The discovery that pseudoscalar invariants cause symmetries of the original equations to be dynamically broken and induce a nonergodic structure on the associated phase space is the primary result presented here. Applicability of this result to dissipative turbulence is also discussed.
Download or read book The Statistical Dynamics of Turbulence written by Jovan Jovanovic and published by Springer. This book was released on 2011-12-12 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Homogeneous Isotropic Turbulence written by W. David McComb and published by OUP Oxford. This book was released on 2014-02-27 with total page 429 pages. Available in PDF, EPUB and Kindle. Book excerpt: Fluid turbulence is often referred to as `the unsolved problem of classical physics'. Yet, paradoxically, its mathematical description resembles quantum field theory. The present book addresses the idealised problem posed by homogeneous, isotropic turbulence, in order to concentrate on the fundamental aspects of the general problem. It is written from the perspective of a theoretical physicist, but is designed to be accessible to all researchers in turbulence, both theoretical and experimental, and from all disciplines. The book is in three parts, and begins with a very simple overview of the basic statistical closure problem, along with a summary of current theoretical approaches. This is followed by a precise formulation of the statistical problem, along with a complete set of mathematical tools (as needed in the rest of the book), and a summary of the generally accepted phenomenology of the subject. Part 2 deals with current issues in phenomenology, including the role of Galilean invariance, the physics of energy transfer, and the fundamental problems inherent in numerical simulation. Part 3 deals with renormalization methods, with an emphasis on the taxonomy of the subject, rather than on lengthy mathematical derivations. The book concludes with some discussion of current lines of research and is supplemented by three appendices containing detailed mathematical treatments of the effect of isotropy on correlations, the properties of Gaussian distributions, and the evaluation of coefficients in statistical theories.
Download or read book The Theory of Homogeneous Turbulence written by G. K. Batchelor and published by Cambridge University Press. This book was released on 1953 with total page 216 pages. Available in PDF, EPUB and Kindle. Book excerpt: This is a reissue of Professor Batchelor's text on the theory of turbulent motion, which was first published by Cambridge Unviersity Press in 1953. It continues to be widely referred to in the professional literature of fluid mechanics, but has not been available for several years. This classic account includes an introduction to the study of homogeneous turbulence, including its mathematic representation and kinematics. Linear problems, such as the randomly-perturbed harmonic oscillator and turbulent flow through a wire gauze, are then treated. The author also presents the general dynamics of decay, universal equilibrium theory, and the decay of energy-containing eddies. There is a renewed interest in turbulent motion, which finds applications in atmospheric physics, fluid mechanics, astrophysics, and planetary science.
Download or read book Statistical Mechanics of Turbulent Flows written by Stefan Heinz and published by Springer Science & Business Media. This book was released on 2003-08-04 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: The simulation of turbulent reacting flows, connected with environmental protection and the design of chemical and mechanical processes, is increasingly important. Statistical Mechanics of Turbulent Flows presents a modern overview of basic ways to calculate such flows. It discusses the fundamental problems related to the use of basic equations and their modifications. Special emphasis is placed on the discussion of very promising statistical methods which provide solutions to these problems by models for the underlying stochastic physics of turbulent reacting flows. Their foundations and important new developments up through current challenges are systematically explained. Students and researchers in atmospheric sciences and oceanography, mechanical and chemical engineering and applied mathematics and physics may use Statistical Mechanics of Turbulent Flows as a guide to solve many problems related, e.g. to the assessment of complex atmospheric chemistry, chemical reactor processes, turbulent combustion, and multi-phase flows.
Download or read book Homogeneous Turbulence Dynamics written by Pierre Sagaut and published by Springer. This book was released on 2018-03-23 with total page 912 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides state-of-the-art results and theories in homogeneous turbulence, including anisotropy and compressibility effects with extension to quantum turbulence, magneto-hydodynamic turbulence and turbulence in non-newtonian fluids. Each chapter is devoted to a given type of interaction (strain, rotation, shear, etc.), and presents and compares experimental data, numerical results, analysis of the Reynolds stress budget equations and advanced multipoint spectral theories. The role of both linear and non-linear mechanisms is emphasized. The link between the statistical properties and the dynamics of coherent structures is also addressed. Despite its restriction to homogeneous turbulence, the book is of interest to all people working in turbulence, since the basic physical mechanisms which are present in all turbulent flows are explained. The reader will find a unified presentation of the results and a clear presentation of existing controversies. Special attention is given to bridge the results obtained in different research communities. Mathematical tools and advanced physical models are detailed in dedicated chapters.
Download or read book Statistical Theories of Turbulence written by Chia-Ch'iao Lin and published by Princeton University Press. This book was released on 2017-03-14 with total page 68 pages. Available in PDF, EPUB and Kindle. Book excerpt: Part of the Princeton Aeronautical Paperback series designed to bring to students and research engineers outstanding portions of the twelve-volume High Speed Aerodynamics and Jet Propulsion series. These books have been prepared by direct reproduction of the text from the original series and no attempt has been made to provide introductory material or to eliminate cross reference to other portions of the original volumes. Originally published in 1961. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.
Download or read book Statistical Physics Approaches to Homogeneous and Isotropic Turbulence written by Elias Kohler and published by . This book was released on 2023 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Statistical Approach to Wall Turbulence written by Sedat Tardu and published by John Wiley & Sons. This book was released on 2013-02-07 with total page 234 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wall turbulence is encountered in many technological applications as well as in the atmosphere, and a detailed understanding leading to its management would have considerable beneficial consequences in many areas. A lot of inspired work by experimenters, theoreticians, engineers and mathematicians has been accomplished over recent decades on this important topic and Statistical Approach to Wall Turbulence provides an updated and integrated view on the progress made in this area. Wall turbulence is a complex phenomenon that has several industrial applications, such as in aerodynamics, turbomachinery, geophysical flows, internal engines, etc. Several books exist on fluid turbulence, but Statistical Approach to Wall Turbulence is original in the sense that it focuses solely on the turbulent flows bounded by solid boundaries. The book covers the different physical aspects of wall turbulence, beginning with classical phenomenological aspects before advancing to recent research in the effects of the Reynolds numbers, near wall coherent structures, and wall turbulent transport process. This book would be of interest to postgraduate and undergraduate students in mechanical, chemical, and aerospace engineering, as well as researchers in aerodynamics, combustion, and all applications of wall turbulence.
Download or read book Numerical Experiments in Homogeneous Turbulence written by Robert Sugden Rogallo and published by . This book was released on 1981 with total page 98 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Studies in Turbulence written by Thomas B. Gatski and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 609 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains contributions by former students, colleagues and friends of Professor John L. Lumley, on the occasion of his 60th birthday, in recognition of his enormous impact on the advancement of turbulence research. A variety of experimental, computational and theoretical topics, including turbulence modeling, direct numerical simulations, compressible turbulence, turbulent shear flows, coherent structures and the Proper Orthogonal Decomposition are contained herein. The diversity and scope of these contributions are further acknowledgment of John Lumley's wide ranging influence in the field of turbulence. The large number of contributions by the authors, many of whom were participants in The Lumley Symposium: Recent Developments in Turbulence (held at ICASE, NASA Langley Research Center on November 12 & 13, 1990), has presented us with the unique opportu nity to select a few numerical and theoretical papers for inclusion in the journal Theoretical and Computational Fluid Dynamics for which Professor Lumley serves as Editor. Extended Abstracts of these pa pers are included in this volume and are appropriately marked. The special issue of TCFD will appear this year and will serve as an additional tribute to John Lumley. As is usually the case, the efforts of others have significantly eased our tasks. We would like to express our deep appreciation to Drs. R.
Download or read book Turbulent Flows written by Jean Piquet and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 767 pages. Available in PDF, EPUB and Kindle. Book excerpt: obtained are still severely limited to low Reynolds numbers (about only one decade better than direct numerical simulations), and the interpretation of such calculations for complex, curved geometries is still unclear. It is evident that a lot of work (and a very significant increase in available computing power) is required before such methods can be adopted in daily's engineering practice. I hope to l"Cport on all these topics in a near future. The book is divided into six chapters, each· chapter in subchapters, sections and subsections. The first part is introduced by Chapter 1 which summarizes the equations of fluid mechanies, it is developed in C~apters 2 to 4 devoted to the construction of turbulence models. What has been called "engineering methods" is considered in Chapter 2 where the Reynolds averaged equations al"C established and the closure problem studied (§1-3). A first detailed study of homogeneous turbulent flows follows (§4). It includes a review of available experimental data and their modeling. The eddy viscosity concept is analyzed in §5 with the l"Csulting ~alar-transport equation models such as the famous K-e model. Reynolds stl"Css models (Chapter 4) require a preliminary consideration of two-point turbulence concepts which are developed in Chapter 3 devoted to homogeneous turbulence. We review the two-point moments of velocity fields and their spectral transforms (§ 1), their general dynamics (§2) with the particular case of homogeneous, isotropie turbulence (§3) whel"C the so-called Kolmogorov's assumptions are discussed at length.
Download or read book Statistical Fluid Mechanics Volume I written by A. S. Monin and published by Dover Publications. This book was released on 2007-05-11 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: "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 working in the fields of turbulence, oceanography, and atmospheric physics, this two-volume survey is renowned for its clarity as well as its comprehensive treatment. Volume One 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.
Download or read book Statistical Theory and Modeling for Turbulent Flows written by P. A. Durbin and published by John Wiley & Sons. This book was released on 2011-06-28 with total page 347 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Download or read book Turbulence in Fluids written by Marcel Lesieur and published by Springer. This book was released on 1990-10-31 with total page 456 pages. Available in PDF, EPUB and Kindle. Book excerpt: Turbulence is a dangerous topic which is often at the origin of serious fights in the scientific meetings devoted to it since it represents extremely different points of view, all of which have in common their complexity, as well as an inability to solve the problem. It is even difficult to agree on what exactly is the problem to be solved. Extremely schematically, two opposing points of view have been advocated during these last ten years: the first one is "statistical", and tries to model the evolution of averaged quantities of the flow. This com has followed the glorious trail of Taylor and Kolmogorov, munity, which believes in the phenomenology of cascades, and strongly disputes the possibility of any coherence or order associated to turbulence. On the other bank of the river stands the "coherence among chaos" community, which considers turbulence from a purely deterministic po int of view, by studying either the behaviour of dynamical systems, or the stability of flows in various situations. To this community are also associated the experimentalists who seek to identify coherent structures in shear flows.
