The Kolmogorov Obukhov Theory Of Turbulence

Author : Bjorn Birnir
Publisher : Springer Science & Business Media
Page : 117 pages
File Size : 53,9 Mb
Release : 2013-01-31
Category : Mathematics
ISBN : 9781461462620

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The Kolmogorov-Obukhov Theory of Turbulence by Bjorn Birnir Pdf

​​​​​​​Turbulence is a major problem facing modern societies. It makes airline passengers return to their seats and fasten their seatbelts but it also creates drag on the aircraft that causes it to use more fuel and create more pollution. The same applies to cars, ships and the space shuttle. The mathematical theory of turbulence has been an unsolved problems for 500 years and the development of the statistical theory of the Navier-Stokes equations describes turbulent flow has been an open problem. The Kolmogorov-Obukhov Theory of Turbulence develops a statistical theory of turbulence from the stochastic Navier-Stokes equation and the physical theory, that was proposed by Kolmogorov and Obukhov in 1941. The statistical theory of turbulence shows that the noise in developed turbulence is a general form which can be used to present a mathematical model for the stochastic Navier-Stokes equation. The statistical theory of the stochastic Navier-Stokes equation is developed in a pedagogical manner and shown to imply the Kolmogorov-Obukhov statistical theory. This book looks at a new mathematical theory in turbulence which may lead to many new developments in vorticity and Lagrangian turbulence. But even more importantly it may produce a systematic way of improving direct Navier-Stokes simulations and lead to a major jump in the technology both preventing and utilizing turbulence.

Author : Uriel Frisch
Publisher : Cambridge University Press
Page : 314 pages
File Size : 54,6 Mb
Release : 1995-11-30
Category : Science
ISBN : 0521457130

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Turbulence by Uriel Frisch Pdf

This textbook presents a modern account of turbulence, one of the greatest challenges in physics. The state-of-the-art is put into historical perspective five centuries after the first studies of Leonardo and half a century after the first attempt by A.N. Kolmogorov to predict the properties of flow at very high Reynolds numbers. Such "fully developed turbulence" is ubiquitous in both cosmical and natural environments, in engineering applications and in everyday life. First, a qualitative introduction is given to bring out the need for a probabilistic description of what is in essence a deterministic system. Kolmogorov's 1941 theory is presented in a novel fashion with emphasis on symmetries (including scaling transformations) which are broken by the mechanisms producing the turbulence and restored by the chaotic character of the cascade to small scales. Considerable material is devoted to intermittency, the clumpiness of small-scale activity, which has led to the development of fractal and multifractal models. Such models, pioneered by B. Mandelbrot, have applications in numerous fields besides turbulence (diffusion limited aggregation, solid-earth geophysics, attractors of dynamical systems, etc). The final chapter contains an introduction to analytic theories of the sort pioneered by R. Kraichnan, to the modern theory of eddy transport and renormalization and to recent developments in the statistical theory of two-dimensional turbulence. The book concludes with a guide to further reading. The intended readership for the book ranges from first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, to professional scientists and engineers.

Author : John Cannon,Bhimsen Shivamoggi
Publisher : CRC Press
Page : 208 pages
File Size : 40,7 Mb
Release : 2006-06-15
Category : Science
ISBN : 9781420014976

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Mathematical and Physical Theory of Turbulence by John Cannon,Bhimsen Shivamoggi Pdf

Although the current dynamical system approach offers several important insights into the turbulence problem, issues still remain that present challenges to conventional methodologies and concepts. These challenges call for the advancement and application of new physical concepts, mathematical modeling, and analysis techniques. Bringing together experts from physics, applied mathematics, and engineering, Mathematical and Physical Theory of Turbulence discusses recent progress and some of the major unresolved issues in two- and three-dimensional turbulence as well as scalar compressible turbulence. Containing introductory overviews as well as more specialized sections, this book examines a variety of turbulence-related topics. The authors concentrate on theory, experiments, computational, and mathematical aspects of Navier–Stokes turbulence; geophysical flows; modeling; laboratory experiments; and compressible/magnetohydrodynamic effects. The topics discussed in these areas include finite-time singularities and inviscid dissipation energy; validity of the idealized model incorporating local isotropy, homogeneity, and universality of small scales of high Reynolds numbers, Lagrangian statistics, and measurements; and subrigid-scale modeling and hybrid methods involving a mix of Reynolds-averaged Navier–Stokes (RANS), large-eddy simulations (LES), and direct numerical simulations (DNS). By sharing their expertise and recent research results, the authoritative contributors in Mathematical and Physical Theory of Turbulence promote further advances in the field, benefiting applied mathematicians, physicists, and engineers involved in understanding the complex issues of the turbulence problem.

Author : David Clement Leslie
Publisher : Unknown
Page : 392 pages
File Size : 42,5 Mb
Release : 1973
Category : Science
ISBN : UCAL:B4359613

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Developments in the Theory of Turbulence by David Clement Leslie Pdf

Author : Vladimir E. Zakharov,Victor S. L'vov,Gregory Falkovich
Publisher : Springer Science & Business Media
Page : 275 pages
File Size : 49,9 Mb
Release : 2012-12-06
Category : Science
ISBN : 9783642500527

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Kolmogorov Spectra of Turbulence I by Vladimir E. Zakharov,Victor S. L'vov,Gregory Falkovich Pdf

Since the human organism is itself an open system, we are naturally curious about the behavior of other open systems with fluxes of matter, energy or information. Of the possible open systems, it is those endowed with many degrees of freedom and strongly deviating from equilibrium that are most challenging. A simple but very significant example of such a system is given by developed turbulence in a continuous medium, where we can discern astonishing features of universality. This two-volume monograph deals with the theory of turbulence viewed as a general physical phenomenon. In addition to vortex hydrodynamic turbulence, it considers various cases of wave turbulence in plasmas, magnets, atmosphere, ocean and space. A sound basis for discussion is provided by the concept of cascade turbulence with relay energy transfer over different scales and modes. We shall show how the initial cascade hypothesis turns into an elegant theory yielding the Kolmogorov spectra of turbulence as exact solutions. We shall describe the further development of the theory discussing stability prob lems and modes of Kolmogorov spectra formation, as well as their matching with sources and sinks. This volume is dedicated to developed wave turbulence in different media.

Author : Andre? Sergeevich Monin,A. M. I?A?glom,John Leask Lumley
Publisher : Courier Corporation
Page : 898 pages
File Size : 48,9 Mb
Release : 2007-01-01
Category : Science
ISBN : 9780486458915

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Statistical Fluid Mechanics by Andre? Sergeevich Monin,A. M. I?A?glom,John Leask Lumley Pdf

"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. 1975 edition.

Author : Nathan Blaunstein,Natan Kopeika
Publisher : CRC Press
Page : 305 pages
File Size : 55,8 Mb
Release : 2017-09-22
Category : Computers
ISBN : 9781351402675

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Optical Waves and Laser Beams in the Irregular Atmosphere by Nathan Blaunstein,Natan Kopeika Pdf

The book introduces optical wave propagation in the irregular turbulent atmosphere and the relations to laser beam and LIDAR applications for both optical communication and imaging. It examines atmosphere fundamentals, structure, and content. It explains specific situations occurring in the irregular atmosphere and for specific natural phenomena that affect optical ray and laser beam propagation. It emphasizes how to use LIDAR to investigate atmospheric phenomena and predict primary parameters of the irregular turbulent atmosphere and suggests what kinds of optical devices to operate in different atmospheric situations to minimize the deleterious effects of natural atmospheric phenomena.

Author : P. A. Davidson
Publisher : Cambridge University Press
Page : 701 pages
File Size : 53,7 Mb
Release : 2013-09-12
Category : Science
ISBN : 9781107434349

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Turbulence in Rotating, Stratified and Electrically Conducting Fluids by P. A. Davidson Pdf

There are two recurring themes in astrophysical and geophysical fluid mechanics: waves and turbulence. This book investigates how turbulence responds to rotation, stratification or magnetic fields, identifying common themes, where they exist, as well as the essential differences which inevitably arise between different classes of flow. The discussion is developed from first principles, making the book suitable for graduate students as well as professional researchers. The author focuses first on the fundamentals and then progresses to such topics as the atmospheric boundary layer, turbulence in the upper atmosphere, turbulence in the core of the earth, zonal winds in the giant planets, turbulence within the interior of the sun, the solar wind, and turbulent flows in accretion discs. The book will appeal to engineers, geophysicists, astrophysicists and applied mathematicians who are interested in naturally occurring turbulent flows.

Author : Alexandre Boritchev,Sergei Kuksin
Publisher : American Mathematical Soc.
Page : 192 pages
File Size : 42,9 Mb
Release : 2021-07-01
Category : Education
ISBN : 9781470464363

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One-Dimensional Turbulence and the Stochastic Burgers Equation by Alexandre Boritchev,Sergei Kuksin Pdf

This book is dedicated to the qualitative theory of the stochastic one-dimensional Burgers equation with small viscosity under periodic boundary conditions and to interpreting the obtained results in terms of one-dimensional turbulence in a fictitious one-dimensional fluid described by the Burgers equation. The properties of one-dimensional turbulence which we rigorously derive are then compared with the heuristic Kolmogorov theory of hydrodynamical turbulence, known as the K41 theory. It is shown, in particular, that these properties imply natural one-dimensional analogues of three principal laws of the K41 theory: the size of the Kolmogorov inner scale, the 2/3 2/3-law, and the Kolmogorov–Obukhov law. The first part of the book deals with the stochastic Burgers equation, including the inviscid limit for the equation, its asymptotic in time behavior, and a theory of generalised L 1 L1-solutions. This section makes a self-consistent introduction to stochastic PDEs. The relative simplicity of the model allows us to present in a light form many of the main ideas from the general theory of this field. The second part, dedicated to the relation of one-dimensional turbulence with the K41 theory, could serve for a mathematical reader as a rigorous introduction to the literature on hydrodynamical turbulence, all of which is written on a physical level of rigor.

Author : Gregory D. Fleishman,Igor N. Toptygin
Publisher : Springer Science & Business Media
Page : 729 pages
File Size : 46,8 Mb
Release : 2013-03-21
Category : Science
ISBN : 9781461457824

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Cosmic Electrodynamics by Gregory D. Fleishman,Igor N. Toptygin Pdf

This book presents the fundamental concepts of the theory, illustrated by numerous examples of astrophysical applications. Classical concepts are combined with new developments and the authors demarcate what is well established and what is still under debate. To book illustrates how apparently complicated phenomena can be addressed and understood using well-known physical principles and equations within appropriate approximations and simplifications. For this purpose, a number of astrophysical examples are considered in greater detail than what is normally presented in a regular textbook. In particular, a number of nonlinear self-consistent models are considered, which is motivated by the latest observational data and modern theory.

Author : S. Panchev
Publisher : Elsevier
Page : 458 pages
File Size : 40,6 Mb
Release : 2016-10-27
Category : Technology & Engineering
ISBN : 9781483145594

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Random Functions and Turbulence by S. Panchev Pdf

International Series of Monographs in Natural Philosophy, Volume 32: Random Functions and Turbulence focuses on the use of random functions as mathematical methods. The manuscript first offers information on the elements of the theory of random functions. Topics include determination of statistical moments by characteristic functions; functional transformations of random variables; multidimensional random variables with spherical symmetry; and random variables and distribution functions. The book then discusses random processes and random fields, including stationarity and ergodicity of random processes; influence of finiteness of the interval of averaging; scalar and vector random fields; and statistical moments. The text takes a look at the statistical theory of turbulence. Topics include turbulence with very large Reynolds numbers; emergence of turbulent motion; and energy spectrum in isothermal turbulent shear flow. The book also discusses small-scale and large-scale atmospheric turbulence and applications to numerical weather analysis and prediction. The manuscript is a vital source of data for readers interested in random theory.

Author : A. Tsinober
Publisher : Springer Science & Business Media
Page : 328 pages
File Size : 48,8 Mb
Release : 2006-04-11
Category : Science
ISBN : 9780306483844

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An Informal Introduction to Turbulence by A. Tsinober Pdf

To Turbulence by ARKADY TSINOBER Department of Fluid Mechanics, Faculty of Engineering, Tel Aviv University, Tel Aviv, Israel KLUWER ACADEMIC PUBLISHERS NEW YORK, BOSTON, DORDRECHT, LONDON, MOSCOW eBookISBN: 0-306-48384-X Print ISBN: 1-4020-0110-X ©2004 Kluwer Academic Publishers NewYork, Boston, Dordrecht, London, Moscow Print ©2001 Kluwer Academic Publishers Dordrecht All rights reserved No part of this eBook maybe reproducedor transmitted inanyform or byanymeans, electronic, mechanical, recording, or otherwise, without written consent from the Publisher Created in the United States of America Visit Kluwer Online at: http://kluweronline. com and Kluwer's eBookstoreat: http://ebooks. kluweronline. com TO My WITS TABLE OF CONTENTS 1 INTRODUCTION 1 Brief history 1 1. 1 1. 2 Nature and major qualitative universal features of turbulent flows 2 1. 2. 1 Representative examples of turbulent flows 2 1. 2. 2 In lieu of definition: major qualitative universal f- tures of turbulent flows 15 1. 3 Why turbulence is so impossibly difficult? The three N's 19 On the Navier-Stokes equations 19 1. 3. 1 1. 3. 2 On the nature of the problem 21 1. 3. 3 Nonlinearity 22 1. 3. 4 Noninegrability 22 Nonlocality 1. 3. 5 23 1. 3. 6 On physics of turbulence 24 1. 3. 7 On statistical theories 24 1. 4 Outline of the following material 25 1. 5 In lieu of summary 26 2 ORIGINS OF TURBULENCE 27 2. 1 Instability 27 2. 2 Transition to turbulence versus routes to chaos 29 2.

Author : Giovanni P. Galdi,Malcolm I. Heywood,Rolf Rannacher
Publisher : Birkhäuser
Page : 152 pages
File Size : 53,6 Mb
Release : 2012-10-23
Category : Science
ISBN : 3034896069

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Contributions to Current Challenges in Mathematical Fluid Mechanics by Giovanni P. Galdi,Malcolm I. Heywood,Rolf Rannacher Pdf

This volume consists of five research articles, each dedicated to a significant topic in the mathematical theory of the Navier-Stokes equations, for compressible and incompressible fluids, and to related questions. All results given here are new and represent a noticeable contribution to the subject. One of the most famous predictions of the Kolmogorov theory of turbulence is the so-called Kolmogorov-obukhov five-thirds law. As is known, this law is heuristic and, to date, there is no rigorous justification. The article of A. Biryuk deals with the Cauchy problem for a multi-dimensional Burgers equation with periodic boundary conditions. Estimates in suitable norms for the corresponding solutions are derived for "large" Reynolds numbers, and their relation with the Kolmogorov-Obukhov law are discussed. Similar estimates are also obtained for the Navier-Stokes equation. In the late sixties J. L. Lions introduced a "perturbation" of the Navier Stokes equations in which he added in the linear momentum equation the hyper dissipative term (-Ll),Bu, f3 ~ 5/4, where Ll is the Laplace operator. This term is referred to as an "artificial" viscosity. Even though it is not physically moti vated, artificial viscosity has proved a useful device in numerical simulations of the Navier-Stokes equations at high Reynolds numbers. The paper of of D. Chae and J. Lee investigates the global well-posedness of a modification of the Navier Stokes equation similar to that introduced by Lions, but where now the original dissipative term -Llu is replaced by (-Ll)O:u, 0 S Ct

Author : Ole E. Barndorff-Nielsen,Fred Espen Benth,Almut E. D. Veraart
Publisher : Springer
Page : 402 pages
File Size : 44,9 Mb
Release : 2018-11-01
Category : Mathematics
ISBN : 9783319941295

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Ambit Stochastics by Ole E. Barndorff-Nielsen,Fred Espen Benth,Almut E. D. Veraart Pdf

Drawing on advanced probability theory, Ambit Stochastics is used to model stochastic processes which depend on both time and space. This monograph, the first on the subject, provides a reference for this burgeoning field, complete with the applications that have driven its development. Unique to Ambit Stochastics are ambit sets, which allow the delimitation of space-time to a zone of interest, and ambit fields, which are particularly well-adapted to modelling stochastic volatility or intermittency. These attributes lend themselves notably to applications in the statistical theory of turbulence and financial econometrics. In addition to the theory and applications of Ambit Stochastics, the book also contains new theory on the simulation of ambit fields and a comprehensive stochastic integration theory for Volterra processes in a non-semimartingale context. Written by pioneers in the subject, this book will appeal to researchers and graduate students interested in empirical stochastic modelling.

Author : G. I. Barenblatt
Publisher : Cambridge University Press
Page : 277 pages
File Size : 43,8 Mb
Release : 2014-06-05
Category : Science
ISBN : 9780521887526

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Flow, Deformation and Fracture by G. I. Barenblatt Pdf

Over forty years of teaching experience are distilled into this text. The guiding principle is the wide use of the concept of intermediate asymptotics, which enables the natural introduction of the modeling of real bodies by continua. Beginning with a detailed explanation of the continuum approximation for the mathematical modeling of the motion and equilibrium of real bodies, the author continues with a general survey of the necessary methods and tools for analyzing models. Next, specific idealized approximations are presented, including ideal incompressible fluids, elastic bodies and Newtonian viscous fluids. The author not only presents general concepts but also devotes chapters to examining significant problems, including turbulence, wave-propagation, defects and cracks, fatigue and fracture. Each of these applications reveals essential information about the particular approximation. The author's tried and tested approach reveals insights that will be valued by every teacher and student of mechanics.