The Kolmogorov Obukhov Theory Of Turbulence
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| Author | : Bjorn Birnir |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 117 |
| Release | : 2013-01-31 |
| Genre | : Mathematics |
| ISBN | : 1461462622 |
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 | : P. A. Davidson |
| Publisher | : Cambridge University Press |
| Total Pages | : 701 |
| Release | : 2013-09-12 |
| Genre | : Science |
| ISBN | : 1107434343 |
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 | : Uriel Frisch |
| Publisher | : Cambridge University Press |
| Total Pages | : 318 |
| Release | : 1995-11-30 |
| Genre | : Science |
| ISBN | : 1139935976 |
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. The intended readership for the book ranges from first-year graduate students in mathematics, physics, astrophysics, geosciences and engineering, to professional scientists and engineers. Elementary presentations of dynamical systems ideas, of probabilistic methods (including the theory of large deviations) and of fractal geometry make this a self-contained textbook.
| Author | : Vladimir E. Zakharov |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 275 |
| Release | : 2012-12-06 |
| Genre | : Science |
| ISBN | : 3642500528 |
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 | : S. Panchev |
| Publisher | : Elsevier |
| Total Pages | : 459 |
| Release | : 2016-10-27 |
| Genre | : Technology & Engineering |
| ISBN | : 148314559X |
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 | : G. I. Barenblatt |
| Publisher | : Cambridge University Press |
| Total Pages | : 187 |
| Release | : 2003-11-13 |
| Genre | : Mathematics |
| ISBN | : 0521826578 |
The author describes and teaches the art of discovering scaling laws, starting from dimensional analysis and physical similarity, which are here given a modern treatment. He demonstrates the concepts of intermediate asymptotics and the renormalisation group as natural consequences of self-similarity and shows how and when these notions and tools can be used to tackle the task at hand, and when they cannot. Based on courses taught to undergraduate and graduate students, the book can also be used for self-study by biologists, chemists, astronomers, engineers and geoscientists.
| Author | : Alexandre J. Chorin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 181 |
| Release | : 2013-12-01 |
| Genre | : Mathematics |
| ISBN | : 1441987282 |
This book provides an introduction to the theory of turbulence in fluids based on the representation of the flow by means of its vorticity field. It has long been understood that, at least in the case of incompressible flow, the vorticity representation is natural and physically transparent, yet the development of a theory of turbulence in this representation has been slow. The pioneering work of Onsager and of Joyce and Montgomery on the statistical mechanics of two-dimensional vortex systems has only recently been put on a firm mathematical footing, and the three-dimensional theory remains in parts speculative and even controversial. The first three chapters of the book contain a reasonably standard intro duction to homogeneous turbulence (the simplest case); a quick review of fluid mechanics is followed by a summary of the appropriate Fourier theory (more detailed than is customary in fluid mechanics) and by a summary of Kolmogorov's theory of the inertial range, slanted so as to dovetail with later vortex-based arguments. The possibility that the inertial spectrum is an equilibrium spectrum is raised.
| Author | : Oleg G. Bakunin |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 269 |
| Release | : 2008-08-15 |
| Genre | : Science |
| ISBN | : 3540682228 |
This book is intended to serve as an introduction to the multidisciplinary ?eld of anomalous diffusion in complex systems such as turbulent plasma, convective rolls, zonal ?ow systems, stochastic magnetic ?elds, etc. In spite of its great importance, turbulent transport has received comparatively little treatment in published mo- graphs. This book attempts a comprehensive description of the scaling approach to turbulent diffusion. From the methodological point of view, the book focuses on the general use of correlation estimates, quasilinear equations, and continuous time random walk - proach. I provide a detailed structure of some derivations when they may be useful for more general purposes. Correlation methods are ?exible tools to obtain tra- port scalings that give priority to the richness of ingredients in a physical pr- lem. The mathematical description developed here is not meant to provide a set of “recipes” for hydrodynamical turbulence or plasma turbulence; rather, it serves to develop the reader’s physical intuition and understanding of the correlation mec- nisms involved.
| Author | : David Ting |
| Publisher | : Academic Press |
| Total Pages | : 258 |
| Release | : 2016-02-23 |
| Genre | : Science |
| ISBN | : 0128039833 |
Basics of Engineering Turbulence introduces flow turbulence to engineers and engineering students who have a fluid dynamics background, but do not have advanced knowledge on the subject. It covers the basic characteristics of flow turbulence in terms of its many scales. The author uses a pedagogical approach to help readers better understand the fundamentals of turbulence scales, especially how they are derived through the order of magnitude analysis. This book is intended for those who have an interest in flowing fluids. It provides some background, though of limited scope, on everyday flow turbulence, especially in engineering applications. The book begins with the 'basics' of turbulence which is necessary for any reader being introduced to the subject, followed by several examples of turbulence in engineering applications. This overall approach gives readers all they need to grasp both the fundamentals of turbulence and its applications in practical instances. - Focuses on the basics of turbulence for applications in engineering and industrial settings - Provides an understanding of concepts that are often challenging, such as energy distribution among the turbulent structures, the effective diffusivity, and the theory behind turbulence scales - Offers a user-friendly approach with clear-and-concise explanations and illustrations, as well as end-of-chapter problems
| Author | : Gregory D. Fleishman |
| Publisher | : Springer Science & Business Media |
| Total Pages | : 729 |
| Release | : 2013-03-21 |
| Genre | : Science |
| ISBN | : 1461457823 |
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.
