The Statistical Mechanics Of Ideal Homogeneous Turbulence
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The Statistical Mechanics Of Ideal Homogeneous Turbulence
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Author : John V. Shebalin
language : en
Publisher:
Release Date : 2002
The Statistical Mechanics Of Ideal Homogeneous Turbulence written by John V. Shebalin and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002 with Ergodic theory categories.
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).
The Statistical Mechanics Of Ideal Homogeneous Turbulence
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Author : John V. Shebalin
language : en
Publisher: BiblioGov
Release Date : 2013-07
The Statistical Mechanics Of Ideal Homogeneous Turbulence written by John V. Shebalin and has been published by BiblioGov this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-07 with categories.
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.
The Statistical Mechanics Of Ideal Homogeneous Turbulence
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Author : National Aeronautics and Space Administration (NASA)
language : en
Publisher: Createspace Independent Publishing Platform
Release Date : 2018-06-15
The Statistical Mechanics Of Ideal Homogeneous Turbulence written by National Aeronautics and Space Administration (NASA) and has been published by Createspace Independent Publishing Platform this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-06-15 with categories.
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
Theories Of Turbulence
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Author : Martin Oberlack
language : en
Publisher: Springer
Release Date : 2014-05-04
Theories Of Turbulence written by Martin Oberlack and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-04 with Science categories.
The term "turbulence” is used for a large variety of dynamical phenomena of fluids in motion whenever the details of the flow appear to be random and average properties are of primary interest. Just as wide ranging are the theoretical methods that have been applied towards a better understanding of fluid turbulence. In this book a number of these methods are described and applied to a broad range of problems from the transition to turbulence to asymptotic turbulence when the inertial part of the spectrum is fully developed. Statistical as well as nonstatistical treatments are presented, but a complete coverage of the subject is not attempted. The book will be of interest to scientists and engineers who wish to familiarize themselves with modern developments in theories of turbulence. The fact that the properties of turbulent fluid flow are addressed from very different points of view makes this volume rather unique among presently available books on turbulence.
The Theory Of Homogeneous Turbulence
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Author : G. K. Batchelor
language : en
Publisher: Cambridge University Press
Release Date : 1953
The Theory Of Homogeneous Turbulence written by G. K. Batchelor and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1953 with Mathematics categories.
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.
Paolo Grigolini And 50 Years Of Statistical Physics
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Author : Bruce J. West
language : en
Publisher: Cambridge Scholars Publishing
Release Date : 2023-04-03
Paolo Grigolini And 50 Years Of Statistical Physics written by Bruce J. West and has been published by Cambridge Scholars Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2023-04-03 with Science categories.
This volume celebrates the over fifty-year career in non-equilibrium statistical physics of Professor Paolo Grigolini of the Center for Nonlinear Science at the University of North Texas. It begins by positioning Grigolini in a five-dimensional science-personality space with the following axes: Sleeper, Keeper, Leaper, Creeper and Reaper. This introduction to the person is followed by a sequence of papers in the various areas of science where his work has had impact, including subtle questions concerned with the connection between classical and quantum systems; a two-level atom coupled to a radiation field; classical probability calculus; anomalous diffusion that is Brownian yet non-Gaussian; a new method for detecting scaling in time series; and the effect of strong Anderson localization on ultrasound transmission, among other topics.
Turbulence And Nonlinear Processes In Astrophysical Plasmas
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Author : Dastgeer Shaikh
language : en
Publisher: American Institute of Physics
Release Date : 2007-09-27
Turbulence And Nonlinear Processes In Astrophysical Plasmas written by Dastgeer Shaikh and has been published by American Institute of Physics this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-09-27 with Science categories.
This book contains the peer-reviewed papers presented at the Sixth Annual International Astrophysics Conference. This conference brought together a range of topics that shed light on our understanding and status of turbulence and nonlinear processes in astrophysical plasmas. Coverage in this volume includes turbulent relaxation in laboratory and space plasmas and its application to coronal flux tubes, coronal heating, and the diffusion of energetic particles.
Magnetohydrodynamic Turbulence
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Author : Dieter Biskamp
language : en
Publisher: Cambridge University Press
Release Date : 2003-07-31
Magnetohydrodynamic Turbulence written by Dieter Biskamp and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-07-31 with Science categories.
This book presents an introduction to, and modern account of, magnetohydrodynamic (MHD) turbulence, an active field both in general turbulence theory and in various areas of astrophysics. The book starts by introducing the MHD equations, certain useful approximations and the transition to turbulence. The second part of the book covers incompressible MHD turbulence, the macroscopic aspects connected with the different self-organization processes, the phenomenology of the turbulence spectra, two-point closure theory, and intermittency. The third considers two-dimensional turbulence and compressible (in particular, supersonic) turbulence. Because of the similarities in the theoretical approach, these chapters start with a brief account of the corresponding methods developed in hydrodynamic turbulence. The final part of the book is devoted to astrophysical applications: turbulence in the solar wind, in accretion disks, and in the interstellar medium. This book is suitable for graduate students and researchers working in turbulence theory, plasma physics and astrophysics.
Vorticity And Turbulence
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Author : Alexandre J. Chorin
language : en
Publisher: Springer Science & Business Media
Release Date : 1994-06-24
Vorticity And Turbulence written by Alexandre J. Chorin and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 1994-06-24 with Mathematics categories.
This book provides an introduction to turbulence in vortex systems, and to turbulence theory for incompressible flow described in terms of the vorticity field. It is the author's hope that by the end of the book the reader will believe that these subjects are identical, and constitute a special case of fairly standard statistical mechanics, with both equilibrium and non-equilibrium aspects. The author's main goal is to relate turbulence to statistical mechanics. The book is organized as follows: the first three chapters constitute a fairly standard introduction to homogeneous turbulence in incompressible flow; a quick review of fluid mechanics; a summary of the appropriate Fourier theory; a summary of Kolmogorov's theory of the inertial range. The next four chapters present the statistical theory of vortex notion, and the vortex dynamics of turbulence. The book ends with the major conclusion that turbulence can no longer be viewed as incomprehensible. This book will be appropriate for professionals in the fields of applied mathematics, mechanical engineering, or physics, as well as graduate students in these noted areas.
Discrete And Continuous Dynamical Systems
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Author :
language : en
Publisher:
Release Date : 2005
Discrete And Continuous Dynamical Systems written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2005 with Differentiable dynamical systems categories.