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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.
This self-contained volume introduces modern methods of statistical mechanics in turbulence, with three harmonised lecture courses by world class experts.
This self-contained volume introduces modern methods of statistical mechanics in turbulence, with three harmonised lecture courses by world class experts.
This work presents the construction of an asymptotic technique for solving the Liouville equation, which is an analogue of the Enskog-Chapman technique for the Boltzmann equation. Because the assumption of molecular chaos has not been introduced, the macroscopic variables defined by the arithmetic means of the corresponding microscopic variables are random in general. Therefore, it is convenient for describing the turbulence phenomena. The asymptotic technique for the Liouville equation reveals a term showing the interaction between the temperature and the velocity of the fluid flows, which will be lost under the assumption of molecular chaos.
This book stresses the role of uncorrelated exchange of properties between macroscopic systems and their surroundings as the only source of dynamic irreversibility. To that end, fundamentals of statistical thermodynamics extended to the non-equilibrium are worked out carefully. The principles are then applied to selected problems in classical fluid dynamics. Transport coefficients are first derived from basic laws. This is followed by a full discussion of transitions to dissipative structures in selected systems far removed from equilibrium (Bénard and Taylor vortices, calculation of the critical Reynolds number for transition to turbulence in Poiseuille flow). The final part focuses on interaction of matter with light. Fundamentals are extended towards quantum-mechanical systems. Applied to coherent radiation and its interaction with matter, the proposed thermodynamic treatment introduces an original discussion into the quantum nature of micro-physics.The book questions and reconsiders a deeply rooted paradigm in macroscopic dynamics concerning the cause of irreversibility. The new proposal is illustrated by application to a couple of well documented non-equilibrium domains, namely fluid dynamics and laser physics.
This book concentrates on the properties of the stationary states in chaotic systems of particles or fluids, leaving aside the theory of the way they can be reached. The stationary states of particles or of fluids (understood as probability distributions on microscopic configurations or on the fields describing continua) have received important new ideas and data from numerical simulations and reviews are needed. The starting point is to find out which time invariant distributions come into play in physics. A special feature of this book is the historical approach. To identify the problems the author analyzes the papers of the founding fathers Boltzmann, Clausius and Maxwell including translations of the relevant (parts of) historical documents. He also establishes a close link between treatment of irreversible phenomena in statistical mechanics and the theory of chaotic systems at and beyond the onset of turbulence as developed by Sinai, Ruelle, Bowen (SRB) and others: the author gives arguments intending to support strongly the viewpoint that stationary states in or out of equilibrium can be described in a unified way. In this book it is the "chaotic hypothesis", which can be seen as an extension of the classical ergodic hypothesis to non equilibrium phenomena, that plays the central role. It is shown that SRB - often considered as a kind of mathematical playground with no impact on physical reality - has indeed a sound physical interpretation; an observation which to many might be new and a very welcome insight. Following this, many consequences of the chaotic hypothesis are analyzed in chapter 3 - 4 and in chapter 5 a few applications are proposed. Chapter 6 is historical: carefully analyzing the old literature on the subject, especially ergodic theory and its relevance for statistical mechanics; an approach which gives the book a very personal touch. The book contains an extensive coverage of current research (partly from the authors and his coauthors publications) presented in enough detail so that advanced students may get the flavor of a direction of research in a field which is still very much alive and progressing. Proofs of theorems are usually limited to heuristic sketches privileging the presentation of the ideas and providing references that the reader can follow, so that in this way an overload of this text with technical details could be avoided.
The turbulent equations for a neutral fluid are derived from the standpoint of Statistical Mechanics. The Three-Point Method of turbulence was investigated for limitations on the theory. Turbulent equations applicable to the adiabatic response of a plasma are developed.
This book is a printed edition of the Special Issue Intermittency and Self-Organisation in Turbulence and Statistical Mechanics that was published in Entropy
This textbook offers an advanced undergraduate or initial graduate level introduction to topics such as kinetic theory, equilibrium statistical mechanics and the theory of fluctuations from a modern perspective. The aim is to provide the reader with the necessary tools of probability theory and thermodynamics (especially the thermodynamic potentials) to enable subsequent study at advanced graduate level. At the same time, the book offers a bird's eye view on arguments that are often disregarded in the main curriculum courses. Further features include a focus on the interdisciplinary nature of the subject and in-depth discussion of alternative interpretations of the concept of entropy. While some familiarity with basic concepts of thermodynamics and probability theory is assumed, this does not extend beyond what is commonly obtained in basic undergraduate curriculum courses.
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 ex