Instabilities Chaos And Turbulence

This book (2nd edition) is a self-contained introduction to a wide body of knowledge on nonlinear dynamics and chaos. Manneville emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. He explains the theoretical framework using pedagogical examples from fluid dynamics, though prior knowledge of this field is not required. Heuristic arguments and worked examples replace most esoteric technicalities. Only basic understanding of mathematics and physics is required, at the level of what is currently known after one or two years of undergraduate training: elementary calculus, basic notions of linear algebra and ordinary differential calculus, and a few fundamental physical equations (specific complements are provided when necessary). Methods presented are of fully general use, which opens up ample windows on topics of contemporary interest. These include complex dynamical processes such as patterning, chaos control, mixing, and even the Earth's climate. Numerical simulations are proposed as a means to obtain deeper understanding of the intricacies induced by nonlinearities in our everyday environment, with hints on adapted modelling strategies and their implementation./a

This book (2nd edition) is a self-contained introduction to a wide body of knowledge on nonlinear dynamics and chaos. Manneville emphasises the understanding of basic concepts and the nontrivial character of nonlinear response, contrasting it with the intuitively simple linear response. He explains the theoretical framework using pedagogical examples from fluid dynamics, though prior knowledge of this field is not required. Heuristic arguments and worked examples replace most esoteric technicalities. Only basic understanding of mathematics and physics is required, at the level of what is currently known after one or two years of undergraduate training: elementary calculus, basic notions of linear algebra and ordinary differential calculus, and a few fundamental physical equations (specific complements are provided when necessary). Methods presented are of fully general use, which opens up ample windows on topics of contemporary interest. These include complex dynamical processes such as patterning, chaos control, mixing, and even the Earth's climate. Numerical simulations are proposed as a means to obtain deeper understanding of the intricacies induced by nonlinearities in our everyday environment, with hints on adapted modelling strategies and their implementation.

The present collection of reprints covers the main contributions of David Ruelle, and coauthors, to the theory of chaos and its applications. Several of the papers reproduced here are classics in the field. Others (that were published in less accessible places) may still surprise the reader.The collection contains mathematical articles relevant to chaos, specific articles on the theory, and articles on applications to hydrodynamical turbulence, chemical oscillations, etc.A sound judgement of the value of techniques and applications is crucial in the interdisciplinary field of chaos. For a critical assessment of what has been achieved in this area, the present volume is an invaluable contribution.

Turbulence is one of the most wide-spread phenomena in the universe. It relates to processes within the atmosphere, ocean, deep within the earth, as well as to the stars. The general public usually knows about turbulence from the unpleasant shaking of an airplane, or from disastrous atmospheric phenomena such as typhoons and hurricanes. The chaotic and unpredictable behavior of turbulent movement makes it very difficult to study. The degree of understanding of turbulence is still far from being complete. Some progress was made with the recent advent of a new science--chaos theory. The authors succeeded in examining one basic feature of turbulence called helicity (or spirality) which is the foundation of explaining and predicting the generation of large turbulent structures (e.g. typhoons). Helicity is a universal feature existing not only in fluid flows but also in solid bodies and even in living organisms. This book can be especially useful for researchers and students in fluid mechanics, plasma, geophysics, biology, and meteorology. * Examines the helical mechanism of self-organization in nature and laboratory * Presents a unified approach to chaos and theory * Discusses similarities and differences in the formation of dynamic and magnetic structures * Successfully combines profound theoretical and experimental knowledge * Includes a disk with an expanded bibliographical database

The second volume in a study of nonlinear stability, chaos and turbulence. It demonstrates the importance of mathematical, computational and experimental techniques to the advancement of research in nonlinear instability, chaotic motions and turbulent flow systems.

Monograph presents the newest results in the numerical modeling and computer simulation of turbulence.