Instabilities Chaos And Turbulence

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.

Instabilities, Chaos and Turbulence

Nonlinear Instability, Chaos and Turbulence

This is a collection of research and research-expository articles written by leading experts who have made important contributions to the areas of non-linear instability, chaos and turbulence. It brings together developments in the theory and applications of the subjects and related topics which are likely to determine fruitful directions for further study and research. It is also intended as a reference guide for the readers interested in advance study and research in non-linear phenomena.