Introduction To Turbulent Dynamical Systems In Complex Systems
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Introduction to Turbulent Dynamical Systems in Complex Systems
This volume is a research expository article on the applied mathematics of turbulent dynamical systems through the paradigm of modern applied mathematics. It involves the blending of rigorous mathematical theory, qualitative and quantitative modeling, and novel numerical procedures driven by the goal of understanding physical phenomena which are of central importance to the field. The contents cover general framework, concrete examples, and instructive qualitative models. Accessible open problems are mentioned throughout. Topics covered include: · Geophysical flows with rotation, topography, deterministic and random forcing · New statistical energy principles for general turbulent dynamical systems, with applications · Linear statistical response theory combined with information theory to cope with model errors · Reduced low order models · Recent mathematical strategies for online data assimilation of turbulent dynamical systems as well as rigorous results for finite ensemble Kalman filters The volume will appeal to graduate students and researchers working mathematics, physics and engineering and particularly those in the climate, atmospheric and ocean sciences interested in turbulent dynamical as well as other complex systems.
Dynamical Systems Approach to Turbulence
Author: Tomas Bohr
language: en
Publisher: Cambridge University Press
Release Date: 2005-08-22
In recent decades, turbulence has evolved into a very active field of theoretical physics. The origin of this development is the approach to turbulence from the point of view of deterministic dynamical systems, and this book shows how concepts developed for low dimensional chaotic systems are applied to turbulent states. This book centers around a number of important simplified models for turbulent behavior in systems ranging from fluid motion (classical turbulence) to chemical reactions and interfaces in disordered systems. The theory of fractals and multifractals now plays a major role in turbulence research, and turbulent states are being studied as important dynamical states of matter occurring also in systems outside the realm of hydrodynamics. The book contains simplified models of turbulent behavior, notably shell models, coupled map lattices, amplitude equations and interface models.
Filtering Complex Turbulent Systems
Author: Andrew J. Majda
language: en
Publisher: Cambridge University Press
Release Date: 2012-02-23
The authors develop a systematic applied mathematics perspective on the problems associated with filtering complex turbulent systems. The book contains background material from filtering, turbulence theory and numerical analysis, making it suitable for graduate courses as well as for researchers in a range of disciplines where applied mathematics is required.