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Multi-scale systems, involving complex interacting processes that occur over a range of temporal and spatial scales, are present in a broad range of disciplines. Several methodologies exist to retrieve this multi-scale information from a given time series; however, each method has its own limitations. This book presents the mathematical theory behind the stochastic analysis of scaling time series, including a general historical introduction to the problem of intermittency in turbulence, as well as how to implement this analysis for a range of different applications. Covering a variety of statistical methods, such as Fourier analysis and wavelet transforms, it provides readers with a thorough understanding of the techniques and when to apply them. New techniques to analyse stochastic processes, including empirical mode decomposition, are also explored. Case studies, in turbulence and ocean sciences, are used to demonstrate how these statistical methods can be applied in practice, for students and researchers.
List of contents
Preface; 1. Introduction: a multiscale and turbulent-like world; 2. Homogeneous turbulence and intermittency; 3. Scaling and intermittent stochastic processes; 4. New methodologies to deal with nonlinear and scaling time series; 5. Applications: case studies in turbulence; 6. Applications: case studies in ocean and atmospheric sciences; References; Index.
About the author
François G. Schmitt is Research Professor in the Laboratory of Oceanography and Geosciences at the Centre National de la Recherche Scientifique (CNRS), France. His research interests include turbulence and nonlinear variability in geophysics, marine turbulence, and multifractal analysis and modelling.Yongxiang Huang is Associate Professor in the State Key Laboratory of Marine Environmental Science at Xiamen University, China. He was awarded the 2013 Division Outstanding Young Scientists Award by the European Geosciences Union in Nonlinear Processes in Geosciences.
Summary
Covering a variety of statistical methods, this book provides readers with a thorough understanding of the techniques used to retrieve multi-scale information from time series data, particularly in relation to turbulence. Case studies and MATLAB codes are supplied, making this an excellent resource for graduate students and researchers.
