Book contents
- Frontmatter
- Contents
- List of contributors
- Preface to the paperback edition
- Preface to the first edition
- 0 A guided tour through the book
- 1 Wavelet analysis: a new tool in physics
- 2 The 2-D wavelet transform, physical applications and generalizations
- 3 Wavelets and astrophysical applications
- 4 Turbulence analysis, modelling and computing using wavelets
- 5 Wavelets and detection of coherent structures in fluid turbulence
- 6 Wavelets, non-linearity and turbulence in fusion plasmas
- 7 Transfers and fluxes of wind kinetic energy between orthogonal wavelet components during atmospheric blocking
- 8 Wavelets in atomic physics and in solid state physics
- 9 The thermodynamics of fractals revisited with wavelets
- 10 Wavelets in medicine and physiology
- 11 Wavelet dimensions and time evolution
- Index
6 - Wavelets, non-linearity and turbulence in fusion plasmas
Published online by Cambridge University Press: 27 January 2010
- Frontmatter
- Contents
- List of contributors
- Preface to the paperback edition
- Preface to the first edition
- 0 A guided tour through the book
- 1 Wavelet analysis: a new tool in physics
- 2 The 2-D wavelet transform, physical applications and generalizations
- 3 Wavelets and astrophysical applications
- 4 Turbulence analysis, modelling and computing using wavelets
- 5 Wavelets and detection of coherent structures in fluid turbulence
- 6 Wavelets, non-linearity and turbulence in fusion plasmas
- 7 Transfers and fluxes of wind kinetic energy between orthogonal wavelet components during atmospheric blocking
- 8 Wavelets in atomic physics and in solid state physics
- 9 The thermodynamics of fractals revisited with wavelets
- 10 Wavelets in medicine and physiology
- 11 Wavelet dimensions and time evolution
- Index
Summary
Abstract
Two fundamental properties of turbulence are intermittency and non-linearity. They imply that the standard Fourier spectral techniques are inadequate for its analysis. Spectral analysis based on wavelets provides a means to handle intermittency. New tools are required to handle non-linearity.
In this chapter, we redesign spectral analysis in terms of wavelet methods, paying particular attention to statistical stability, error estimates and nonlinearity. The application to both computer simulations and measurements carried out in fusion plasmas provide some illustrative examples.
Introduction
Although the phenomenon of turbulence is only partially understood, there seems to be consensus on several aspects. First, that intermittency is a basic property of turbulence. This means that the characteristics of the turbulence (spectral distribution, amplitude etc.) vary on a short time scale. Analysis techniques that rely on the accumulation of data over time scales larger than this characteristic time scale will then average out much of the dynamics and obliterate relevant information (as may occur with Fourier analyses). Wavelet analysis provides an interesting starting point for redesigning the standard analysis techniques in order to tackle this problem. In this chapter we shall redefine some basic Fourier analysis techniques in terms of wavelets, such as cross coherence. We shall emphasize the need for statistical stability and provide noise level estimates. Finally, we provide some examples of these techniques.
Second, it is generally accepted that turbulence only arises in non-linear systems. Therefore, to understand the nature of turbulence, it is essential to employ analysis tools that are capable of handling this non-linearity.
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- Wavelets in Physics , pp. 227 - 262Publisher: Cambridge University PressPrint publication year: 1999
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