Statistically robust linear and nonlinear wavelet analysis applied to plasma edge turbulence

Abstract

Application of wavelet multiresolution analysis to the study of self-similarity and intermittency of plasma turbulence Rev. Sci. Instrum. 77, 083505 (2006); 10.1063/1.2336754 Wavelet-based time-delay estimation for time-resolved turbulent flow analysis Rev. Sci. Instrum. 72, 996 (2001); 10.1063/1.1326009 Wavelet analysis of plasma fluctuations in microwave reflectometry Rev.Application of wavelet spectral analysis to plasma fluctuation measurements using beam emission spectroscopy Rev.The analysis of turbulence requires adequate analysis tools. In particular, two general properties of turbulence make the application of standard analysis tools ͑spectral analysis͒ difficult: ͑1͒ intermittency, which causes the characteristics of turbulence to change on a relatively short time scale, implies that analysis tools must not integrate over time scales longer than the intermittent time scale; ͑2͒ nonlinearity, a basic property of all numerical models of chaos and turbulence, requires specially adapted tools for its proper detection. In the present work, we develop a statistically stable formalism for the application of wavelet analysis techniques to the analysis of turbulence. We apply these techniques to the analysis of Langmuir probe data in the plasma edge region of the TJ-IU Torsatron. We draw some tentative conclusions about radial correlation lengths. Further, we analyze the L/H transition at the Continous Current Tokamak and reconstruct a radial profile of bicoherence in the plasma edge in the H-mode.

Coherence analysis between respiration and heart rate variability using continuous wavelet transform

“…The wavelet transform coherence (WTC) is a known, though infrequently used, tool in scientific areas, where random-like, yet deterministic, signals are created by complex and not fully understood mechanisms. Areas such as weather in geophysics (Grinsted et al 2004), turbulence in plasma physics (Van Milligen et al 1997) and brain dynamics in physiology (Klein et al 2006) are using wavelet coherence in order to find transient correlations between signals. Unlike the use of coherence in cardiovascular variability, the wavelet coherence was mainly used for the purpose of finding correlated areas between signals that are uncorrelated most of the time.…”

A novel technique in analyzing non-linear wave-wave interaction

“…In order to have a statistical stability the wavelet power spectrum is integrated over a finite time interval (Milligen et al, 1995(Milligen et al, , 1997. The wavelet power spectrum: …”

Wavelet bicoherence analysis of wind–wave interaction

“…In order to have statistical stability the wavelet power spectrum is integrated over a finite time interval (Milligen et al, 1995(Milligen et al, , 1997. The wavelet power spectrum: …”