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TJ-II:Turbulence: Difference between revisions
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=== Bicoherence and wavelets === | === Bicoherence and wavelets === | ||
[[File:Bicoherence.png|300px|thumb|right|Bicoherence graph during a spontaneous confinement transition at TJ-II, showing the coupling of high to low frequencies (horizontal and diagonal lines), i.e., an inverse spectral cascade | [[File:Bicoherence.png|300px|thumb|right|Bicoherence graph during a spontaneous confinement transition at TJ-II, showing the coupling of high to low frequencies (horizontal and diagonal lines), i.e., an inverse spectral cascade. (from B.Ph. van Milligen et al, Nucl. Fusion 48 (2008) 115003)]] | ||
Turbulence is essentially non-linear. | Turbulence is essentially non-linear. | ||
Non-linear interactions can be detected by means of higher-order spectra (e.g. quadratic interactions can be detected through the bi-spectrum). With Fourier analysis, however, in order to achieve statistically significant values for the bi-spectrum, very long time series are necessary. This fact has mostly precluded its use in fields like plasma turbulence, since long steady-state data series are not generally available. In our work, for the first time, the bicoherence was calculated using wavelet transforms, thus making the detection of non-linear interactions with time resolution possible. | Non-linear interactions can be detected by means of higher-order spectra (e.g. quadratic interactions can be detected through the bi-spectrum). With Fourier analysis, however, in order to achieve statistically significant values for the bi-spectrum, very long time series are necessary. This fact has mostly precluded its use in fields like plasma turbulence, since long steady-state data series are not generally available. In our work, for the first time, the bicoherence was calculated using wavelet transforms, thus making the detection of non-linear interactions with time resolution possible. | ||