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TJ-II:Turbulence: Difference between revisions
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Our work on turbulence has focussed mainly on the analysis of edge [[TJ-II:Langmuir Probes|Langmuir probe]] data, although some analysis was done on other types of data (e.g., [[TJ-II:Reflectometry|reflectometry]] signals). Much effort was devoted to the development of new analysis techniques. | Our work on turbulence has focussed mainly on the analysis of edge [[TJ-II:Langmuir Probes|Langmuir probe]] data, although some analysis was done on other types of data (e.g., [[TJ-II:Reflectometry|reflectometry]] signals). Much effort was devoted to the development of new analysis techniques. | ||
=== | === Bicoherence and wavelets === | ||
[[File:Bicoherence.png|300px|thumb|right|Auto-[[Bicoherence|bicoherence]] graph (''E<sub>θ</sub>'') during a spontaneous confinement transition at TJ-II, showing the coupling of high to low frequencies (horizontal and diagonal lines), i.e., a possible inverse spectral cascade. (from B.Ph. van Milligen et al, Nucl. Fusion 48 (2008) 115003)]] | [[File:Bicoherence.png|300px|thumb|right|Auto-[[Bicoherence|bicoherence]] graph (''E<sub>θ</sub>'') during a spontaneous confinement transition at TJ-II, showing the coupling of high to low frequencies (horizontal and diagonal lines), i.e., a possible 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|bicoherence]] was calculated using wavelet transforms, thus making the detection of non-linear interactions with time resolution possible. | ||
<ref>[http://link.aps.org/doi/10.1103/PhysRevLett.74.395 B.Ph. van Milligen et al, ''Nonlinear phenomena and intermittency in plasma turbulence'', Phys. Rev. Lett. '''74''', 3 (1995) 395]</ref> | <ref>[http://link.aps.org/doi/10.1103/PhysRevLett.74.395 B.Ph. van Milligen et al, ''Nonlinear phenomena and intermittency in plasma turbulence'', Phys. Rev. Lett. '''74''', 3 (1995) 395]</ref> | ||
<ref>[http://link.aip.org/link/?PHPAEN/2/3017/1 B.Ph. van Milligen et al, ''Wavelet bicoherence: a new turbulence analysis tool'', Phys. Plasmas '''2''', 8 (1995) 3017]</ref> | <ref>[http://link.aip.org/link/?PHPAEN/2/3017/1 B.Ph. van Milligen et al, ''Wavelet bicoherence: a new turbulence analysis tool'', Phys. Plasmas '''2''', 8 (1995) 3017]</ref> | ||