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Bicoherence: Difference between revisions
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The two-dimensional bicoherence graph tends to show mainly two types of structures: | The two-dimensional bicoherence graph tends to show mainly two types of structures: | ||
* 'Points': indicating sharply defined, unchanging, locked frequencies (as occurs with a driving mode and a slave mode; energy transfer in a single direction). | * 'Points': indicating sharply defined, unchanging, locked frequencies (as occurs with a driving mode and a slave mode; energy transfer in a single direction). | ||
* 'Lines': these are more difficult to interpret. It is often stated that 'lines' are due to single mode (frequency) interacting with a broad range of frequencies (e.g., a [[Geodesic Acoustic Mode]] and broad-band turbulence) - but it is not evident that this is the only explanation. Particularly, two interacting oscillators (continuously exchanging energy) ''also'' produce lines in the bicoherence graph. | * 'Lines': these are more difficult to interpret. It is often stated that 'lines' are due to single mode (frequency) interacting with a broad range of frequencies (e.g., a [[Geodesic Acoustic Mode]] and broad-band turbulence) - but it is not evident that this is the only explanation. Particularly, two interacting oscillators (continuously exchanging energy) ''also'' produce lines in the bicoherence graph.<ref name="milligen1995"></ref><ref>[[doi:10.1088/0029-5515/52/1/013006|B.Ph. van Milligen, L. García, B.A. Carreras, M.A. Pedrosa, C. Hidalgo, J.A. Alonso, T. Estrada and E. Ascasíbar, MHD mode activity and the velocity shear layer at TJ-II, Nucl. Fusion 52 (2012) 013006]]</ref> | ||
== Notes == | == Notes == | ||
* The bicoherence can be computed using the (continuous) wavelet transform instead of the Fourier transform, in order to improve statistics. <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> | * The bicoherence can be computed using the (continuous) wavelet transform instead of the Fourier transform, in order to improve statistics. <ref name="milligen1995">[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> | ||
* The bicoherence can of course be defined in wavenumber space instead of frequency space by applying the replacements ''t → x'' and ''ω → k''. | * The bicoherence can of course be defined in wavenumber space instead of frequency space by applying the replacements ''t → x'' and ''ω → k''. | ||
* Combined temporal-spatial studies are also possible. <ref>[http://link.aip.org/link/PHPAEN/v17/i5/p052313/s1 T. Yamada, S.-I. Itoh, S. Inagaki, Y. Nagashima, S. Shinohara, N. Kasuya, K. Terasaka, K. Kamataki, H. Arakawa, M. Yagi, A. Fujisawa, and K. Itoh, ''Two-dimensional bispectral analysis of drift wave turbulence in a cylindrical plasma'' , Phys. Plasmas '''17''' (2010) 052313]</ref> | * Combined temporal-spatial studies are also possible. <ref>[http://link.aip.org/link/PHPAEN/v17/i5/p052313/s1 T. Yamada, S.-I. Itoh, S. Inagaki, Y. Nagashima, S. Shinohara, N. Kasuya, K. Terasaka, K. Kamataki, H. Arakawa, M. Yagi, A. Fujisawa, and K. Itoh, ''Two-dimensional bispectral analysis of drift wave turbulence in a cylindrical plasma'' , Phys. Plasmas '''17''' (2010) 052313]</ref> | ||