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Author(s):
S.-I. Itoh, A. Kitazawa, M. Yagi and K. Itoh
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Title:
Bifurcation and Phase Diagram of Turbulence Constituted from Three Different Scale-length Modes
Date of publication:
Apr. 2002
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Key words:
multiple scale-lengths, turbulence transition, strong turbulence, statistical theory, renormalization, subcritical bifurcation, phase diagram
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Abstract:
Cases where three kinds of fluctuations having the different typical scale-lengths coexist are analyzed, and the statistical theory of strong turbulence in inhomogeneous plasmas is developed. Statistical nonlinear interactions between fluctuations are kept in the analysis as the renormalized drag, statistical noise and the averaged drive. The nonlinear interplay through them induces a quenching or suppressing effect, even if all the modes are unstable when they are analyzed independently. Variety in mode appearance takes place: one mode quenches the other two modes, or one mode is quenched by the other two modes, etc. The bifurcation of turbulence is analyzed and a phase diagram is drawn. Phase diagrams with cusp type catastrophe and butterfly type catastrophe are obtained. The subcritical bifurcation is possible to occur through the nonlinear interplay, even though each one is supercritical turbulence when analyzed independently. Analysis reveals that the nonlinear stability boundary
(marginal point) and the amplitude of each mode may substantially shift from the conventional results of independent analyses.
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