Shapes of the Power Spectrum of Intermittent Turbulence near Its Onset Point : Condensed Matter and Statistical Physics

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A general theory of shapes of the power spectrum of intermittent turbulence is developed from a phenomenological point of view by assuming that bursts at different times are statistically independent of each other. It is found that bursts in phase and amplitude give shapes of different types. Near the onset point, the spectrum consists of a number of Lorentzian lines with equal spacing. If the fluctuation of phase jumps by bursts is small, then the envelope of the Lorentzian lines obeys the power law 1/∣ω-ω_0∣^4 or 1/∣ω-ω_0∣^2 in a small frequency region around the eigenfrequencyω_0 of the laminar state. Pomeau and Manneville's intermittency turns out to give an envelope of the form 1/ω^2 around ω=0. Just before the tangent bifurcation to the P-3 window of the quadratic map, the line widths are larger than the line separation due to a large fluctuation of phase jumps, and the spectrum turns out to have a broad peak aroundω_0 = 2π/3 in agreement with numerical experiments by Hirsch, Huberman and Scalapino.
理論物理学刊行会の論文
1984-03-25