Spectral structure of intermittent chaos

Abstract

A statistical-physical theory of power spectra of intermittent chaos near it onset point is developed and is applied to the type I intermittency generated by the collapse of a stable and an unstable cycle with a eigenfrequency ω 0. When the variance of phase jumps by turbulent bursts is small, the power spectra around ω 0 are shown to consist of equally-spaced sharp lines if the variance σ of durations of laminar motions between two consecutive bursts is small compared to the mean duration τ̄. Their envelope obeys an inverse-power law ∥ω-ω 0∥ ζ, where ζ=3 if the mean value ξ of phase jumps is nonzero, whereas ζ=1 if ξ=0. The relative fluctuation σ τ ̄ depends on the type of the reinjection into laminar motions by bursts. As σ τ ̄ increase, the lines become broad and overlap each other. When σ ≫ τ̄ the power spectra become the 1 ⨍ spectra irrespective of ξ.