Global Spectral Structures of Intermittent Chaos

Abstract

Power spectra of intermittent chaos near its onset point are formulated in order to clarify fluctuations of periodic laminar motions caused by turbulent bursts. It is shown that the power spectra exhibit eminent peaks at selected frequencies mω0 with m=0, 1, 2, … and an eigenfrequency ω0 of the laminar motions. The peak at zero frequency is produced by fluctuations of durations of the laminar motions, whereas the peaks at nonzero frequencies are generated by jumps of phase shifts of the laminar motions by bursts. The shape of each peak turns out to obey an inverse-power law 1/| ω- mω0|ζm with a universal exponent ζm. For the type I intermittency caused by the saddle-node bifurcation, ζ0=1, ζ1=2 under normal reinjections, whereas ζ0=ζm=1 if reinjections are restricted to the upper half of a narrow channel of the tangent map. For the type of III intermittency caused by the inverted period-doubling bifurcation, ζm=3/2 for m≧1.