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 mΩ_{0} with m=0, 1, 2, \cdots and an eigenfrequency Ω_{0} 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 inversepower law 1/ Ω  mΩ_{0}^{ζ m} with a universal exponent ζ_{m}. For the type I intermittency caused by the saddlenode bifurcation, ζ_{0}=1, ζ_{1}=2 under normal reinjections, whereas ζ_{0}=ζ_{m}=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 perioddoubling bifurcation, ζ_{m}=3/2 for mgeqq 1.
 Publication:

Progress of Theoretical Physics
 Pub Date:
 October 1986
 DOI:
 10.1143/PTP.76.784
 Bibcode:
 1986PThPh..76..784M