Spectral structure of intermittent chaos (Q1081933)

A statistical-physical theory of power spectra of intermittent chaos near its onset point is developed and is applied to the type I intermittency generated by the collapse of a stable and an unstable cycle with an eigenfrequency \(\omega_ 0\). When the variance of phase jumps by turbulent bursts is small, the power spectra around \(\omega_ 0\) are shown to consist of equally-spaced sharp lines if the variance \(\sigma\) of durations of laminar motions between two consecutive bursts is small compared to the mean duration \({\bar \tau}\). Their envelope obeys an inverse-power law \(| \omega -\omega_ 0|^{-\zeta}\), where \(\zeta =3\) if the mean value \(\xi\) of phase jumps is nonzero, whereas \(\zeta =1\) if \(\xi =0\). The relative fluctuation \(\sigma\) /\({\bar \tau}\) depends on the type of the reinjection into laminar motions by bursts. As \(\sigma\) /\({\bar \tau}\) increases, the lines become broad and overlap each other. When \(\sigma \gg {\bar \tau}\), the power spectra become the 1/f spectra irrespective of \(\xi\).