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Prog. Theor. Phys. Vol. 71 No. 3 (1984) pp. 458-473

[ Full Text PDF : FREE ACCESS (909K) ]

Shapes of the Power Spectrum of Intermittent Turbulence near Its Onset Point

Kazuhisa Shobu, Tomoaki Ose and Hazime Mori

Department of Physics, Kyushu University, Fukuoka 812

(Received November 9, 1983)

Abstract:

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- ω0|4 or 1/ |ω- ω0|2 in a small frequency region around the eigenfrequency ω0 of the laminar state.
Pomeau and Manneville's intermittency turns out to give an envelope of the form 1/ω2 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 around ω0 = 2π/ 3 in agreement with numerical experiments by Hirsch, Huberman and Scalapino.


URL : http://ptp.ipap.jp/link?PTP/71/458/
DOI : 10.1143/PTP.71.458

[ Full Text PDF : FREE ACCESS (909K) ] Citation:

References:

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Citing Article(s) :

  1. Progress of Theoretical Physics Vol. 72 No. 6 (1984) pp. 1258-1261 :
    Power Spectra of the Intermittent Chaos Generated by the Quadratic Tangent Bifurcation
    Byon Chol So and Hazime Mori
  2. Progress of Theoretical Physics Vol. 76 No. 3 (1986) pp. 582-591 :
    Intermittency Caused by Chaotic Modulation. I
    Tomoji Yamada and Hirokazu Fujisaka
  3. Progress of Theoretical Physics Vol. 76 No. 4 (1986) pp. 784-801 :
    Global Spectral Structures of Intermittent Chaos
    Hazime Mori, Hisao Okamoto, Byon Chol So and Shoichi Kuroki
  4. Progress of Theoretical Physics Vol. 79 No. 3 (1988) pp. 581-599 :
    Global Spectral Structures of Type III Intermittent Chaos
    Hisao Okamoto, Hazime Mori and Shoichi Kuroki
  5. Progress of Theoretical Physics Vol. 79 No. 6 (1988) pp. 1260-1264 :
    Power Spectra of Intermittent Chaos Due to the Collapse of Period-3 Windows
    Nobuyuki Mori, Shoichi Kuroki and Hazime Mori
  6. Progress of Theoretical Physics Vol. 80 No. 6 (1988) pp. 953-972 :
    Scaling Structures of Chaotic Attractors and q-Phase Transitions at Crises in the Hénon and the Annulus Maps
    Koji Tomita, Hiroki Hata, Takehiko Horita, Hazime Mori and Terumitsu Morita
  7. Progress of Theoretical Physics Vol. 81 No. 1 (1989) pp. 60-77 :
    Scaling Structures and Statistical Mechanics of Type I Intermittent Chaos
    Nobuyuki Mori, Tatsuharu Kobayashi, Hiroki Hata, Terumitsu Morita, Takehiko Horita and Hazime Mori
  8. Progress of Theoretical Physics Vol. 82 No. 1 (1989) pp. 1-6 :
    Critical Scaling Laws of Dynamic Structure Functions for Type I Intermittent Chaos
    Tatsuharu Kobayashi, Nobuyuki Mori, Hiroki Hata, Tekehiko Horita, Takeshi Yoshida and Hazime Mori
  9. Progress of Theoretical Physics Vol. 82 No. 5 (1989) pp. 879-896 :
    The q-Phase Transition and Critical Scaling Laws near the Band-Crisis Point of Chaotic Attractors
    Takeshi Yoshida, Syuji Miyazaki, Hazime Mori, Tatsuharu Kobayashi, Takehiko Horita and Hiroki Hata
  10. Progress of Theoretical Physics Vol. 86 No. 3 (1991) pp. 581-586 :
    Intermittent Chaos Generated by Logarithmic Map
    Takeshi Kawabe and Yoshiro Kondo
  11. Progress of Theoretical Physics Supplement No.99 (1989) pp. 1-63 :
    Statistical Mechanics of Dynamical Systems
    Hazime Mori, Hiroki Hata, Takehiko Horita and Tatsuharu Kobayashi

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