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Intermittency, chaos and singular fluctuations in the mixed Obukhov-Novikov shell model of turbulence. (English) Zbl 0947.76042
Summary: The multiscaling properties of the mixed Obukhov-Novikov (ON) shell model of turbulence are investigated numerically and compared with those of the complex Gledzer-Okhitani-Yamada (GOY) model, mostly studied in recent years. Two types of generic singular fluctuations are identified: first, self-similar solutions propagating from large to small scales and building up intermittency, second, complex-time singularities which are argued to encode “blockings” in the cascade. A robust dynamic rescaling method is developed to characterize these objects. It is shown that the scaling exponent of self-similar solutions selected by the dynamics is compatible with large-order statistics, only when it departs enough from the Kolmogorov value. Complex-time singularities on the other hand suffer a “depinning” transition which, in a remarkable way, is found to occur in the phase diagrams of both the ON and GOY models at a place such that the scaling exponent of corresponding self-similar solutions take the same value \(\approx 0.855\).

MSC:
76F99 Turbulence
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[1] Yamada, M.; Okhitani, K., Phys. rev. lett., 60, 983, (1988)
[2] Okhitani, K.; Yamada, M., Prog. theoret. phys., 81, 329, (1989)
[3] Jensen, M.H.; Paladin, G.; Vulpiani, A., Phys. rev. A, 43, 798, (1991)
[4] Benzi, R.; Biferale, L.; Parisi, G., Physica D, 65, 163, (1993)
[5] Biferale, L.; Lambert, A.; Lima, R.; Paladin, G., Physica D, 80, 105, (1995)
[6] Kadanoff, L.; Lohse, D.; Wang, J.; Benzi, R., Phys. fluids, 7, 617, (1995)
[7] Obukhov, A.M., Atmos. oceanic phys., 7, 41, (1971)
[8] Desnyansky, V.I.; Novikov, E.A., Sov. J. appl. mech., 38, 507, (1974)
[9] Gledzer, E.B.; Glukhovsky, A.B.; Obukhov, A.M., J. theoret. appl. mech., 7, 111, (1988)
[10] Siggia, E.D., Phys. rev. A, 17, 1166, (1978)
[11] Nakano, T., Prog. theoret. phys., 79, 569, (1988)
[12] G. Parisi, University of Rom, preprint ROM2F-90/37.
[13] Uhlig, C.; Eggers, J., Singularities in cascade models of the Euler equation, (1996), preprint
[14] Pisarenko, D.; Biferale, L.; Courvoisier, D.; Frisch, U.; Vergassola, M., Phys. fluids A, 5, 2533, (1993)
[15] Gat, O.; Procaccia, I.; Zeitak, R., Phys. rev. E, 51, 1148, (1995)
[16] She, Z.S.; Lévêque, E., Phys. rev. lett., 72, 336, (1994)
[17] Frisch, U.; Morf, R., Phys. rev. A, 23, 2673, (1981)
[18] Tabor, M., Chaos and integrability in nonlinear dynamics: an introduction, (1989), Wiley New York · Zbl 0682.58003
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