### Abstract

Both static and dynamic multiscalings of fluctuations of energy flux and energy dissipation rate in the Gledzer-Ohkitani-Yamada (GOY) shell model of turbulence are numerically investigated. We compute the large deviation rate function of energy flux not only in the inertial range (IR) but also around the crossover between the inertial range and the dissipation range (DR). The rate function in IR exists to be concave, which assures the applicability of the Legendre transformation with the anomalous scaling exponents that have been investigated so far, and turns out to be independent of the Reynolds number. On the contrary, near the crossover scale, an intermediate dissipation range (IMDR) scaling is observed with the rate function in IMDR, which is accounted with the argument on dissipation scale fluctuation dominated by the energy flux fluctuation in the inertial range. Furthermore, to study the difference between IR intermittency and DR intermittency, we compute finite time-averaged quantities of energy flux and energy dissipation rate and investigate their multiscaling behavior. The difference observed in terms of their dynamic multiscaling is discussed.

Original language | English |
---|---|

Number of pages | 1 |

Journal | Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics |

Volume | 64 |

Issue number | 5 |

DOIs | |

Publication status | Published - Jan 1 2001 |

Externally published | Yes |

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### All Science Journal Classification (ASJC) codes

- Statistical and Nonlinear Physics
- Mathematical Physics
- Condensed Matter Physics
- Physics and Astronomy(all)

### Cite this

**Self-similar fluctuation and large deviation statistics in the shell model of turbulence.** / Nakayama, Yasuya; Watanabe, Takeshi; Fujisaka, Hirokazu.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Self-similar fluctuation and large deviation statistics in the shell model of turbulence

AU - Nakayama, Yasuya

AU - Watanabe, Takeshi

AU - Fujisaka, Hirokazu

PY - 2001/1/1

Y1 - 2001/1/1

N2 - Both static and dynamic multiscalings of fluctuations of energy flux and energy dissipation rate in the Gledzer-Ohkitani-Yamada (GOY) shell model of turbulence are numerically investigated. We compute the large deviation rate function of energy flux not only in the inertial range (IR) but also around the crossover between the inertial range and the dissipation range (DR). The rate function in IR exists to be concave, which assures the applicability of the Legendre transformation with the anomalous scaling exponents that have been investigated so far, and turns out to be independent of the Reynolds number. On the contrary, near the crossover scale, an intermediate dissipation range (IMDR) scaling is observed with the rate function in IMDR, which is accounted with the argument on dissipation scale fluctuation dominated by the energy flux fluctuation in the inertial range. Furthermore, to study the difference between IR intermittency and DR intermittency, we compute finite time-averaged quantities of energy flux and energy dissipation rate and investigate their multiscaling behavior. The difference observed in terms of their dynamic multiscaling is discussed.

AB - Both static and dynamic multiscalings of fluctuations of energy flux and energy dissipation rate in the Gledzer-Ohkitani-Yamada (GOY) shell model of turbulence are numerically investigated. We compute the large deviation rate function of energy flux not only in the inertial range (IR) but also around the crossover between the inertial range and the dissipation range (DR). The rate function in IR exists to be concave, which assures the applicability of the Legendre transformation with the anomalous scaling exponents that have been investigated so far, and turns out to be independent of the Reynolds number. On the contrary, near the crossover scale, an intermediate dissipation range (IMDR) scaling is observed with the rate function in IMDR, which is accounted with the argument on dissipation scale fluctuation dominated by the energy flux fluctuation in the inertial range. Furthermore, to study the difference between IR intermittency and DR intermittency, we compute finite time-averaged quantities of energy flux and energy dissipation rate and investigate their multiscaling behavior. The difference observed in terms of their dynamic multiscaling is discussed.

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U2 - 10.1103/PhysRevE.64.056304

DO - 10.1103/PhysRevE.64.056304

M3 - Article

AN - SCOPUS:85035270218

VL - 64

JO - Physical Review E

JF - Physical Review E

SN - 2470-0045

IS - 5

ER -