### Abstract

The two-dimensional isotropic turbulence in an incompressible fluid is investigated using the modified zero fourth-order cumulant approximation. The dynamical equation for the energy spectrum obtained under this approximation is solved numerically and the similarity laws governing the solution in the energy-containing and enstrophy-dissipation ranges are derived analytically. At large Reynolds numbers the numerical solutions yield the k** minus **3 inertial subrange spectrum which was predicted by R. H. Kraichnan, C. E. Leith (1968) and G. K. Batchelor assuming a finite enstrophy dissipation in the inviscid limit. There exists a critical time t//c in which the enstrophy dissipation vanishes and remains non-zero respectively in the inviscid limit. Unlike the case of three-dimensional turbulence, t//c is not fixed but increases indefinitely as the viscosity tends to zero. Refs.

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

Pages (from-to) | 475-496 |

Number of pages | 22 |

Journal | Journal of Fluid Mechanics |

Volume | 110 |

Publication status | Published - Sep 1981 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Computational Mechanics
- Mechanics of Materials
- Physics and Astronomy(all)
- Condensed Matter Physics

### Cite this

*Journal of Fluid Mechanics*,

*110*, 475-496.

**MODIFIED CUMULANT EXPANSION FOR TWO-DIMENSIONAL ISOTROPIC TURBULENCE.** / Tatsumi, Tomomasa; Yanase, Shinichiro.

Research output: Contribution to journal › Article

*Journal of Fluid Mechanics*, vol. 110, pp. 475-496.

}

TY - JOUR

T1 - MODIFIED CUMULANT EXPANSION FOR TWO-DIMENSIONAL ISOTROPIC TURBULENCE.

AU - Tatsumi, Tomomasa

AU - Yanase, Shinichiro

PY - 1981/9

Y1 - 1981/9

N2 - The two-dimensional isotropic turbulence in an incompressible fluid is investigated using the modified zero fourth-order cumulant approximation. The dynamical equation for the energy spectrum obtained under this approximation is solved numerically and the similarity laws governing the solution in the energy-containing and enstrophy-dissipation ranges are derived analytically. At large Reynolds numbers the numerical solutions yield the k** minus **3 inertial subrange spectrum which was predicted by R. H. Kraichnan, C. E. Leith (1968) and G. K. Batchelor assuming a finite enstrophy dissipation in the inviscid limit. There exists a critical time t//c in which the enstrophy dissipation vanishes and remains non-zero respectively in the inviscid limit. Unlike the case of three-dimensional turbulence, t//c is not fixed but increases indefinitely as the viscosity tends to zero. Refs.

AB - The two-dimensional isotropic turbulence in an incompressible fluid is investigated using the modified zero fourth-order cumulant approximation. The dynamical equation for the energy spectrum obtained under this approximation is solved numerically and the similarity laws governing the solution in the energy-containing and enstrophy-dissipation ranges are derived analytically. At large Reynolds numbers the numerical solutions yield the k** minus **3 inertial subrange spectrum which was predicted by R. H. Kraichnan, C. E. Leith (1968) and G. K. Batchelor assuming a finite enstrophy dissipation in the inviscid limit. There exists a critical time t//c in which the enstrophy dissipation vanishes and remains non-zero respectively in the inviscid limit. Unlike the case of three-dimensional turbulence, t//c is not fixed but increases indefinitely as the viscosity tends to zero. Refs.

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UR - http://www.scopus.com/inward/citedby.url?scp=0019611853&partnerID=8YFLogxK

M3 - Article

AN - SCOPUS:0019611853

VL - 110

SP - 475

EP - 496

JO - Journal of Fluid Mechanics

JF - Journal of Fluid Mechanics

SN - 0022-1120

ER -