### Abstract

We explore some implications of the observed multifractal nature of the turbulent energy-dissipation field and of velocity derivatives of increasing order on the near-singularities of the Navier-Stokes equations and the singularities of Euler equations. Although these singularities occur on fractal sets of dimension close to (and only marginally less than) 3, it is shown that most of the energy dissipation is concentrated on a subset of fractal dimension about 2.87 and volume zero. Similar statements can be made with respect to velocity derivatives. In particular, it is shown that the higher the order of the velocity derivative, the less space filling the corresponding singularities become.

Original language | English (US) |
---|---|

Pages (from-to) | 6287-6295 |

Number of pages | 9 |

Journal | Physical Review A |

Volume | 38 |

Issue number | 12 |

DOIs | |

State | Published - 1988 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Atomic and Molecular Physics, and Optics

### Cite this

*Physical Review A*,

*38*(12), 6287-6295. https://doi.org/10.1103/PhysRevA.38.6287

**Singularities of the equations of fluid motion.** / Sreenivasan, K. R.; Meneveau, C.

Research output: Contribution to journal › Article

*Physical Review A*, vol. 38, no. 12, pp. 6287-6295. https://doi.org/10.1103/PhysRevA.38.6287

}

TY - JOUR

T1 - Singularities of the equations of fluid motion

AU - Sreenivasan, K. R.

AU - Meneveau, C.

PY - 1988

Y1 - 1988

N2 - We explore some implications of the observed multifractal nature of the turbulent energy-dissipation field and of velocity derivatives of increasing order on the near-singularities of the Navier-Stokes equations and the singularities of Euler equations. Although these singularities occur on fractal sets of dimension close to (and only marginally less than) 3, it is shown that most of the energy dissipation is concentrated on a subset of fractal dimension about 2.87 and volume zero. Similar statements can be made with respect to velocity derivatives. In particular, it is shown that the higher the order of the velocity derivative, the less space filling the corresponding singularities become.

AB - We explore some implications of the observed multifractal nature of the turbulent energy-dissipation field and of velocity derivatives of increasing order on the near-singularities of the Navier-Stokes equations and the singularities of Euler equations. Although these singularities occur on fractal sets of dimension close to (and only marginally less than) 3, it is shown that most of the energy dissipation is concentrated on a subset of fractal dimension about 2.87 and volume zero. Similar statements can be made with respect to velocity derivatives. In particular, it is shown that the higher the order of the velocity derivative, the less space filling the corresponding singularities become.

UR - http://www.scopus.com/inward/record.url?scp=0001149206&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001149206&partnerID=8YFLogxK

U2 - 10.1103/PhysRevA.38.6287

DO - 10.1103/PhysRevA.38.6287

M3 - Article

AN - SCOPUS:0001149206

VL - 38

SP - 6287

EP - 6295

JO - Physical Review A

JF - Physical Review A

SN - 2469-9926

IS - 12

ER -