### Abstract

The Hamiltonian formulation of hydrodynamics in Clebsch variables is used for construction of a statistical theory of turbulence. The statistics of the Clebsch field is assumed to be close to Gaussian. It is shown that the energy spectrum consists of two ranges with E(k)≈k^{ -5 3} and E(k)≈k^{-1}. The spectrum of the dissipation rate fluctuations has three scaling regimes: E^{ε{lunate}}(k)≈k^{-1}; k^{ -1 3} and k^{0} at the large, intermediate and small scales, respectively. The origin of the exponential distribution of velocity differences is discussed. The new scaling regime corresponds to a hidden conservation law, discovered in the Clebsch formulation of hydrodynamics. It is shown that viscous effects are responsible for production of the conserved quantity. The theoretical predictions are compared with results of numerical simulations of decaying turbulence.

Original language | English (US) |
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Pages (from-to) | 379-394 |

Number of pages | 16 |

Journal | Physica D: Nonlinear Phenomena |

Volume | 64 |

Issue number | 4 |

DOIs | |

State | Published - Apr 30 1993 |

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### ASJC Scopus subject areas

- Applied Mathematics
- Statistical and Nonlinear Physics

### Cite this

**Hidden conservation laws in hydrodynamics; energy and dissipation rate fluctuation spectra in strong turbulence.** / Yakhot, Victor; Zakharov, Vladimir E.

Research output: Contribution to journal › Article

*Physica D: Nonlinear Phenomena*, vol. 64, no. 4, pp. 379-394. https://doi.org/10.1016/0167-2789(93)90050-B

}

TY - JOUR

T1 - Hidden conservation laws in hydrodynamics; energy and dissipation rate fluctuation spectra in strong turbulence

AU - Yakhot, Victor

AU - Zakharov, Vladimir E

PY - 1993/4/30

Y1 - 1993/4/30

N2 - The Hamiltonian formulation of hydrodynamics in Clebsch variables is used for construction of a statistical theory of turbulence. The statistics of the Clebsch field is assumed to be close to Gaussian. It is shown that the energy spectrum consists of two ranges with E(k)≈k -5 3 and E(k)≈k-1. The spectrum of the dissipation rate fluctuations has three scaling regimes: Eε{lunate}(k)≈k-1; k -1 3 and k0 at the large, intermediate and small scales, respectively. The origin of the exponential distribution of velocity differences is discussed. The new scaling regime corresponds to a hidden conservation law, discovered in the Clebsch formulation of hydrodynamics. It is shown that viscous effects are responsible for production of the conserved quantity. The theoretical predictions are compared with results of numerical simulations of decaying turbulence.

AB - The Hamiltonian formulation of hydrodynamics in Clebsch variables is used for construction of a statistical theory of turbulence. The statistics of the Clebsch field is assumed to be close to Gaussian. It is shown that the energy spectrum consists of two ranges with E(k)≈k -5 3 and E(k)≈k-1. The spectrum of the dissipation rate fluctuations has three scaling regimes: Eε{lunate}(k)≈k-1; k -1 3 and k0 at the large, intermediate and small scales, respectively. The origin of the exponential distribution of velocity differences is discussed. The new scaling regime corresponds to a hidden conservation law, discovered in the Clebsch formulation of hydrodynamics. It is shown that viscous effects are responsible for production of the conserved quantity. The theoretical predictions are compared with results of numerical simulations of decaying turbulence.

UR - http://www.scopus.com/inward/record.url?scp=4243329996&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=4243329996&partnerID=8YFLogxK

U2 - 10.1016/0167-2789(93)90050-B

DO - 10.1016/0167-2789(93)90050-B

M3 - Article

VL - 64

SP - 379

EP - 394

JO - Physica D: Nonlinear Phenomena

JF - Physica D: Nonlinear Phenomena

SN - 0167-2789

IS - 4

ER -