### Abstract

A method is developed for generating the Taylor expansions in powers of the time difference of the Lagrangian and Eulerian two-point two-time velocity correlations in turbulence. The expansions are based on the Taylor series of the Eulerian and Lagrangian velocity fields subject to given dynamics along with initial and boundary conditions. The lowest few coefficients in the expansions enable us to construct approximations to the correlations. An application of the method to turbulence obeying the Navier-Stokes dynamics yields approximations, particularly Padé approximations that agree well with direct numerical simulations of homogeneous isotropic turbulence at moderate Reynolds numbers. The ratios of the second-order to the zeroth-order coefficients of the Taylor series of the Lagrangian and Eulerian correlations give, respectively, the estimates for the Lagrangian and Eulerian micro time scales τ_{L} and τ_{E}. An analysis of a high resolution (512^{3} grid points) direct numerical simulation database at large Reynolds number suggests the scalings τ_{L}α^{-2/3} and τ_{E} αk^{-1} for wave numbers k in the inertial subrange. The role of flow structures in turbulence in determining the time scales is also discussed.

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

Pages (from-to) | 2154-2166 |

Number of pages | 13 |

Journal | Physics of Fluids |

Volume | 11 |

Issue number | 8 |

DOIs | |

Publication status | Published - Jan 1 1999 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

*Physics of Fluids*,

*11*(8), 2154-2166. https://doi.org/10.1063/1.870077

**Taylor expansions in powers of time of Lagrangian and Eulerian two-point two-time velocity correlations in turbulence.** / Kaneda, Yukio; Ishihara, Takashi; Gotoh, Koji.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 11, no. 8, pp. 2154-2166. https://doi.org/10.1063/1.870077

}

TY - JOUR

T1 - Taylor expansions in powers of time of Lagrangian and Eulerian two-point two-time velocity correlations in turbulence

AU - Kaneda, Yukio

AU - Ishihara, Takashi

AU - Gotoh, Koji

PY - 1999/1/1

Y1 - 1999/1/1

N2 - A method is developed for generating the Taylor expansions in powers of the time difference of the Lagrangian and Eulerian two-point two-time velocity correlations in turbulence. The expansions are based on the Taylor series of the Eulerian and Lagrangian velocity fields subject to given dynamics along with initial and boundary conditions. The lowest few coefficients in the expansions enable us to construct approximations to the correlations. An application of the method to turbulence obeying the Navier-Stokes dynamics yields approximations, particularly Padé approximations that agree well with direct numerical simulations of homogeneous isotropic turbulence at moderate Reynolds numbers. The ratios of the second-order to the zeroth-order coefficients of the Taylor series of the Lagrangian and Eulerian correlations give, respectively, the estimates for the Lagrangian and Eulerian micro time scales τL and τE. An analysis of a high resolution (5123 grid points) direct numerical simulation database at large Reynolds number suggests the scalings τLα-2/3 and τE αk-1 for wave numbers k in the inertial subrange. The role of flow structures in turbulence in determining the time scales is also discussed.

AB - A method is developed for generating the Taylor expansions in powers of the time difference of the Lagrangian and Eulerian two-point two-time velocity correlations in turbulence. The expansions are based on the Taylor series of the Eulerian and Lagrangian velocity fields subject to given dynamics along with initial and boundary conditions. The lowest few coefficients in the expansions enable us to construct approximations to the correlations. An application of the method to turbulence obeying the Navier-Stokes dynamics yields approximations, particularly Padé approximations that agree well with direct numerical simulations of homogeneous isotropic turbulence at moderate Reynolds numbers. The ratios of the second-order to the zeroth-order coefficients of the Taylor series of the Lagrangian and Eulerian correlations give, respectively, the estimates for the Lagrangian and Eulerian micro time scales τL and τE. An analysis of a high resolution (5123 grid points) direct numerical simulation database at large Reynolds number suggests the scalings τLα-2/3 and τE αk-1 for wave numbers k in the inertial subrange. The role of flow structures in turbulence in determining the time scales is also discussed.

UR - http://www.scopus.com/inward/record.url?scp=0001566892&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0001566892&partnerID=8YFLogxK

U2 - 10.1063/1.870077

DO - 10.1063/1.870077

M3 - Article

AN - SCOPUS:0001566892

VL - 11

SP - 2154

EP - 2166

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 8

ER -