### Abstract

We report basic results from new numerical simulations of passive scalar mixing at Schmidt numbers (Sc) of the order of 1000 in isotropic turbulence. The required high grid-resolution is made possible by simulating turbulence at very low Reynolds numbers, which nevertheless possesses universality in dissipative scales of motion. The results obtained are qualitatively consistent with those based on another study (Yeung et al., Phys. Fluids 14 (2002) 4178-4191) with a less extended Schmidt number range and a higher Reynolds number. In the stationary state maintained by a uniform mean scalar gradient, the scalar variance increases slightly with Sc but scalar dissipation is nearly constant. As the Schmidt number increases, there is an increasing trend towards k ^{-1} scaling predicted by Batchelor (Batchelor, J. Fluid Mech. 5 (1959) 113-133) for the viscous-convective range of the scalar spectrum; the scalar gradient skewness approaches zero; and the intermittency measured by the scalar gradient flatness approaches its asymptotic state. However, the value of Sc needed for the asymptotic behavior to emerge appears to increase with decreasing Reynolds number of the turbulence. In the viscous-diffusive range, the scalar spectrum is in better agreement with Kraichnan's (Kraichnan., Phys. Fluids 11 (1968) 945-953) result than with Batchelor's.

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

Pages (from-to) | 333-347 |

Number of pages | 15 |

Journal | Flow, Turbulence and Combustion |

Volume | 72 |

Issue number | 2-4 SPEC. ISS. |

DOIs | |

State | Published - 2004 |

### Fingerprint

### Keywords

- Mixing
- Numerical simulation
- Passive scalars
- Scaling
- Schmidt number
- Turbulence

### ASJC Scopus subject areas

- Fluid Flow and Transfer Processes
- Physical and Theoretical Chemistry
- Computational Mechanics
- Mechanics of Materials

### Cite this

*Flow, Turbulence and Combustion*,

*72*(2-4 SPEC. ISS.), 333-347. https://doi.org/10.1023/B:APPL.0000044400.66539.78

**Simulations of three-dimensional turbulent mixing for schmidt numbers of the order 1000.** / Yeung, P. K.; Xu, S.; Donzis, D. A.; Sreenivasan, K. R.

Research output: Contribution to journal › Article

*Flow, Turbulence and Combustion*, vol. 72, no. 2-4 SPEC. ISS., pp. 333-347. https://doi.org/10.1023/B:APPL.0000044400.66539.78

}

TY - JOUR

T1 - Simulations of three-dimensional turbulent mixing for schmidt numbers of the order 1000

AU - Yeung, P. K.

AU - Xu, S.

AU - Donzis, D. A.

AU - Sreenivasan, K. R.

PY - 2004

Y1 - 2004

N2 - We report basic results from new numerical simulations of passive scalar mixing at Schmidt numbers (Sc) of the order of 1000 in isotropic turbulence. The required high grid-resolution is made possible by simulating turbulence at very low Reynolds numbers, which nevertheless possesses universality in dissipative scales of motion. The results obtained are qualitatively consistent with those based on another study (Yeung et al., Phys. Fluids 14 (2002) 4178-4191) with a less extended Schmidt number range and a higher Reynolds number. In the stationary state maintained by a uniform mean scalar gradient, the scalar variance increases slightly with Sc but scalar dissipation is nearly constant. As the Schmidt number increases, there is an increasing trend towards k -1 scaling predicted by Batchelor (Batchelor, J. Fluid Mech. 5 (1959) 113-133) for the viscous-convective range of the scalar spectrum; the scalar gradient skewness approaches zero; and the intermittency measured by the scalar gradient flatness approaches its asymptotic state. However, the value of Sc needed for the asymptotic behavior to emerge appears to increase with decreasing Reynolds number of the turbulence. In the viscous-diffusive range, the scalar spectrum is in better agreement with Kraichnan's (Kraichnan., Phys. Fluids 11 (1968) 945-953) result than with Batchelor's.

AB - We report basic results from new numerical simulations of passive scalar mixing at Schmidt numbers (Sc) of the order of 1000 in isotropic turbulence. The required high grid-resolution is made possible by simulating turbulence at very low Reynolds numbers, which nevertheless possesses universality in dissipative scales of motion. The results obtained are qualitatively consistent with those based on another study (Yeung et al., Phys. Fluids 14 (2002) 4178-4191) with a less extended Schmidt number range and a higher Reynolds number. In the stationary state maintained by a uniform mean scalar gradient, the scalar variance increases slightly with Sc but scalar dissipation is nearly constant. As the Schmidt number increases, there is an increasing trend towards k -1 scaling predicted by Batchelor (Batchelor, J. Fluid Mech. 5 (1959) 113-133) for the viscous-convective range of the scalar spectrum; the scalar gradient skewness approaches zero; and the intermittency measured by the scalar gradient flatness approaches its asymptotic state. However, the value of Sc needed for the asymptotic behavior to emerge appears to increase with decreasing Reynolds number of the turbulence. In the viscous-diffusive range, the scalar spectrum is in better agreement with Kraichnan's (Kraichnan., Phys. Fluids 11 (1968) 945-953) result than with Batchelor's.

KW - Mixing

KW - Numerical simulation

KW - Passive scalars

KW - Scaling

KW - Schmidt number

KW - Turbulence

UR - http://www.scopus.com/inward/record.url?scp=5744250246&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=5744250246&partnerID=8YFLogxK

U2 - 10.1023/B:APPL.0000044400.66539.78

DO - 10.1023/B:APPL.0000044400.66539.78

M3 - Article

VL - 72

SP - 333

EP - 347

JO - Flow, Turbulence and Combustion

JF - Flow, Turbulence and Combustion

SN - 1386-6184

IS - 2-4 SPEC. ISS.

ER -