### Abstract

In a recent direct numerical simulation (DNS) study [P. K. Yeung and K. R. Sreenivasan, "Spectrum of passive scalars of highmolecular diffusivity in turbulent mixing," J. Fluid Mech. 716, R14 (2013)] with Schmidt number as low as 1/2048, we verified the essential physical content of the theory of Batchelor, Howells, and Townsend ["Small-scale variation of convected quantities like temperature in turbulent fluid. 2. The case of large conductivity," J. Fluid Mech. 5, 134 (1959)] for turbulent passive scalar fields with very strong diffusivity, decaying in the absence of any production mechanism. In particular,we confirmed the existence of the-17/3 power of the scalar spectral density in the so-called inertial-diffusive range. In the present paper, we consider the DNS of the same problem, but in the presence of a uniform mean gradient, which leads to the production of scalar fluctuations at (primarily) the large scales. For the parameters of the simulations, the presence of themean gradient alters the physics of mixing fundamentally at low Peclet numbers. While the spectrum still follows a -17/3 power law in the inertial-diffusive range, the pre-factor is non-universal and depends on the magnitude of the mean scalar gradient. Spectral transfer is greatly reduced in comparison with those for moderately and weakly diffusive scalars, leading to several distinctive features such as the absence of dissipative anomaly and a new balance of terms in the spectral transfer equation for the scalar variance, differing from the case of zero gradient. We use the DNS results to present an alternative explanation for the observed scaling behavior, and discuss a few spectral characteristics in detail.

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

Article number | 015107 |

Journal | Physics of Fluids |

Volume | 26 |

Issue number | 1 |

DOIs | |

State | Published - Jan 13 2014 |

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### ASJC Scopus subject areas

- Condensed Matter Physics

### Cite this

**Direct numerical simulation of turbulent mixing at very low schmidt number with a uniform mean gradient.** / Yeung, P. K.; Sreenivasan, K. R.

Research output: Contribution to journal › Article

*Physics of Fluids*, vol. 26, no. 1, 015107. https://doi.org/10.1063/1.4861070

}

TY - JOUR

T1 - Direct numerical simulation of turbulent mixing at very low schmidt number with a uniform mean gradient

AU - Yeung, P. K.

AU - Sreenivasan, K. R.

PY - 2014/1/13

Y1 - 2014/1/13

N2 - In a recent direct numerical simulation (DNS) study [P. K. Yeung and K. R. Sreenivasan, "Spectrum of passive scalars of highmolecular diffusivity in turbulent mixing," J. Fluid Mech. 716, R14 (2013)] with Schmidt number as low as 1/2048, we verified the essential physical content of the theory of Batchelor, Howells, and Townsend ["Small-scale variation of convected quantities like temperature in turbulent fluid. 2. The case of large conductivity," J. Fluid Mech. 5, 134 (1959)] for turbulent passive scalar fields with very strong diffusivity, decaying in the absence of any production mechanism. In particular,we confirmed the existence of the-17/3 power of the scalar spectral density in the so-called inertial-diffusive range. In the present paper, we consider the DNS of the same problem, but in the presence of a uniform mean gradient, which leads to the production of scalar fluctuations at (primarily) the large scales. For the parameters of the simulations, the presence of themean gradient alters the physics of mixing fundamentally at low Peclet numbers. While the spectrum still follows a -17/3 power law in the inertial-diffusive range, the pre-factor is non-universal and depends on the magnitude of the mean scalar gradient. Spectral transfer is greatly reduced in comparison with those for moderately and weakly diffusive scalars, leading to several distinctive features such as the absence of dissipative anomaly and a new balance of terms in the spectral transfer equation for the scalar variance, differing from the case of zero gradient. We use the DNS results to present an alternative explanation for the observed scaling behavior, and discuss a few spectral characteristics in detail.

AB - In a recent direct numerical simulation (DNS) study [P. K. Yeung and K. R. Sreenivasan, "Spectrum of passive scalars of highmolecular diffusivity in turbulent mixing," J. Fluid Mech. 716, R14 (2013)] with Schmidt number as low as 1/2048, we verified the essential physical content of the theory of Batchelor, Howells, and Townsend ["Small-scale variation of convected quantities like temperature in turbulent fluid. 2. The case of large conductivity," J. Fluid Mech. 5, 134 (1959)] for turbulent passive scalar fields with very strong diffusivity, decaying in the absence of any production mechanism. In particular,we confirmed the existence of the-17/3 power of the scalar spectral density in the so-called inertial-diffusive range. In the present paper, we consider the DNS of the same problem, but in the presence of a uniform mean gradient, which leads to the production of scalar fluctuations at (primarily) the large scales. For the parameters of the simulations, the presence of themean gradient alters the physics of mixing fundamentally at low Peclet numbers. While the spectrum still follows a -17/3 power law in the inertial-diffusive range, the pre-factor is non-universal and depends on the magnitude of the mean scalar gradient. Spectral transfer is greatly reduced in comparison with those for moderately and weakly diffusive scalars, leading to several distinctive features such as the absence of dissipative anomaly and a new balance of terms in the spectral transfer equation for the scalar variance, differing from the case of zero gradient. We use the DNS results to present an alternative explanation for the observed scaling behavior, and discuss a few spectral characteristics in detail.

UR - http://www.scopus.com/inward/record.url?scp=84899646240&partnerID=8YFLogxK

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U2 - 10.1063/1.4861070

DO - 10.1063/1.4861070

M3 - Article

VL - 26

JO - Physics of Fluids

JF - Physics of Fluids

SN - 1070-6631

IS - 1

M1 - 015107

ER -