## Abstract

Regions of negative turbulent kinetic energy (TKE) production are observed and studied in two different flows, namely in turbulent thermal Rayleigh-Bénard convection in a cubic cell, and in a mechanically agitated shear flow in absence of buoyancy, with a main focus on the small scale structure of the flow. The experimental investigation is performed using three-dimensional (3D) particle tracking velocimetry, which allows for measuring the three velocity components and the full tensor of velocity derivatives in a finite 3D volume. The capability to compute the TKE production term in its complete form P=-u_{j}u_{j}S_{ij} is crucial due to the three dimensionality of the flows. A comparative analysis of four different flow situations is performed in regions with positive and negative TKE production with and without buoyancy effects. In both, convective shear flow and shear flow without buoyancy, negative TKE production is associated with the unusual, more pronounced alignment of the velocity vector u with the first eigenvector λ_{1}^{S} of the mean rate-of-strain tensor, related to the stretching eigenvalue, Λ_{1}^{S}, in contrast to the positive TKE production associated with the alignment with the third eigenvector (i.e., related to the negative, compressing eigenvalue). In the negative TKE production region of convective flow we find (i) increased values for mean strain, (ii) increased values of the first contribution P_{Λ1} in the eigenframe of the mean rate-of-strain tensor, and decreased values of the vertical contribution to the production term in a fixed frame of reference, (iii) stronger anisotropy of u, (iv) higher levels of fluctuating strain s^{2} and enstrophy ω^{2}, as well as (v) higher rates of their production, -S_{ij}S_{jk}S_{ki} and ω_{i}ω_{j}S_{ij}, compared to the respective values in positive TKE production region. In the shear flow without buoyancy, all the mentioned quantities are lower in the negative TKE production region than in the positive TKE production region. From this we conclude that the inverse energy transfer in the shear flow case without buoyancy is associated with depletion of the field of velocity derivatives. This does not occur in the cubic Rayleigh-Bénard convection cell. In this flow, buoyancy is observed to have an effect on three levels: the field of velocity derivatives, velocity fluctuations, and the mean flow field. It is inferred that buoyancy is able to maintain a region with the negative TKE production by acting on all these levels simultaneously.

Original language | English (US) |
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Article number | 095110 |

Pages (from-to) | 1-11 |

Number of pages | 11 |

Journal | Physics of Fluids |

Volume | 17 |

Issue number | 9 |

DOIs | |

State | Published - Sep 2005 |

### Bibliographical note

Funding Information:This research is supported by ETH research fund, under Grant No. TH-18/02-4.