## Abstract

Direct numerical simulation is conducted for a spatially developing shear mixing layer to investigate the spatial transition of the dissipation coefficient of the turbulent kinetic energy, C_{ϵ}. The scaling law suggested by Goto and Vassilicos [Phys. Rev. E 94, 053108 (2016)], C_{ϵ}∼Re_{λ} ^{−1}, holds over a wide area in the upstream region (0.3 ≤ x/L_{0} ≤ 1.9, where x is the streamwise direction and L_{0} is the height of the computational domain), and C_{ϵ} takes a constant value in the further downstream region, where Re_{λ} is the turbulent Reynolds number based on Taylor's microscale. Proper orthogonal decomposition (POD) analysis is performed to investigate the distributions of the streamwise length of the large-scale energy-containing structure, which is estimated from the cycle of the zero-crossing point of the time-series data composed of the sum of the POD modes until the cumulative energy rate exceeds 60 %. It is shown that C_{ϵ} becomes a constant when the distributions of the length of the large-scale structure reach a self-similar state. This result suggests that it is necessary to satisfy the self-similarity of the distribution of the length of the large-scale energy-containing structure in order to apply the condition that C_{ϵ} is a constant.

Original language | English |
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Pages (from-to) | 77-85 |

Number of pages | 9 |

Journal | International Journal of Heat and Fluid Flow |

Volume | 75 |

DOIs | |

Publication status | Published - 2019 Feb |

## Keywords

- Direct numerical simulation
- Dissipation coefficient
- Mixing layer
- Proper orthogonal decomposition
- Self-similarity
- Transition

## ASJC Scopus subject areas

- Condensed Matter Physics
- Mechanical Engineering
- Fluid Flow and Transfer Processes