TY - JOUR

T1 - Dissipation scaling in the transition region of turbulent mixing layer

AU - Takamure, K.

AU - Sakai, Y.

AU - Ito, Y.

AU - Iwano, K.

AU - Hayase, T.

N1 - Funding Information:
We deeply thank Professor Susumu Goto (Osaka University) for his valuable comments as well as Mr. Shuichi Higaki (Nagoya University) for stimulating discussions. The numerical simulations were carried out at NEC SX-9 (Institute of Fluid Science, Tohoku University) and NEC SX-ACE (JAMSTEC). This work was supported by JSPS KAKENHI Grant No. 18H01369.
Publisher Copyright:
© 2018

PY - 2019/2

Y1 - 2019/2

N2 - 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, Cϵ. The scaling law suggested by Goto and Vassilicos [Phys. Rev. E 94, 053108 (2016)], Cϵ∼Reλ −1, holds over a wide area in the upstream region (0.3 ≤ x/L0 ≤ 1.9, where x is the streamwise direction and L0 is the height of the computational domain), and Cϵ takes a constant value in the further downstream region, where Reλ 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 Cϵ 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 Cϵ is a constant.

AB - 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, Cϵ. The scaling law suggested by Goto and Vassilicos [Phys. Rev. E 94, 053108 (2016)], Cϵ∼Reλ −1, holds over a wide area in the upstream region (0.3 ≤ x/L0 ≤ 1.9, where x is the streamwise direction and L0 is the height of the computational domain), and Cϵ takes a constant value in the further downstream region, where Reλ 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 Cϵ 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 Cϵ is a constant.

KW - Direct numerical simulation

KW - Dissipation coefficient

KW - Mixing layer

KW - Proper orthogonal decomposition

KW - Self-similarity

KW - Transition

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U2 - 10.1016/j.ijheatfluidflow.2018.11.012

DO - 10.1016/j.ijheatfluidflow.2018.11.012

M3 - Article

AN - SCOPUS:85057469900

SN - 0142-727X

VL - 75

SP - 77

EP - 85

JO - International Journal of Heat and Fluid Flow

JF - International Journal of Heat and Fluid Flow

ER -