Statistical properties of the local structure of homogeneous isotropic turbulence and turbulent channel flows

Abstract

Statistical properties of the local structure are investigated using the data of direct numerical simulation of homogeneous isotropic turbulence for Re _λ=60.1∼287.6 and turbulent channel flows for Re _τ = 180, 400, 800, and 1270. The dimensionless second invariant is used as the representative local structure, and is defined as the second invariant of a velocity gradient tensor normalized by the magnitude of the velocity gradient tensor. In homogeneous isotropic turbulence, the probability density function (pdf) profiles of the dimensionless second invariant show good agreement for different values of Reynolds number. The volume fraction, the average, and the variance of the dimensionless second invariant converge to certain values at high Reynolds number, respectively. For the turbulent channel flows, the pdf profiles of the dimensionless second invariant for different values of Reynolds number coincide very well for the distance from the wall in wall units. The probability density and the volume fraction of the dimensionless second invariant at the center of the channel are in good agreement with those of homogeneous isotropic turbulence.

Keywords:

• statistical property
• homogeneous isotropic turbulence
• turbulent channel flow
• direct numerical simulation
• turbulence structure

Acknowledgements

We would like to thank Mr. Yasuhiro Tominaga and Mr. Taisuke Kubota for their support to analyze the DNS data. This work was supported by KAKENHI (20760119) of Japan Society for the Promotion of Science, and HK gratefully acknowledges its support.